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ADVANTAGES OF WRITING BLOG.

March 2, 2008

The Advantages Of Writing Articles.

If you are into your website or blog development, then every SEO people suggests to write articles. Writing a single article will provide multiple advantages. It is actually a boon for the people who have the ability to write articles even with limited information. Now I am going to show you, in how many ways you are getting benefited for writing articles.First of all, writing articles is not that easy. You need to develop the way you should write articles. If you can see my posts in the month of March and April you can clearly understand how I was writing. I was a novice at the time. I was not clear in my explanation. But if you can see my posts right now, you an understand the difference in my previous posts and present posts. So, for writing articles you need to be a bit fast in your typing. Don’t worry even though you are slow you can develop your typing skill too.

So, now I am going to explain the advantages of writing articles. But remember in every article make sure to add a hyperlink of your blog or website.

(1)Getting Easily Indexed:-

If you have started a blog or a website, then you can easily get indexed into big search engines like google, yahoo etc.

Generally you will be thinking that, it will be enough if you are submitting your articles for directories. But the disadvantage is it takes much time around 3 to 4 weeks for getting your site approved. Even though after your site is approved, it is not sure that your site is getting indexed.

But if you are submitting articles to article directories then getting your article accepted is very easy. It takes only 1 to 2 days to get published. But the only thing is, you need to submit your articles to sites which allow to add at least one link in your article. Now after writing that article you can link it to your blog. And the advantage of article submission sites are, there will be less links ( because every one is not interested in writing articles) and hence that site will be able to share its PR to less number of links.

(2)Free Backlink For Your Site:-

Getting free backlinks is not an easy thing. Generally people need to do a lot of work to get back links for their site. But the advantage of submitting your articles is, you will be getting a free back link for your site. Generally you can write to article submission directories, but at times you can also get chances for writing articles to other blogs or sites. Generally there are many bloggers who are good at promoting their blog or website but not good enough to write content for their blogs. So what is their work is, they will be collecting different articles and copy-paste them on to their blog. So, if you can find such blogs then you can provide articles for their blog and ask them to add a link of your site in their blog. So, you will be getting a backlink from other site which is really worthfull.
helps your blogging skills

(3)Increase In Traffic For Your Blog:-

This is the most considered for a blog or a website for its development. Writing quality articles will provide a good traffic for your site. If you write a quality article and a unique one which no one have written before, your article will be read by many people and at the bottom near adding your link write some thing which makes those readers visit your blog. Generally we can write “for more information please visit this blog” or provide some offers etc.

So, once they visit your site if they find it useful then ultimately you can get very good traffic for your blog. Generally there are many such sites, if you are willing to write articles. But my favourite one is submitting your great article which is related to your site to ezine.

(4)Getting Paid For Your Work:-

This is not provided by many sites, but there are some sites which gives you money for submitting articles to them. Some such sites is Helium,Wiseorb,Shvoong etc. But among them my favourite one is Associated Content. It is because getting paid is on one hand and at the same time getting a back link is also possible with this site.

(5)Testimonals:-

Generally if you are willing to write articles about new sites, then another advantage is, you may get a chance of getting your link placed on the home page of that site. Generally the home page of sites will be a minimum of 4 and hence getting a backlink from a site with a minimum of PR4 is OMG!

(6)For Writing Good Posts:-

If you are a blogger then writing articles provide you with good experience and you can increase the quality of your post. If you can see my old posts you can find how poor I was in writing posts at that time. But you can see now, how I have improved in writing my posts.

Hence this is the greatest advantage of writing articles. So writing articles became a part and parcel of every blogger and article writing is important from the time a site starts. So, I wish my readers to write articles for their sites.

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ROLES OF TEACHERS.

March 2, 2008

A traditional view of the teacher is of someone who dispenses knowledge: someone who lectures, tells, feeds, disseminates, covers material, teaches the subject matter more than the students. The students sit passively while the teacher is on show. Desks in rows and a blackboard and podium up front are an arrangement designed for this role of a teacher. However, lectures are effective for giving short sets of instructions, background information, guidelines, or other information that is needed in a short time frame (e.g., before doing a class project, lab, or group activity).

Demonstrating, on the other hand, allow students to experience more fully the information and concepts the teacher wants to impart during the lesson. Although the teacher is still the center of the action and the dispenser of knowledge, students can more easily see what they need to know and more efficiently link it to prior knowledge in their own ways. Students remember much better what they have both heard and seen (or even touched, smelled, or tasted)!
Listening is a very important teacher role, something that we don’t usually think of in connection with the lecturer role, however. Listening is crucial for assessment of learning (checking comprehension and appropriate challenge level), for collaboration between teachers and students (coaching instead of just judging), and for giving students a real sense of ownership of classroom activities as well as for allowing students to articulate and internalize the learning processes. Teachers who listen can turn around and provide very effective support structures to guide students on to the next level of challenge.

Empowering is really what teaching is all about. Ironically, though, many teachers act as if empowering students means weakening themselves–their authority as both a classroom disciplinarian and a subject-matter authority. But maybe power is like love: the more you give, the more you get.

Obviously, teachers wear many hats: friend, counselor, judge, mentor–hundreds of roles and different roles for different classes, students, and extra curricular duties. The above animations, however, are meant to show the different effects on students of different teacher behaviors.

Teachers are: cultural organizers, cultural mediators, and orchestrates of social contexts for learning (Gay, 2000).

Cultural Organizers

Gay (2000) explains that teachers must be competent in understanding the dynamics and uses of culture in their classroom. Daily classroom activities should facilitate learning environments that reflect cultural and ethnic diversity while also promoting academic achievement for all. Students from different ethnic groups should be able to voice their cultural expression in order to enhance content and learning processes.

Cultural Mediators

Teachers should expose students to multiple perspectives and allow students to critically analyze differences between mainstream cultural ideals and those of different cultural systems. Teachers guide students to reflect on their own ethnic identities and facilitate them in honoring other cultures and developing positive cross-cultural relationships. Classroom activities should enhance students’ abilities to identify stereotypes and prejudices and also teach students how to avoid perpetuating racism (Gay, 2000).

Orchestrators of Social Contexts

Gay (2000) also asserts that it is very important for teachers to appreciate the impact culture has on learning. Furthermore, they must make their teaching well-suited to the sociocultural contexts and frames of reference of ethnically diverse students. They are also guides in helping students know how to utilize their cultural cognition in order to facilitate their learning. Following is Spring’s (1995) definition of a cultural frame of reference, “those elements that cause a cultural group to interpret the world. . . in a particular manner” (p. 5), or the filter through which perceptions of, encounters with, and understandings of the outside world are ordered and made meaningful (Gay, 2000).

Examples of teachers’ roles:-

  • Representative of society (Inculcates moral precepts)
  • Judge (Gives marks and ratings)
  • Resource (Possesses knowledge and skill)
  • Helper (Provides guidance for pupil difficulties)
  • Referee (Settles disputes amongst pupils)
  • Detective (Discovers rule-breakers)
  • Object of identification (Possesses traits which children imitate)
  • Ego-supporter /Helps pupils to have confidence in themselves)
  • Parent surrogate (Acts as object of bids for attention from younger children)
  • Target for hostilities (Acts as object of aggression arising from Frustration created by adults)
  • Friend and confidante (Establishes warm relationship with children and shares confidences)
  • Object of affection (Meets the psychological needs of children)

In Conclusion, ‘the teacher has two basic sets of roles to fulfill. One set corresponds with the major functions of instruction, socialization, and evaluation. The second set is concerned with motivating pupils, maintaining control, and generally creating an environment for learning.’

#The Role of the Teacher“…the successful teacher will be highly adaptable in his behavior. The skillful teacher can play the role of comedian, kindly uncle, confidante, or any other informal role, but yet retain the capacity to return with ease to a more detached role when necessary without losing the goodwill of his pupils. A less accomplished teacher may play his informal roles successfully, but then have difficulty in reasserting his authority and lose the goodwill which he has generated by becoming aggressive in his struggle to retain control…. We might say that the successful teacher is one who:

a) has the skill to form accurate perceptions of the classroom situation and the changes which occur within this situation,

b) is aware of the teacher roles which are appropriate to different situations

c) possesses the personality skills which allow him to adapt to changing situations.

 

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IMPORTANCE OF EDUCATION.

March 2, 2008

Education has an immense impact on the human society. One can safely assume that a person is not in the proper sense till he is educated. It trains the human mind to think and take the right decision. In other words, man becomes a rational animal when he is educated.

It is through education that knowledge and information is received and spread throughout the world. An uneducated person cannot read and write and hence he is closed to all the knowledge and wisdom he can gain through books and other mediums. In other words, he is shut off from the outside world. In contrast, an educated man lives in a room with all its windows open towards outside world.

The quality of human resource of a nation is easily judged by the number of literate population living in it. This is to say that education is a must if a nation aspires to achieve growth and development and more importantly sustain it. This may well explain the fact that rich and developed nations of the world have very high literacy rate and productive human resource. In fact these nations have started imparting selective training and education programs so as to meet the new technical and business demands of the 21st century.

In the US, many educational institutes offer vocational as well as other training programs apart from the normal credit programs. To cater to the educational needs of the working population, many colleges offer online education. The degrees and certificates offered by these online colleges and universities are very convenient for working people as well as students. Working people needs these degrees to update their knowledge and skill level which will come handy in their promotion and achieving growth as professionals. Students can also pursue an online degree and work and earn at the same time.

In fact, certain professionals like doctors and dentists, are obliged to follow mandatory lifelong learning. This is done so that they keep pace with all the research and development done in the medical field. These professionals not only needs to update themselves about these developments, but also learn new techniques of practice and perfect old ones. Learning about patient management and the delivery of care is rather a continuing process. Since these professionals, especially doctors have huge moral responsibility towards the patients and society in general, continuing education is a must for them.

It is in such a scenario that distance education comes into the picture. Since professionals do not have the time to attend classroom classes, distance education comes as a convenient alternative. They can learn at a time convenient to them and from the comfort of their homes.

Keeping the importance of education in mind, the US Department of Education aims to promote student achievement and preparation for global competitiveness by fostering educational excellence and ensuring equal access. It also establishes policies regarding federal financial aid for education, and distributing as well as monitoring those funds. It also continuously strives to focus national attention on key educational issues and providing equal access to education.

The importance of education cannot be neglected by any nation. And in today’s world, the role of education has become even more vital. It is an absolute necessity for economic and social development of any nation.

The importance of education is quite clear. Education is the knowledge of putting one’s potentials to maximum use. One can safely say that a human being is not in the proper sense till he is educated.

This importance of education is basically for two reasons. The first is that the training of a human mind is not complete without education. Education makes man a right thinker. It tells man how to think and how to make decision.

The second reason for the importance of education is that only through the attainment of education, man is enabled to receive information from the external world; to acquaint himself with past history and receive all necessary information regarding the present. Without education, man is as though in a closed room and with education he finds himself in a room with all its windows open towards outside world.

This is why Islam attaches such great importance to knowledge and education. When the Qur’an began to be revealed, the first word of its first verse was ‘Iqra’ that is, read. Education is thus the starting point of every human activity.

A scholar (alim) is accorded great respect in the hadith. According to a hadith the ink of the pen of a scholar is more precious than the blood of a martyr. The reason being that a martyr is engaged in defense work while an alim (scholar) builds individuals and nations along positive lines. In this way he bestows a real life to the world.

The Qur’an repeatedly asks us to observe the earth and the heavens. This instills in man a desire to learn natural science. All the books of hadith have a chapter on knowledge (ilm). In Sahih Bukhari there is a chapter entitled “The virtue of one who acquires ilm (learning) and imparts that to others.”

How great importance is attached to learning in Islam can be understood from an event in the life of the Prophet. At the battle of Badr in which the Prophet gained victory over his opponents, seventy people of the enemy rank were taken prisoner. These prisoners of war were literate people. In order to benefit from their education the Prophet declared that if one prisoner teaches ten Medinan children how to read and write, this will serve as his ransom and he will be set free.

This was the first school in the history of Islam established by the Prophet himself with all its teachers being non-Muslims. Furthermore, they were all war prisoners. There was all the risk that after their release they will again create problems for Islam and Muslims. This Sunnah of the Prophet shows that education is to be received whatever the risk involved.

On the one hand Islam places great emphasis on learning, on the other, all those factors which are necessary to make progress in learning have provided by God. One of these special factors is the freedom of research. One example of it is that in Makkah, the birthplace of the Prophet, dates were not grown. Afterwards the Prophet migrated to Medina, the city of dates. One day the Prophet saw that some people were atop the date trees busy in doing something. On being asked what they were engaged in, they replied that they were pollinating.

The Prophet suggested them not to do so. The following year date yield was considerably very low. The Prophet enquired them of the reason. They told him that the date crop depended on pollination. Since he suggested them to do otherwise, they had refrained from that. The Prophet then told them to go on doing as they used to, and that, “You know the worldly matters better than me.”

In this way, the Prophet of Islam separated scientific research from religion. This meant that in the world of nature, man must enjoy full opportunity to conduct free research and adopt the conclusions arrived at after the research. Placing such great emphasis on knowledge.

This process began in Makkah, then it reached to Medina and Damascus, afterwards it found its center in Baghdad. Ultimately it entered Spain. Spain flourished with extraordinary progress made in various academic and scientific disciplines. This flood of scientific progress entered Europe and ultimately resulted in producing the modern scientific age.


The Real Purpose of Education

Education—like democracy, free markets, freedom of the press, and “universal human rights” — is one of those subjects whose virtue is considered self-evident. So is the superiority of the industrially advanced countries in attaining them. Consequently, any package that arrives with one of these magic labels on it, automatically qualifies for the “green channel” at our entry ports. No questions asked. This uncritical acceptance has severely crippled our discussion of all these vital topics. For example in education most of our discussion centers around literacy statistics and the need to have so many graduates, masters, Phd’s, and so many professionals — engineers, doctors, etc.— in a given country based on the standards in the industrially advanced countries. The central issue of curriculum, and even more fundamental issue of the purpose of education normally do not attract our attention; they have already been decided by the “advanced’ countries for us and our job is only to follow in their footsteps to achieve their level of progress.

Indeed they have. In the “first” world, education has become an extension of the capitalist system. Its purpose is to provide qualified workforce for its machinery of production and eager consumers for its products. Stated in a more polished form, the purpose of education is to provide for the economic prosperity of a country. Similarly on a personal level today the purpose of education is to be able to earn a respectable living.

While earning halal living and providing for the economic well being of a country are certainly important Islamic goals as well, the linking of education to financial goals is extremely unfortunate. It turns the centers of learning into mere vocational centers in their outlook and spirit. It degrades education and through it the society.

To bring home the pivotal but forgotten role of education we need to recall that there is a fundamental difference between human beings and animals. Instincts and physical needs alone can bring ants, bees, or herds of beasts together to live in a perfectly functioning animal society. Human beings do not function that way. They are not constrained by nature to follow only those ways that are necessary for the harmonious operation of their society. If they are to form a viable, thriving society, they must chose to do so. What drives that choice is the sharing of common goals, beliefs, values and outlook on life. Without a common framework binding its members, a human society cannot continue to exist; it will disintegrate and be absorbed by other societies. Further, the society must ensure that the common ground will continue to hold from generation to generation. This is the real purpose of education. The education system of a society produces the citizens and leaders needed for the smooth operation of that society, now and into the future. Its state of health or sickness translates directly into the health or sickness of the society that it is meant to serve.

Today we find many internal problems — corruption, injustice, oppression, crippling poverty — everywhere we turn in the Muslim world. If we think about it, we may realize that most of these problems are man-made. Which is another way of saying that they are largely traceable, directly or indirectly, to the education system that produced the people who perpetuate the problems. The rulers who sell out to foreign powers and subjugate their people; the bureaucrats who enforce laws based on injustice; the generals who wage war against their own people; the businessmen who exploit and cheat; the journalists who lie, sensationalize, and promote indecencies, they are all educated people, in many cases “highly” educated people. Their education was meant to prepare them for the roles they are playing in real life. And it has, although in a very unexpected way!

The problem plagues all layers of society. Why are Muslim communities in the grip of so much materialism today? What should we expect when our entire education system is preaching the gospel of materialism? Why have we effectively relegated Islam to a small inconsequential quarter in our public life? Because that is precisely where our secular education system has put it. Why in our behavior toward each other we see so little display of Islamic manners and morals? Because our imported education system is devoid of all moral training. Why our societies are sick? Because our education system is sick.

This is the real crisis of education. Before we got into this mess by importing from the Colonial powers what was current and popular, education in our societies was always the means of nurturing the human being. Moral training, tarbiya, was always an inalienable part of it. The ustaz,(teacher), was not just a lecturer or mere professional, but a mentor and moral guide. We remembered the hadith then, “No father has given a greater gift to his children than good moral training.” [Tirmidhi]. Our education system was informed by this hadith. Our darul-ulooms still maintain that tradition but the number of students who pass through their gates is minuscule compared to the secular schools.

In the U.S. and Europe, the schools were started by the church. Later as forces of capitalism overtook them, they molded them into their image. Moral training was a casualty of that takeover. But capitalism and their political economy did need people trained to work under these systems. So citizenship training was retained as an important, though diminishing, component of the curriculum— a religion-free subset of the moral training it displaced. Whatever civility we see here is largely a result of that leftover component. The imported versions in the Muslim countries, though, had even that component filtered out. And the results are visible.

We can solve our problem once we realize our mistakes. The first purpose of our education system must be to produce qualified citizens and leaders for the Islamic society. Tarbiya, real Islamic moral training, must be an integral part of it. This must be the soul of our education, not a ceremonial husk. All plans for improving our education will be totally useless unless they are based on a full understanding of this key fact. This requires revamping our curricula, rewriting our textbooks, retraining our teachers, and realizing that we must do all this ourselves. We do have a rich history of doing it. Are we finally willing to turn to our own in-house treasures to redo education the way it should always have been?

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COMPUTER ASSISTED SECOND LANGUAGE VOCABULARY ACQUISITION

February 27, 2008

 ABSTRACT

During the initial stages of instructed L2 acquisition students learn a couple thousand, mainly high frequency words. Functional language proficiency, however, requires mastery of a considerably larger number of words. It is therefore necessary at the intermediate and advanced stages of language acquisition to learn a large vocabulary in a short period of time. There is not enough time to copy the natural (largely incidental) L1 word acquisition process. Incidental acquisition of the words is only possible up to a point, because, on account of their low frequency, they do not occur often enough in the L2 learning material. Acquisition of new words from authentic L2 reading texts by means of strategies such as contextual deduction is also not a solution for a number of reasons. There appears to be no alternative to intentional learning of a great many new words in a relatively short period of time. The words to be learned may be presented in isolation or in context. Presentation in bilingual word lists seems an attractive shortcut because it takes less time than contextual presentation and yields excellent short term results. Long term retention, however, is often disappointing so contextual presentation seems advisable. Any suggestions how to implement this in pedagogic contexts should be based on a systematic analysis of the two most important aspects of the L2 word learning problem, that is to say, selecting the relevant vocabulary (which and how many words) and creating optimal conditions for the acquisition process. This article sets out to describe a computer assisted word acquisition programme (CAVOCA) which tries to do precisely this: the programme operationalises current theoretical thinking about word acquisition, and its contents are based on a systematic inventory of the vocabulary relevant for the target group. To establish its efficiency, the programme was contrasted in a number of experimental settings with a paired associates method of learning new words. The experimental results suggest that an approach combining the two methods is most advisable.

The naive view that the vocabulary of a language should be seen as a “set of basic irregularities” impervious to systematic study, and its acquisition as a haphazard process of learning largely unrelated elements is long outdated. Furthermore, the language teaching profession has come to realise that in foreign language teaching, a grammar-oriented approach is not, to understate the case, the most efficient way to achieve communicative competence. An integrated approach combining systematic attention to the acquisition of both grammar and vocabulary is considered much more effective. This fuller appreciation of the importance of vocabulary teaching gives rise to a number of questions concerning the way in which it should be selected and presented for learning.

HOW TO TEACH/LEARN THE WORDS?

In connection with word learning, a distinction is commonly drawn between incidental and intentional learning. Unless one narrowly defines incidental learning as excluding any conscious attention to the words being learned, the two learning modes are not always easy to differentiate and show a considerable overlap, not unlike the acquisition/learning dichotomy suggested by Krashen. In this paper, intentional learning will be used to refer to any learning activity the learner undertakes with the intention of gaining new knowledge. As such it differs from incidental learning where there is no such intention (Anderson, 1990). From a pedagogic perspective, however, the distinction is still useful in a discussion on the optimal way of presenting new L2 words in instructional contexts.

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Lifelong learning

February 27, 2008

Lifelong learning is the concept that “It’s never too soon or too late for learning”, a philosophy that has taken root in a whole host of different organisations. Lifelong learning is attitudinal; that one can and should be open to new ideas, decisions, skills or behaviours. Lifelong learning throws the axiom “You can’t teach an old dog new tricks” out the door. Lifelong learning sees citizens provided with learning opportunities at all ages and in numerous contexts: at work, at home and through leisure activities, not just through formal channels such as school and higher education.Lifelong education is a form of pedagogy often accomplished through distance learning or e-learning, continuing education, homeschooling or correspondence courses. It also includes postgraduate programmes for those who want to improve their qualifications, bring their skills up to date or retrain for a new line of work. Internal corporate training has similar goals, with the concept of lifelong learning used by organisations to promote a more dynamic employee base, better able to react in an agile manner to a rapidly changing climate. In later life, especially in retirement, continued learning takes diverse forms, crossing traditional academic bounds and including recreational activities.One of the reasons why lifelong education has become so important is the acceleration of scientific and technological progress. Despite the increased duration of primary, secondary and university education (14-18 years depending on the country), the knowledge and skills acquired there are usually not sufficient for a professional career spanning three or four decades. The European Union adopted a Communication in October 2006 entitled “It’s never too late to learn”. This document suggests lifelong learning to be the core of the ambitious Lisbon 2010-process, in which the whole of the European Union should become a learning area. The OECD is also conducting research on lifelong learning.

The latest knowledge and successful practices of planning and implementing education for lifelong learning suggest that lifelong learning is more than just education and training beyond formal schooling.  A lifelong learning framework encompasses learning throughout the life cycle, from birth to grave and in different learning environments, formal, non-formal and informal.

 

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Effective Teaching

February 23, 2008

What is Effective Teaching?

Effective teaching is the basis of successful learning. Effective teaching identifies and builds on prior knowledge, makes real-life connections, develops deep understanding and monitors and reflects on learning.

Premises of Teaching

  • There is no one right teaching style.
  • Your teaching style is an extension of your personality, thus some techniques will appeal to you more than others.
  • Teaching may appear easier and “more natural” for some than for others, but there are no “born teachers” who don’t need to improve or others who can never improve regardless of effort.
  • Good teachers work at being good and are constantly looking for ways to improve.
  • Not all techniques are effective in every setting, in every situation of the same setting, and with every group.
  • A new approach should not be tried only because it is new, nor rejected for the same reason.

greybtn2.gif (273 bytes)Selecting the Instructional Format

No one instructional format is best for all course objectives. Learning can often be enhanced by providing the instructional process through a variety of formats. Since a major goal of Curriculum 2000 is to help students become seekers of information, not merely receptacles of information, instructional formats should be selected with this goal in mind. Since using the same format throughout can cause students to become weary of the approach, if not the content, course directors are encouraged to provide as much variation in instructional format as is educationally appropriate. Some instructional formats are as follows:

  • Independent reading (textbook, journal article, explanatory handout)
  • Computer-assisted instruction
  • Demonstration
  • Small-group discussion for real or hypothetical cases
  • Lecture
  • Laboratory
  • Individualized

greybtn2.gif (273 bytes)Teaching & Learning: Points to Consider

Effective teaching should be thought of as helping students learn, and every student encounter should be thought of as a student’s opportunity for learning.

Foster a good learning atmosphere.

  • Be serious without creating excessive tension.
  • Be prepared—have a flexible teaching plan in mind, but be ever on the lookout for the “teachable moment”.
  • Be positive toward learners—guard against sending unintentional messages (disdain, condescension, racism, sexism, etc.).
  • Be confident (not arrogant) but comfortable in not knowing everything.

Use effective teaching techniques.

  • State what should be learned here.
  • Situate the topic in the “bigger picture”—provide adequate context.
  • Involve learners in the process by having them, for example, present the problem, respond to questions, summarize the findings and discussion, and research and report on unanswered questions.
  • Use questions effectively.
  • Summarize the “take-home” points at the end of the discussion/activity.
  • Use follow-up research and reporting to the group as an “inquisitive” exercise rather than a “punitive” exercise for not having the answer initially.

Effective Teaching: Examples in History, Mathematics, and Science

 The preceding chapter explored implications of research on learning for general issues relevant to the design of effective learning environments. We now move to a more detailed exploration of teaching and learning in three disciplines: history, mathematics, and science. We chose these three areas in order to focus on the similarities and differences of disciplines that use different methods of inquiry and analysis. A major goal of our discussion is to explore the knowledge required to teach effectively in a diversity of disciplines.

     We noted that expertise in particular areas involves more than a set of general problem-solving skills; it also requires well-organized knowledge of concepts and inquiry procedures. Different disciplines are organized differently and have different approaches to inquiry. For example, the evidence needed to support a set of historical claims is different from the evidence needed to prove a mathematical conjecture, and both of these differ from the evidence needed to test a scientific theory. Discussion also differentiated between expertise in a discipline and the ability to help others learn about that discipline. To use Shulman’s (1987) language, effective teachers need pedagogical content knowledge (knowledge about how to teach in particular disciplines) rather than only knowledge of a particular subject matter.

Pedagogical content knowledge is different from knowledge of general teaching methods. Expert teachers know the structure of their disciplines, and this knowledge provides them with cognitive roadmaps that guide the assignments they give students, the assessments they use to gauge students’ progress, and the questions they ask in the give and take of classroom life. In short, their knowledge of the discipline and their knowledge of pedagogy interact. But knowledge of the discipline structure does not in itself guide the teacher. For example, expert teachers are sensitive to those aspects of the discipline that are especially hard or easy for new students to master. This means that new teachers must develop the ability to “understand in a pedagogically reflective way; they must not only know their own way around a discipline, but must know the ‘conceptual barriers’ likely to hinder others” (McDonald and Naso, 1986:8). These conceptual barriers differ from discipline to discipline.

An emphasis on interactions between disciplinary knowledge and pedagogical knowledge directly contradicts common misconceptions about what teachers need to know in order to design effective learning environments for their students. The misconceptions are that teaching consists only of a set of general methods, that a good teacher can teach any subject, or that content knowledge alone is sufficient.

Some teachers are able to teach in ways that involve a variety of disciplines. However, their ability to do so requires more than a set of general teaching skills. Consider the case of Barb Johnson, who has been a sixth- grade teacher for 12 years at Monroe Middle School. By conventional standards Monroe is a good school. Standardized test scores are about average, class size is small, the building facilities are well maintained, the administrator is a strong instructional leader, and there is little faculty and staff turnover. However, every year parents sending their fifth-grade students from the local elementary schools to Monroe jockey to get their children assigned to Barb Johnson’s classes. What happens in her classroom that gives it the reputation of being the best of the best?

During the first week of school Barb Johnson asks her sixth graders two questions: “What questions do you have about yourself?” and “What questions do you have about the world?” The students begin enumerating their questions, “Can they be about silly, little things?” asks one student. “If they’re your questions that you really want answered, they’re neither silly nor little,” replies the teacher. After the students list their individual questions, Barb organizes the students into small groups where they share lists and search for questions they have in common. After much discussion each group comes up with a priority list of questions, rank-ordering the questions about themselves and those about the world.

Back together in a whole group session, Barb Johnson solicits the groups’ priorities and works toward consensus for the class’s combined lists of questions. These questions become the basis for guiding the curriculum in Barb’s class. One question, “Will I live to be 100 years old?” spawned educational investigations into genetics, family and oral history, actuarial science, statistics and probability, heart disease, cancer, and hypertension. The students had the opportunity to seek out information from family members, friends, experts in various fields, on-line computer services, and books, as well as from the teacher. She describes what they had to do as becoming part of a “learning community.” According to Barb Johnson, “We decide what are the most compelling intellectual issues, devise ways to investigate those issues and start off on a learning journey. Sometimes we fall short of our goal. Sometimes we reach our goal, but most times we exceed these goals–we learn more than we initially expected” (personal communication).

At the end of an investigation, Barb Johnson works with the students to help them see how their investigations relate to conventional subject-matter areas. They create a chart on which they tally experiences in language and literacy, mathematics, science, social studies and history, music, and art. Students often are surprised at how much and how varied their learning is. Says one student, “I just thought we were having fun. I didn’t realize we were learning, too!”

Barb Johnson’s teaching is extraordinary. It requires a wide range of disciplinary knowledge because she begins with students’ questions rather than with a fixed curriculum. Because of her extensive knowledge, she can map students’ questions onto important principles of relevant disciplines. It would not work to simply arm new teachers with general strategies that mirror how she teaches and encourage them to use this approach in their classrooms. Unless they have the relevant disciplinary knowledge, the teachers and the classes would quickly become lost. At the same time, disciplinary knowledge without knowledge about how students learn (i.e., principles consistent with developmental and learning psychology) and how to lead the processes of learning (i.e., pedagogical knowledge) would not yield the kind of learning seen in Barb Johnson’s classes (Anderson and Smith, 1987).

In the remainder of this chapter, we present illustrations and discussions of exemplary teaching in history, mathematics, and science. The three examples of history, mathematics, and science are designed to convey a sense of the pedagogical knowledge and content knowledge (Shulman, 1987) that underlie expert teaching. They should help to clarify why effective teaching requires much more than a set of “general teaching skills.”

     Most people have had quite similar experiences with history courses: they learned the facts and dates that the teacher and the text deemed relevant. This view of history is radically different from the way that historians see their work. Students who think that history is about facts and dates miss exciting opportunities to understand how history is a discipline that is guided by particular rules of evidence and how particular analytical skills can be relevant for understanding events in their lives (see Ravitch and Finn, 1987). Unfortunately, many teachers do not present an exciting approach to history, perhaps because they, too, were taught in the dates-facts method.

        Beyond Facts

      We discussed a study of experts in the field of history and learned that they regard the available evidence as more than lists of facts (Wineburg, 1991). The study contrasted a group of gifted high school seniors with a group of working historians. Both groups were given a test of facts about the American Revolution taken from the chapter review section of a popular United States history textbook. The historians who had backgrounds in American history knew most of the items, while historians whose specialties lay elsewhere knew only a third of the test facts. Several students scored higher than some historians on the factual pretest. In addition to the test of facts, however, the historians and students were presented with a set of historical documents and asked to sort out competing claims and to formulate reasoned interpretations. The historians excelled at this task. Most students, on the other hand, were stymied. Despite the volume of historical information the students possessed, they had little sense of how to use it productively for forming interpretations of events or for reaching conclusions.

      Different views of history affect how teachers teach history. For example, Wilson and Wineburg (1993) asked two teachers of American history to read a set of student essays on the causes of the American Revolution not as unbiased or complete and definitive accounts of people and events, but to develop plans for the students’ “remediation or enrichment.” Teachers were provided with a set of essays on the question, “Evaluate the causes of the American Revolution,” written by eleventh-graders for a timed, 45-minute test. Consider the different types of feedback that Mr. Barnes and Ms. Kelsey gave a student paper.

 

     Mr. Barnes’ comments on the actual content of the essays concentrated on the factual level. Ms. Kelsey’s comments addressed broader images of the nature of the domain, without neglecting important errors of fact. Overall, Mr. Barnes saw the papers as an indication of the bell-shaped distribution of abilities; Ms. Kelsey saw them as representing the misconception that history is about memorizing a mass of information and recounting a series of facts. These two teachers had very different ideas about the nature of learning history. Those ideas affected how they taught and what they wanted their students to achieve.

        For expert history teachers, their knowledge of the discipline and beliefs about its structure interacts with their teaching strategies. Rather than simply introduce students to sets of facts to be learned, these teachers help people to understand the problematic nature of historical interpretation and analysis and to appreciate the relevance of history for their everyday lives.

 

      One example of outstanding history teaching comes form the classroom of Bob Bain, a public school teacher in Beechwood, Ohio. Historians, he notes, are cursed with an abundance of data–the traces of the past threaten to overwhelm them unless they find some way of separating what is important from what is peripheral. The assumptions that historians hold about significance shape how they write their histories, the data they select, and the narrative they compose, as well as the larger schemes they bring to organize and periodize the past. Often these assumptions about historical significance remain unarticulated in the classroom. This contributes to students’ beliefs that their textbooks are the history rather than a history.

Bob Bain begins his ninth-grade high school class by having all the students create a time capsule of what they think are the most important artifacts from the past. The students’ task, then, is to put down on paper why they chose the items they did. In this way, the students explicitly articulate their underlying assumptions of what constitutes historical significance. Students’ responses are pooled, and he writes them on a large poster that he hangs on the classroom wall. This poster, which Bob Bain calls “Rules for Determining Historical Significance,” becomes a lightening rod for class discussions throughout the year, undergoing revisions and elaborations as students become better able to articulate their ideas.

At first, students apply the rules rigidly and algorithmically, with little understanding that just as they made the rules, they can also change them. But as students become more practiced in plying their judgments of significance, they come to see the rules as tools for assaying the arguments of different historians, which allows them to begin to understand why historians disagree. In this instance, the students’ growing ability to understand the interpretative nature of history is aided by their teacher’s deep understanding of a fundamental principle of the discipline.

Leinhardt and Greeno (1991, 1994) spent 2 years studying a highly accomplished teacher of advanced placement history in an urban high school in Pittsburgh. The teacher, Ms. Sterling, a veteran of over 20 years, began her school year by having her students ponder the meaning of the statement, “Every true history is contemporary history.” In the first week of the semester, Sterling thrust her students into the kinds of epistemological issues that one might find in a graduate seminar: “What is history?” “How do we know the past?” “What is the difference between someone who sits down to ‘write history’ and the artifacts that are produced as part of ordinary experience?” The goal of this extended exercise is to help students understand history as an evidentiary form of knowledge, not as clusters of fixed names and dates.

One might wonder about the advisability of spending 5 days “defining history” in a curriculum with so much to cover. But it is precisely Sterling’s framework of subject-matter knowledge–her overarching understanding of the discipline as a whole–that permits students entry into the advanced world of historical sense-making. By the end of the course, students moved from being passive spectators of the past to enfranchised agents who could participate in the forms of thinking, reasoning, and engagement that are the hallmark of skilled historical cognition. For example, early in the school year, Ms. Sterling asked her students a question about the Constitutional Convention and “what were men able to do.” Paul took the question literally: “Uh, I think one of the biggest things that they did, that we talked about yesterday, was the establishment of the first settlements in the Northwest area states.” But after 2 months of educating students into a way of thinking about history, Paul began to catch on. By January his responses to questions about the fall of the cotton-based economy in the South were linked to British trade policy and colonial ventures in Asia, as well as to the failure of Southern leaders to read public opinion accurately in Great Britain. Ms. Sterling’s own understanding of history allowed her to create a classroom in which students not only mastered concepts and facts, but also used them in authentic ways to craft historical explanations.

        Debating the Evidence

     Elizabeth Jensen prepares her group of eleventh graders to debate the following resolution:

Resolved: The British government possesses the legitimate authority to tax the American colonies.

     As her students enter the classroom they arrange their desks into three groups–on the left of the room a group of “rebels,” on the right, a group of “loyalists,” and in the front, a group of “judges.” Off to the side with a spiral notebook on her lap sits Jensen, a short woman in her late 30s with a booming voice. But today that voice is silent as her students take up the question of the legitimacy of British taxation in the American colonies.

The rebels’ first speaker, a 16-year-old girl with a Grateful Dead T-shirt and one dangling earring, takes a paper from her notebook and begins:

England says she keeps troops here for our own protection. On face value, this seems reasonable enough, but there is really no substance to their claims. First of all, who do they think they are protecting us from? The French? Quoting from our friend Mr. Bailey on page 54, ‘By the settlement in Paris in 1763, French power was thrown completely off the continent of North America.’ Clearly not the French then. Maybe they need to protect us from the Spanish? Yet the same war also subdued the Spanish, so they are no real worry either. In fact, the only threat to our order is the Indians . . . but . . . we have a decent militia of our own. . . . So why are they putting troops here? The only possible reason is to keep us in line. With more and more troops coming over, soon every freedom we hold dear will be stripped away. The great irony is that Britain expects us to pay for these vicious troops, these British squelchers of colonial justice.

     A loyalist responds:

We moved here, we are paying less taxes than we did for two generations in England, and you complain? Let’s look at why we are being taxed–the main reason is probably because England has a debt of £140,000,000.
. . . This sounds a little greedy, I mean what right do they have to take our money simply because they have the power over us. But did you know that over one-half of their war debt was caused by defending us in the French and Indian War. . . . Taxation without representation isn’t fair. Indeed, it’s tyranny. Yet virtual representation makes this whining of yours an untruth. Every British citizen, whether he had a right to vote or not, is represented in Parliament. Why does this representation not extend to
America?

A rebel questions the loyalist about this:

Rebel:

What benefits do we get out of paying taxes to the crown?

Loyalist:

We benefit from the protection.

Rebel:

(cutting in) Is that the only benefit you claim, protection?

Loyalist:

Yes–and all the rights of an Englishman.

Rebel:

Okay, then what about the Intolerable Acts . . . denying us rights of British subjects. What about the rights we are denied?

Loyalist:

The Sons of Liberty tarred and feather people, pillaged homes–they were definitely deserving of some sort of punishment.

Rebel:

So should all the colonies be punished for the acts of a few colonies?

For a moment, the room is a cacophony of charges and countercharges. “It’s the same as in Birmingham,” shouts a loyalist. A rebel snorts disparagingly, “Virtual representation is bull.” Thirty-two students seem to be talking at once, while the presiding judge, a wiry student with horn-rimmed glasses, bangs his gavel to no avail. The teacher, still in the corner, still with spiral notebook in lap, issues her only command of the day. “Hold still!” she thunders. Order is restored and the loyalists continue their opening argument (from Wineburg and Wilson, 1991).

Another example of Elizabeth Jensen’s teaching involves her efforts to help her high school students understand the debates between Federalists and anti-Federalists. She knows that her 15- and 16-year-olds cannot begin to grasp the complexities of the debates without first understanding that these disagreements were rooted in fundamentally different conceptions of human nature–a point glossed over in two paragraphs in her history textbook. Rather than beginning the year with a unit on European discovery and exploration, as her text dictates, she begins with a conference on the nature of man. Students in her eleventh-grade history class read excerpts from the writings of philosophers (Hume, Locke, Plato, and Aristotle), leaders of state and revolutionaries (Jefferson, Lenin, Gandhi), and tyrants (Hitler, Mussolini), presenting and advocating these views before their classmates. Six weeks later, when it is time to study the ratification of the Constitution, these now-familiar figures–Plato, Aristotle, and others–are reconvened to be courted by impassioned groups of Federalists and anti-Federalists. It is Elizabeth Jensen’s understanding of what she wants to teach and what adolescents already know that allows her to craft an activity that helps students get a feel for the domain that awaits them: decisions about rebellion, the Constitution, federalism, slavery, and the nature of a government.

        Conclusion

      These examples provide glimpses of outstanding teaching in the discipline of history. The examples do not come from “gifted teachers” who know how to teach anything: they demonstrate, instead, that expert teachers have a deep understanding of the structure and epistemologies of their disciplines, combined with knowledge of the kinds of teaching activities that will help students come to understand the discipline for themselves. As we previously noted, this point sharply contradicts one of the popular–and dangerous–myths about teaching: teaching is a generic skill and a good teacher can teach any subject. Numerous studies demonstrate that any curriculum–including a textbook–is mediated by a teacher’s understanding of the subject domain (for history, see Wineburg and Wilson, 1988; for math, see Ball, 1993; for English, see Grossman et al., 1989). The uniqueness of the content knowledge and pedagogical knowledge necessary to teach history becomes clearer as one explores outstanding teaching in other disciplines.

      MATHEMATICS

     As is the case in history, most people believe that they know what mathematics is about–computation. Most people are familiar with only the computational aspects of mathematics and so are likely to argue for its place in the school curriculum and for traditional methods of instructing children in computation. In contrast, mathematicians see computation as merely a tool in the real stuff of mathematics, which includes problem solving, and characterizing and understanding structure and patterns. The current debate concerning what students should learn in mathematics seems to set proponents of teaching computational skills against the advocates of fostering conceptual understanding and reflects the wide range of beliefs about what aspects of mathematics are important to know. A growing body of research provides convincing evidence that what teachers know and believe about mathematics is closely linked to their instructional decisions and actions (Brown, 1985; National Council of Teachers of Mathematics, 1989; Wilson, 1990a, b; Brophy, 1990; Thompson, 1992).

Teachers’ ideas about mathematics, mathematics teaching, and mathematics learning directly influence their notions about what to teach and how to teach it–an interdependence of beliefs and knowledge about pedagogy and subject matter (e.g., Gamoran, 1994; Stein et al., 1990). It shows that teachers’ goals for instruction are, to a large extent, a reflection of what they think is important in mathematics and how they think students best learn it. Thus, as we examine mathematics instruction, we need to pay attention to the subject-matter knowledge of teachers, their pedagogical knowledge (general and content specific), and their knowledge of children as learners of mathematics. Paying attention to these domains of knowledge also leads us to examine teachers’ goals for instruction.

If students in mathematics classes are to learn mathematics with understanding–a goal that is accepted by almost everyone in the current debate over the role of computational skills in mathematics classrooms–then it is important to examine examples of teaching for understanding and to analyze the roles of the teacher and the knowledge that underlies the teacher’s enactments of those roles. In this section, we examine three cases of mathematics instruction that are viewed as being close to the current vision of exemplary instruction and discuss the knowledge base on which the teacher is drawing, as well as the beliefs and goals which guide his or her instructional decisions.

     For teaching multidigit multiplication, teacher-researcher Magdelene Lampert created a series of lessons in which she taught a heterogeneous group of 28 fourth-grade students. The students ranged in computational skill from beginning to learn the single-digit multiplication facts to being able to accurately solve n-digit by n-digit multiplications. The lessons were intended to give children experiences in which the important mathematical principles of additive and multiplicative composition, associativity, commutativity, and the distributive property of multiplication over addition were all evident in the steps of the procedures used to arrive at an answer (Lampert, 1986:316). It is clear from her description of her instruction that both her deep understanding of multiplicative structures and her knowledge of a wide range of representations and problem situations related to multiplication were brought to bear as she planned and taught these lessons. It is also clear that her goals for the lessons included not only those related to students’ understanding of mathematics, but also those related to students’ development as independent, thoughtful problem solvers. Lampert (1986:339) described her role as follows:

My role was to bring students’ ideas about how to solve or analyze problems into the public forum of the classroom, to referee arguments about whether those ideas were reasonable, and to sanction students’ intuitive use of mathematical principles as legitimate. I also taught new information in the form of symbolic structures and emphasized the connection between symbols and operations on quantities, but I made it a classroom requirement that students use their own ways of deciding whether something was mathematically reasonable in doing the work. If one conceives of the teacher’s role in this way, it is difficult to separate instruction in mathematics content from building a culture of sense-making in the classroom, wherein teacher and students have a view of themselves as responsible for ascertaining the legitimacy of procedures by reference to known mathematical principles. On the part of the teacher, the principles might be known as a more formal abstract system, whereas on the part of the learners, they are known in relation to familiar experiential contexts. But what seems most important is that teachers and students together are disposed toward a particular way of viewing and doing mathematics in the classroom.

     Magdelene Lampert set out to connect what students already knew about multidigit multiplication with principled conceptual knowledge. She did so in three sets of lessons. The first set used coin problems, such as “Using only two kinds of coins, make $1.00 using 19 coins,” which encouraged children to draw on their familiarity with coins and mathematical principles that coin trading requires. Another set of lessons used simple stories and drawings to illustrate the ways in which large quantities could be grouped for easier counting. Finally, the third set of lessons used only numbers and arithmetic symbols to represent problems. Throughout the lessons, students were challenged to explain their answers and to rely on their arguments, rather than to rely on the teacher or book for verification of correctness. An example serves to highlight this approach.

Lampert (1986:337) concludes:

. . . Students used principled knowledge that was tied to the language of groups to explain what they were seeing. They were able to talk meaningfully about place value and order of operations to give legitimacy to procedures and to reason about their outcomes, even though they did not use technical terms to do so. I took their experimentations and arguments as evidence that they had come to see mathematics as more than a set of procedures for finding answers.

     Clearly, her own deep understanding of mathematics comes into play as she teaches these lessons. It is worth noting that her goal of helping students see what is mathematically legitimate shapes the way in which she designs lessons to develop students’ understanding of two-digit multiplication.

     Helping third-grade students extend their understanding of numbers from the natural numbers to the integers is a challenge undertaken by another teacher-researcher. Deborah Ball’s work provides another snapshot of teaching that draws on extensive subject content and pedagogical content knowledge. Her goals in instruction include “developing a practice that respects the integrity both of mathematics as a discipline and of children as mathematical thinkers” (Ball, 1993). That is, she not only takes into account what the important mathematical ideas are, but also how children think about the particular area of mathematics on which she is focusing. She draws on both her understanding of the integers as mathematical entities (subject-matter knowledge) and her extensive pedagogical content knowledge specifically about integers. Like Lampert, Ball’s goals go beyond the boundaries of what is typically considered mathematics and include developing a culture in which students conjecture, experiment, build arguments, and frame and solve problems–the work of mathematicians.

     Deborah Ball’s description of work highlights the importance and difficulty of figuring out powerful and effective ways to represent key mathematical ideas to children (see Ball, 1993). A wealth of possible models for negative numbers exists and she reviewed a number of them–magic peanuts, money, game scoring, a frog on a number line, buildings with floors above and below ground. She decided to use the building model first and money later: she was acutely aware of the strengths and limitations of each model as a way for representing the key properties of numbers, particularly those of magnitude and direction. Reading Deborah Ball’s description of her deliberations, one is struck by the complexity of selecting appropriate models for particular mathematical ideas and processes. She hoped that the positional aspects of the building model would help children recognize that negative numbers were not equivalent to zero, a common misconception. She was aware that the building model would be difficult to use for modeling subtraction of negative numbers.

Deborah Ball begins her work with the students, using the building model by labeling its floors. Students readily labeled the underground floors and accepted them as “below zero.” They then explored what happened as little paper people entered an elevator at some floor and rode to another floor. This was used to introduce the conventions of writing addition and subtraction problems involving integers 4 — 6 = —2 and —2 + 5 = 3. Students were presented with increasingly difficult problems. For example, “How many ways are there for a person to get to the second floor?” Working with the building model allowed students to generate a number of observations. For example, one student noticed that “any number below zero plus that same number above zero equals zero” (Ball, 1993:381). However, the model failed to allow for explorations for such problems 5 + (—6) and Ball was concerned that students were not developing a sense that —5 was less than
—2–it was lower, but not necessarily less. Ball then used a model of money as a second representational context for exploring negative numbers, noting that it, too, has limitations.

Clearly, Deborah Ball’s knowledge of the possible representations of integers (pedagogical content knowledge) and her understanding of the important mathematical properties of integers were foundational to her planning and her instruction. Again, her goals related to developing students’ mathematical authority, and a sense of community also came into play. Like Lampert, Ball wanted her students to accept the responsibility of deciding when a solution is reasonable and likely to be correct, rather than depending on text or teacher for confirmation of correctness.

        Guided Discussion

     The work of Lampert and Ball highlights the role of a teacher’s knowledge of content and pedagogical content knowledge in planning and teaching mathematics lessons. It also suggests the importance of the teacher’s understanding of children as learners. The concept of cognitively guided instruction helps illustrate another important characteristic of effective mathematics instruction: that teachers not only need knowledge of a particular topic within mathematics and knowledge of how learners think about the particular topic, but also need to develop knowledge about how the individual children in their classrooms think about the topic (Carpenter and Fennema, 1992; Carpenter et al., 1996; Fennema et al., 1996). Teachers, it is claimed, will use their knowledge to make appropriate instructional decisions to assist students to construct their mathematical knowledge. In this approach, the idea of domains of knowledge for teaching (Shulman, 1986) is extended to include teachers’ knowledge of individual learners in their classrooms.

Cognitively guided instruction is used by Annie Keith, who teaches a combination first- and second-grade class in an elementary school in Madison Wisconsin (Hiebert et al., 1997). Her instructional practices are an example of what is possible when a teacher understands children’s thinking and uses that understanding to guide her teaching. A portrait of Ms. Keith’s classroom reveals also how her knowledge of mathematics and pedagogy influence her instructional decisions.

Word problems form the basis for almost all instruction in Annie Keith’s classroom. Students spend a great deal of time discussing alternative strategies with each other, in groups, and as a whole class. The teacher often participates in these discussions but almost never demonstrates the solution to problems. Important ideas in mathematics are developed as students explore solutions to problems, rather than being a focus of instruction per se. For example, place-value concepts are developed as students use base-10 materials, such as base-10 blocks and counting frames, to solve word problems involving multidigit numbers.

Mathematics instruction in Annie Keith’s class takes place in a number of different settings. Everyday first-grade and second-grade activities, such as sharing snacks, lunch count, and attendance, regularly serve as contexts for problem-solving tasks. Mathematics lessons frequently make use of math centers in which the students do a variety of activities. On any given day, children at one center may solve word problems presented by the teacher while at another center children write word problems to present to the class later or play a math game.

She continually challenges her students to think and to try to make sense of what they are doing in math. She uses the activities as opportunities for her to learn what individual students know and understand about mathematics. As students work in groups to solve problems, she observes the various solutions and mentally makes notes about which students should present their work: she wants a variety of solutions presented so that students will have an opportunity to learn from each other. Her knowledge of the important ideas in mathematics serves as one framework for the selection process, but her understanding of how children think about the mathematical ideas they are using also affects her decisions about who should present. She might select a solution that is actually incorrect to be presented so that she can initiate a discussion of a common misconception. Or she may select a solution that is more sophisticated than most students have used in order to provide an opportunity for students to see the benefits of such a strategy. Both the presentations of solutions and the class discussions that follow provide her with information about what her students know and what problems she should use with them next.

Annie Keith’s strong belief that children need to construct their understanding of mathematical ideas by building on what they already know guides her instructional decisions. She forms hypotheses about what her students understand and selects instructional activities based on these hypotheses. She modifies her instruction as she gathers additional information about her students and compares it with the mathematics she wants them to learn. Her instructional decisions give her clear diagnoses of individual students’ current state of understanding. Her approach is not a free-for-all without teacher guidance: rather, it is instruction that builds on students’ understandings and is carefully orchestrated by the teacher, who is aware of what is mathematically important and also what is important to the learner’s progress.

        Model-Based Reasoning

      Some attempts to revitalize mathematics instruction have emphasized the importance of modeling phenomena. Work on modeling can be done from kindergarten through twelth grade (K-12). Modeling involves cycles of model construction, model evaluation, and model revision. It is central to professional practice in many disciplines, such as mathematics and science, but it is largely missing from school instruction. Modeling practices are ubiquitous and diverse, ranging from the construction of physical models, such as a planetarium or a model of the human vascular system, to the development of abstract symbol systems, exemplified by the mathematics of algebra, geometry, and calculus. The ubiquity and diversity of models in these disciplines suggest that modeling can help students develop understanding about a wide range of important ideas. Modeling practices can and should be fostered at every age and grade level (Clement, 1989; Hestenes, 1992; Lehrer and Romberg, 1996a, b; Schauble et al., 1995.

Taking a model-based approach to a problem entails inventing (or selecting) a model, exploring the qualities of the model, and then applying the model to answer a question of interest. For example, the geometry of triangles has an internal logic and also has predictive power for phenomena ranging from optics to wayfinding (as in navigational systems) to laying floor tile. Modeling emphasizes a need for forms of mathematics that are typically underrepresented in the standard curriculum, such as spatial visualization and geometry, data structure, measurement, and uncertainty. For example, the scientific study of animal behavior, like bird foraging, is severely limited unless one also has access to such mathematical concepts as variability and uncertainty. Hence, the practice of modeling introduces the further explorations of important “big ideas” in disciplines.

        Conclusion

      Increasingly, approaches to early mathematics teaching incorporate the premises that all learning involves extending understanding to new situations, that young children come to school with many ideas about mathematics, that knowledge relevant to a new setting is not always accessed spontaneously, and that learning can be enhanced by respecting and encouraging children to try out the ideas and strategies that they bring to school-based learning in classrooms. Rather than beginning mathematics instruction by focusing solely on computational algorithms, such as addition and subtraction, students are encouraged to invent their own strategies for solving problems and to discuss why those strategies work. Teachers may also explicitly prompt students to think about aspects of their everyday life that are potentially relevant for further learning. For example, everyday experiences of walking and related ideas about position and direction can serve as a springboard for developing corresponding mathematics about the structure of large-scale space, position, and direction (Lehrer and Romberg, 1996b).

As research continues to provide good examples of instruction that help children learn important mathematics, there will be better understanding of the roles that teachers’ knowledge, beliefs, and goals play in their instructional thinking and actions. The examples we have provided here make it clear that the selection of tasks and the guidance of students’ thinking as they work through tasks is highly dependent on teachers’ knowledge of mathematics, pedagogical content knowledge, and knowledge of students in general.

      Two recent examples in physics illustrate how research findings can be used to design instructional strategies that promote the sort of problem-solving behavior observed in experts. Undergraduates who had finished an introductory physics course were asked to spend a total of 10 hours, spread over several weeks, solving physics problems using a computer-based tool that constrained them to perform a conceptual analysis of the problems based on a hierarchy of principles and procedures that could be applied to solve them (Dufresne et al., 1996). This approach was motivated by research on expertise. The reader will recall that, when asked to state an approach to solving a problem, physicists generally discuss principles and procedures. Novices, in contrast, tend to discuss specific equations that could be used to manipulate variables given in the problem (Chi et al., 1981). When compared with a group of students who solved the same problems on their own, the students who used the computer to carry out the hierarchical analyses performed noticeably better in subsequent measures of expertise. For example, in problem solving, those who performed the hierarchical analyses outperformed those who did not, whether measured in terms of overall problem-solving performance, ability to arrive at the correct answer, or ability to apply appropriate principles to solve the problems. Furthermore, similar differences emerged in problem categorization: students who performed the hierarchical analyses considered principles (as opposed to surface features) more often in deciding whether or not two problems would be solved similarly. In both cases, the control group made significant improvements simply as a result of practice (time on task), but the experimental group showed more improvements for the same amount of training time (deliberate practice).

     Introductory physics courses have also been taught successfully with an approach for problem solving that begins with a qualitative hierarchical analysis of the problems (Leonard et al., 1996). Undergraduate engineering students were instructed to write qualitative strategies for solving problems before attempting to solve them (based on Chi et al., 1981). The strategies consisted of a coherent verbal description of how a problem could be solved and contained three components: the major principle to be applied; the justification for why the principle was applicable; and the procedures for applying the principle. That is, the what, why, and how of solving the problem were explicitly delineated. Compared with students who took a traditional course, students in the strategy-based course performed significantly better in their ability to categorize problems according to the relevant principles that could be applied to solve them.

Hierarchical structures are useful strategies for helping novices both recall knowledge and solve problems. For example, physics novices who had completed and received good grades in an introductory college physics course were trained to generate a problem analysis called a theoretical problem description (Heller and Reif, 1984). The analysis consists of describing force problems in terms of concepts, principles, and heuristics. With such an approach, novices substantially improved in their ability to solve problems, even though the type of theoretical problem description used in the study was not a natural one for novices. Novices untrained in the theoretical descriptions were generally unable to generate appropriate descriptions on their own–even given fairly routine problems. Skills, such as the ability to describe a problem in detail before attempting a solution, the ability to determine what relevant information should enter the analysis of a problem, and the ability to decide which procedures can be used to generate problem descriptions and analyses, are tacitly used by experts but rarely taught explicitly in physics courses.

Another approach helps students organize knowledge by imposing a hierarchical organization on the performance of different tasks in physics (Eylon and Reif, 1984). Students who received a particular physics argument that was organized in hierarchical form performed various recall and problem-solving tasks better than subjects who received the same argument non-hierarchically. Similarly, students who received a hierarchical organization of problem-solving strategies performed much better than subjects who received the same strategies organized non-hierarchically. Thus, helping students to organize their knowledge is as important as the knowledge itself, since knowledge organization is likely to affect students’ intellectual performance.

These examples demonstrate the importance of deliberate practice and of having a “coach” who provides feedback for ways of optimizing performance. If students had simply been given problems to solve on their own (an instructional practice used in all the sciences), it is highly unlikely that they would have spent time efficiently. Students might get stuck for minutes, or even hours, in attempting a solution to a problem and either give up or waste lots of time. We discussed ways in which learners profit from errors and that making mistakes is not always time wasted. However, it is not efficient if a student spends most of the problem-solving time rehearsing procedures that are not optimal for promoting skilled performance, such as finding and manipulating equations to solve the problem, rather than identifying the underlying principle and procedures that apply to the problem and then constructing the specific equations needed. In deliberate practice, a student works under a tutor (human or computer based) to rehearse appropriate practices that enhance performance. Through deliberate practice, computer-based tutoring environments have been designed that reduce the time it takes individuals to reach real-world performance criteria from 4 years to 25 hours.

   Before students can really learn new scientific concepts, they often need to re-conceptualize deeply rooted misconceptions that interfere with the learning. As reviewed above, people spend considerable time and effort constructing a view of the physical world through experiences and observations, and they may cling tenaciously to those views–however much they conflict with scientific concepts–because they help them explain phenomena and make predictions about the world (e.g., why a rock falls faster than a leaf).

     One instructional strategy, termed “bridging,” has been successful in helping students overcome persistent misconceptions (Brown, 1992; Brown and Clement, 1989; Clement, 1993). The bridging strategy attempts to bridge from students’ correct beliefs (called anchoring conceptions) to their misconceptions through a series of intermediate analogous situations. Starting with the anchoring intuition that a spring exerts an upward force on the book resting on it, the student might be asked if a book resting on the middle of a long, “springy” board supported at its two ends experiences an upward force from the board. The fact that the bent board looks as if it is serving the same function as the spring helps many students agree that both the spring and the board exert upward forces on the book. For a student who may not agree that the bent board exerts an upward force on the book, the instructor may ask a student to place her hand on top of a vertical spring and push down and to place her hand on the middle of the springy board and push down. She would then be asked if she experienced an upward force that resisted her push in both cases. Through this type of dynamic probing of students’ beliefs, and by helping them come up with ways to resolve conflicting views, students can be guided into constructing a coherent view that is applicable across a wide range of contexts.

Another effective strategy for helping students overcome persistent erroneous beliefs are interactive lecture demonstrations (Sokoloff and Thornton, 1997; Thornton and Sokoloff, 1997). This strategy, which has been used very effectively in large introductory college physics classes, begins with an introduction to a demonstration that the instructor is about to perform, such as a collision between two air carts on an air track, one a stationary light cart, the other a heavy cart moving toward the stationary cart. Each cart has an electronic “force probe” connected to it which displays on a large screen and in real-time the force acting on it during the collision. The teacher first asks the students to discuss the situation with their neighbors and then record a prediction as to whether one of the carts would exert a bigger force on the other during impact or whether the carts would exert equal forces.

The vast majority of students incorrectly predict that the heavier, moving cart exerts a larger force on the lighter, stationary cart. Again, this prediction seems quite reasonable based on experience–students know that a moving Mack truck colliding with a stationary Volkswagen beetle will result in much more damage done to the Volkswagen, and this is interpreted to mean that the Mack truck must have exerted a larger force on the Volkswagen. Yet, notwithstanding the major damage to the Volkswagen, Newton’s Third Law states that two interacting bodies exert equal and opposite forces on each other.

After the students make and record their predictions, the instructor performs the demonstration, and the students see on the screen that the force probes record forces of equal magnitude but oppositely directed during the collision. Several other situations are discussed in the same way: What if the two carts had been moving toward each other at the same speed? What if the situation is reversed so that the heavy cart is stationary and the light cart is moving toward it? Students make predictions and then see the actual forces between the carts displayed as they collide. In all cases, students see that the carts exert equal and opposite forces on each other, and with the help of a discussion moderated by the instructor, the students begin to build a consistent view of Newton’s Third Law that incorporates their observations and experiences.

Consistent with the research on providing feedback, there is other research that suggests that students’ witnessing the force displayed in real-time as the two carts collide helps them overcome their misconceptions; delays of as little as 20-30 minutes in displaying graphic data of an event occurring in real-time significantly inhibits the learning of the underlying concept (Brasell, 1987).

Both bridging and the interactive demonstration strategies have been shown to be effective at helping students permanently overcome misconceptions. This finding is a major breakthrough in teaching science, since so much research indicates that students often can parrot back correct answers on a test that might be erroneously interpreted as displaying the eradication of a misconception, but the same misconception often resurfaces when students are probed weeks or months later (see Mestre, 1994, for a review).

      One of the best examples of translating research into practice is Minstrell’s (1982, 1989, 1992) work with high school physics students. Minstrell uses many research-based instructional techniques (e.g., bridging, making students’ thinking visible, facilitating students’ ability to restructure their own knowledge) to teach physics for understanding. He does this through classroom discussions in which students construct understanding by making sense of physics concepts, with Minstrell playing a coaching role. The following quote exemplifies his innovative and effective instructional strategies (Minstrell, 1989:130-131):

Students’ initial ideas about mechanics are like strands of yarn, some unconnected, some loosely interwoven. The act of instruction can be viewed as helping the students unravel individual strands of belief, label them, and then weave them into a fabric of more complete understanding. An important point is that later understanding can be constructed, to a considerable extent, from earlier beliefs. Sometimes new strands of belief are introduced, but rarely is an earlier belief pulled out and replaced. Rather than denying the relevancy of a belief, teachers might do better by helping students differentiate their present ideas from and integrate them into conceptual beliefs more like those of scientists.

     Describing a lesson on force, Minstrell (1989:130-131) begins by introducing the topic in general terms:

Today we are going to try to explain some rather ordinary events that you might see any day. You will find that you already have many good ideas that will help explain those events. We will find that some of our ideas are similar to those of the scientist, but in other cases our ideas might be different. When we are finished with this unit, I expect that we will have a much clearer idea of how scientists explain those events, and I know that you will feel more comfortable about your explanations . . . A key idea we are going to use is the idea of force. What does the idea of force mean to you?

     Many views emerge from the ensuing classroom discussion, from the typical “push or pull” to descriptions that include sophisticated terms, such as energy and momentum. At some point Minstrell guides the discussion to a specific example: he drops a rock and asks students how the event can be explained using their ideas about force. He asks students to individually formulate their ideas and to draw a diagram showing the major forces on the rock as arrows, with labels to denote the cause of each force. A lengthy discussion follows in which students present their views, views that contain many irrelevant (e.g., nuclear forces) or fictitious forces (e.g., the spin of the earth, air). In his coaching, Minstrell asks students to justify their choices by asking questions, such as “How do you know?” “How did you decide?” “Why do you believe that?”

With this approach, Minstrell has been able to identify many erroneous beliefs of students that stand in the way of conceptual understanding. One example is the belief that only active agents (e.g., people) can exert forces, that passive agents (e.g., a table) cannot. Minstrell (1992) has developed a framework that helps both to make sense of students’ reasoning and to design instructional strategies. (For a related theoretical framework for classifying and explaining student reasoning, see the discussion of “phenomenological primitives” in DiSessa, 1988, 1993.) Minstrell describes identifiable pieces of students’ knowledge as “facets,” a facet being a convenient unit of thought, a piece of knowledge, or a strategy seemingly used by the student in addressing a particular situation. Facets may relate to conceptual knowledge (e.g., passive objects do not exert force), to strategic knowledge (e.g., average velocity can be determined by adding the initial and final velocities and dividing by two), or generic reasoning (e.g., the more the X, the more the Y). Identifying students’ facets, what cues them in different contexts, and how students use them in reasoning are all helpful in devising instructional strategies.

     One of the obstacles to instructional innovation in large introductory science courses at the college level is the sheer number of students who are taught at one time. How does an instructor provide an active learning experience, provide feedback, accommodate different learning styles, make students’ thinking visible, and provide scaffolding and tailored instruction to meet specific student needs when facing more than 100 students at a time? Classroom communication systems can help the instructor of a large class accomplish these objectives. One such system, called Classtalk, consists of both hardware and software that allows up to four students to share an input device (e.g., a fairly inexpensive graphing calculator) to “sign on” to a classroom communication network that permits the instructor to send questions for students to work on and permits students to enter answers through their input device. Answers can then be displayed anonymously in histogram form to the class, and a permanent record of each student’s response is recorded to help evaluate progress as well as the effectiveness of instruction.

     This technology has been used successfully at the University of Massachusetts-Amherst to teach physics to a range of students, from non-science majors to engineering and science majors (Dufresne et al., 1996; Wenk et al., 1997; Mestre et al., 1997). The technology creates an interactive learning environment in the lectures: students work collaboratively on conceptual questions, and the histogram of students’ answers is used as a visual springboard for classwide discussions when students defend the reasoning they used to arrive at their answers. This technology makes students’ thinking visible and promotes critical listening, evaluation, and argumentation in the class. The teacher is a coach, providing scaffolding where needed, tailoring “mini-lectures” to clear up points of confusion, or, if things are going well, simply moderating the discussion and allowing students to figure out things and reach consensus on their own. The technology is also a natural mechanism to support formative assessment during instruction, providing both the teacher and students with feedback on how well the class is grasping the concepts under study. The approach accommodates a wider variety of learning styles than is possible by lectures and helps to foster a community of learners focused on common objectives and goals.

    The examples above present some effective strategies for teaching and learning science for high school and college students. We drew some general principles of learning from these examples and stressed that the findings consistently point to the strong effect of knowledge structures on learning. These studies also emphasize the importance of class discussions for developing a language for talking about scientific ideas, for making students’ thinking explicit to the teacher and to the rest of the class, and for learning to develop a line of argumentation that uses what one has learned to solve problems and explain phenomena and observations.

     The question that immediately occurs is how to teach science to younger children or to students who are considered to be educationally “at risk.” One approach that has been especially useful in science teaching was developed with language-minority grade-school children: Chèche Konnen, which in Haitian Creole means search for knowledge (Rosebery et al., 1992). The approach stresses how discourse is a primary means for the search for knowledge and scientific sense-making. It also illustrates how scientific ideas are constructed. In this way it mirrors science, in the words of Nobel Laureate Sir Peter Medawar (1982:111):

Like other exploratory processes, [the scientific method] can be resolved into a dialogue between fact and fancy, the actual and the possible; between what could be true and what is in fact the case. The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about a Possible World–a story which we invent and criticize and modify as we go along, so that it ends by being, as nearly as we can make it, a story about real life.

     The Chèche Konnen approach to teaching began by creating “communities of scientific practice” in language-minority classrooms in a few Boston and Cambridge, MA public schools. “Curriculum” emerges in these classrooms from the students’ questions and beliefs and is shaped in ongoing interactions that include both the teacher and students. Students explore their own questions, much as we described above in Barb Johnson’s class. In addition, students design studies, collect information, analyze data and construct evidence, and they then debate the conclusions that they derive from their evidence. In effect, the students build and argue about theories.

Students constructed scientific understandings through an iterative process of theory building, criticism, and refinement based on their own questions, hypotheses, and data analysis activities. Question posing, theorizing, and argumentation formed the structure of the students’ scientific activity. Within this structure, students explored the implications of the theories they held, examined underlying assumptions, formulated and tested hypotheses, developed evidence, negotiated conflicts in belief and evidence, argued alternative interpretations, provided warrants for conclusions, and so forth. The process as a whole provided a richer, more scientifically grounded experience than the conventional focus on textbooks or laboratory demonstrations.

The emphasis on establishing communities of scientific practice builds on the fact that robust knowledge and understandings are socially constructed through talk, activity, and interaction around meaningful problems and tools (Vygotsky, 1978). The teacher guides and supports students as they explore problems and define questions that are of interest to them. A community of practice also provides direct cognitive and social support for the efforts of the group’s individual members. Students share the responsibility for thinking and doing: they distribute their intellectual activity so that the burden of managing the whole process does not fall to any one individual. In addition, a community of practice can be a powerful context for constructing scientific meanings. In challenging one another’s thoughts and beliefs, students must be explicit about their meanings; they must negotiate conflicts in belief or evidence; and they must share and synthesize their knowledge to achieve understanding (Brown and Palincsar, 1989; Inagaki and Hatano, 1987).

What do students learn from participating in a scientific sense-making community? Individual interviews with students before and after the water taste test investigation, first in September and again the following June, showed how the students’ knowledge and reasoning changed. In the interviews (conducted in Haitian Creole), the students were asked to think aloud about two open-ended real-world problems–pollution in the Boston Harbor and a sudden illness in an elementary school. The researchers were interested in changes in students’ conceptual knowledge about aquatic ecosystems and in students’ uses of hypotheses, experiments, and explanations to organize their reasoning (for a complete discussion, see Rosebery et al., 1992).

Conceptual Knowledge

Not surprisingly, the students knew more about water pollution and aquatic ecosystems in June than they did in September. They were also able to use this knowledge generatively. One student explained how she would clean the water in Boston Harbor (Rosebery et al., 1992:86).

Like you look for the things, take the garbage out of the water, you put a screen to block all the paper and stuff, then you clean the water; you put chemical products in it to clean the water, and you’d take all the microscopic life out. Chlorine and alum, you put in the water. They’d gather the little stuff, the little stuff would stick to the chemical products, and they would clean the water.

     Note that this explanation contains misconceptions. By confusing the cleaning of drinking water with the cleaning of sea water, the student suggests adding chemicals to take all microscopic life from the water (good for drinking water, but bad for the ecosystem of Boston Harbor). This example illustrates the difficulties in transferring knowledge appropriately from one context to another. Despite these shortcomings, it is clear that this student is starting on the path to scientific thinking, leaving behind the more superficial “I’d take all the bad stuff out of the water” type of explanation. It is also clear that by making the student’s thinking visible, the teacher is in an excellent position to refine her (and perhaps the classes) understanding.

     Striking changes appeared in students’ scientific reasoning. In September, there were three ways in which the students showed little familiarity with scientific forms of reasoning. First, the students did not understand the function of hypotheses or experiments in scientific inquiry. When asked for their ideas about what could be making the children sick, the students tended, with few exceptions, to respond with short, unelaborated, often untestable “hypotheses” that simply restated the phenomena described in the problem: “That’s a thing . . . . Ah, I could say a person, some person that gave them something . . . . Anything, like give poison to make his stomach hurt” (Rosebery et al., 1992:81).

     Second, the students conceptualized evidence as information they already knew, either through personal experience or second-hand sources, rather than data produced through experimentation or observation. When asked to generate an experiment to justify a hypothesis–“How would you find out?”–they typically offered declarations: “Because the garbage is a poison for them . . . . The garbage made the fish die” (Rosebery et al., 1992:78).

Third, the students interpreted an elicitation for an experiment–“How would you be sure?”–as a text comprehension question for which there was a “right” answer. They frequently responded with an explanation or assertion of knowledge and consistently marked their responses as explanatory (“because”): “Because fish don’t eat garbage. They eat plants under the water” (page 78).

In the June interviews, the students showed that they had become familiar with the function of hypotheses and experiments and with reasoning within larger explanatory frameworks. Elinor had developed a model of an integrated water system in which an action or event in one part of the system had consequences for other parts (Rosebery et al., 1992:87):

You can’t leave [the bad stuff] on the ground. If you leave it on the ground, the water that, the earth has water underground; it will still spoil the water underground. Or when it rains it will just take it and, when it rains, the water runs, it will take it and leave it in the river, in where the water goes in. Those things, poison things, you aren’t supposed to leave it on the ground.

     In June, the students no longer invoked anonymous agents, but put forward chains of hypotheses to explain phenomena, such as why children were getting sick (page 88):

Like, you could test what the kids ate and, like, test the water, too; it could be the water that isn’t good, that has microbes, which might have microscopic animals in it to make them sick.

     The June interviews also showed that students had begun to develop a sense of the function and form of experimentation. They no longer depended on personal experience as evidence, but proposed experiments to test specific hypotheses. In response to a question about sick fish, Laure clearly understands how to find a scientific answer (page 91):

I’d put a fish in fresh water and one fish in a water full of garbage. I’d give the fresh water fish food to eat and the other one in the nasty water, I’d give it food to eat to see if the fresh water, if the one in the fresh water would die with the food I gave it, if the one in the dirty water would die with the food I gave it. . . . I would give them the same food to see if the things they eat in the water and the things I give them now, which will make them healthy and which wouldn’t make them healthy.

        Conclusion

     Teaching and learning in science have been influenced very directly by research studies on expertise. The examples discussed in this chapter focus on two areas of science teaching: physics and junior high school biology. Several of the teaching strategies illustrated ways to help students think about the general principles or “big” ideas in physics before jumping to formulas and equations. Others illustrate ways to help students engage in deliberate practice and to monitor their progress.

Learning the strategies for scientific thinking have another objective: to develop thinking acumen needed to promote conceptual change. Often, the barrier to achieving insights to new solutions is rooted in a fundamental misconception about the subject matter. One strategy for helping students in physics begins with an “anchoring intuition” about a phenomenon and then gradually bridging it to related phenomena that are less intuitive to the student but involve the same physics principles. Another strategy involves the use of interactive lecture demonstrations to encourage students to make predictions, consider feedback, and then reconceptualize phenomena.

The example of Chèche Konnen demonstrates the power of a sense-making approach to science learning that builds on the knowledge that students bring with them to school from their home cultures, including their familiar discourse practices. Students learned to think, talk, and act scientifically, and their first and second languages mediated their learning in powerful ways. Using Haitian Creole, they designed their studies, interpreted data, and argued theories; using English, they collected data from their mainstream peers, read standards to interpret their scientific test results, reported their findings, and consulted with experts at the local water treatment facility.

      CONCLUSION

     Outstanding teaching requires teachers to have a deep understanding of the subject matter and its structure, as well as an equally thorough understanding of the kinds of teaching activities that help students understand the subject matter in order to be capable of asking probing questions.

Numerous studies demonstrate that the curriculum and its tools, including textbooks, need to be dissected and discussed in the larger contexts and framework of a discipline. In order to be able to provide such guidance, teachers themselves need a thorough understanding of the subject domain and the epistemology that guides the discipline (for history, see Wineburg and Wilson, 1988; for math and English, see Ball, 1993; Grossman et al., 1989; for science, see Rosebery et al., 1992).

The examples in this chapter illustrate the principles for the design of learning environments that were discussed: they are learner, knowledge, assessment, and community centered. They are learner centered in the sense that teachers build on the knowledge students bring to the learning situation. They are knowledge centered in the sense that the teachers attempt to help students develop an organized understanding of important concepts in each discipline. They are assessment centered in the sense that the teachers attempt to make students’ thinking visible so that ideas can be discussed and clarified, such as having students (1) present their arguments in debates, (2) discuss their solutions to problems at a qualitative level, and (3) make predictions about various phenomena. They are community centered in the sense that the teachers establish classroom norms that learning with understanding is valued and students feel free to explore what they do not understand.

These examples illustrate the importance of pedagogical content knowledge to guide teachers. Expert teachers have a firm understanding of their respective disciplines, knowledge of the conceptual barriers that students face in learning about the discipline, and knowledge of effective strategies for working with students. Teachers’ knowledge of their disciplines provides a cognitive roadmap to guide their assignments to students, to gauge student progress, and to support the questions students ask. The teachers focus on understanding rather than memorization and routine procedures to follow, and they engage students in activities that help students reflect on their own learning and understanding.

The interplay between content knowledge and pedagogical knowledge illustrated in this chapter contradicts a commonly held misconception about teaching–which effective teaching consists of a set of general teaching strategies that apply to all content areas. This notion is erroneous, just as is the idea that expertise in a discipline is a general set of problem-solving skills that lack a content knowledge base to support them.

The outcomes of new approaches to teaching as reflected in the results of summative assessments are encouraging. Studies of students’ discussions in classrooms indicate that they learn to use the tools of systematic inquiry to think historically, mathematically, and scientifically. How these kinds of teaching strategies reveal themselves on typical standardized tests is another matter. In some cases there is evidence that teaching for understanding can increase scores on standardized measures (e.g., Resnick et al., 1991); in other cases, scores on standardized tests are unaffected, but the students show sizable advantages on assessments that are sensitive to their comprehension and understanding rather than reflecting sheer memorization (e.g., Carpenter et al., 1996; Secules et al., 1997).

It is noteworthy that none of the teachers discussed in this chapter felt that he or she was finished learning. Many discussed their work as involving a lifelong and continuing struggle to understand and improve. What opportunities do teachers have to improve their practice? The next chapter explores teachers’ chances to improve and advance their knowledge in order to function as effective professionals.

EFFECTIVE LEARNING AND TEACHING

Although Science for All Americans emphasizes what students should learn, it also recognizes that how science is taught is equally important. In planning instruction, effective teachers draw on a growing body of research knowledge about the nature of learning and on craft knowledge about teaching that has stood the test of time. Typically, they consider the special characteristics of the material to be learned, the background of their students, and the conditions under which the teaching and learning are to take place.

This chapter presents—nonsystematically and with no claim of completeness—some principles of learning and teaching that characterize the approach of such teachers. Many of those principles apply to learning and teaching in general, but clearly some are especially important in science, mathematics, and technology education. For convenience, learning and teaching are presented here in separate sections, even though they are closely interrelated.

PRINCIPLES OF LEARNING

Learning Is Not Necessarily an Outcome of Teaching

Cognitive research is revealing that even with what is taken to be good instruction, many students, including academically talented ones, understand less than we think they do. With determination, students taking an examination are commonly able to identify what they have been told or what they have read; careful probing, however, often shows that their understanding is limited or distorted, if not altogether wrong. This finding suggests that parsimony is essential in setting out educational goals: Schools should pick the most important concepts and skills to emphasize so that they can concentrate on the quality of understanding rather than on the quantity of information presented.

What Students Learn Is Influenced by Their Existing Ideas

People have to construct their own meaning regardless of how clearly teachers or books tell them things. Mostly, a person does this by connecting new information and concepts to what he or she already believes. Concepts—the essential units of human thought—that do not have multiple links with how a student thinks about the world are not likely to be remembered or useful. Or, if they do remain in memory, they will be tucked away in a drawer labeled, say, “biology course, 1995,” and will not be available to affect thoughts about any other aspect of the world. Concepts are learned best when they are encountered in a variety of contexts and expressed in a variety of ways, for that ensures that there are more opportunities for them to become imbedded in a student’s knowledge system.

But effective learning often requires more than just making multiple connections of new ideas to old ones; it sometimes requires that people restructure their thinking radically. That is, to incorporate some new idea, learners must change the connections among the things they already know, or even discard some long-held beliefs about the world. The alternatives to the necessary restructuring are to distort the new information to fit their old ideas or to reject the new information entirely. Students come to school with their own ideas, some correct and some not, about almost every topic they are likely to encounter. If their intuition and misconceptions are ignored or dismissed out of hand, their original beliefs are likely to win out in the long run, even though they may give the test answers their teachers want. Mere contradiction is not sufficient; students must be encouraged to develop new views by seeing how such views help them make better sense of the world.

Progression in Learning Is Usually From the Concrete to the Abstract

Young people can learn most readily about things that are tangible and directly accessible to their senses—visual, auditory, tactile, and kinesthetic. With experience, they grow in their ability to understand abstract concepts, manipulate symbols, reason logically, and generalize. These skills develop slowly, however, and the dependence of most people on concrete examples of new ideas persists throughout life. Concrete experiences are most effective in learning when they occur in the context of some relevant conceptual structure. The difficulties many students have in grasping abstractions are often masked by their ability to remember and recite technical terms that they do not understand. As a result, teachers—from kindergarten through college—sometimes overestimate the ability of their students to handle abstractions, and they take the students’ use of the right words as evidence of understanding.

People Learn to Do Well Only What They Practice Doing

If students are expected to apply ideas in novel situations, then they must practice applying them in novel situations. If they practice only calculating answers to predictable exercises or unrealistic “word problems,” then that is all they are likely to learn. Similarly, students cannot learn to think critically, analyze information, communicate scientific ideas, make logical arguments, work as part of a team, and acquire other desirable skills unless they are permitted and encouraged to do those things over and over in many contexts.

Effective Learning by Students Requires Feedback

The mere repetition of tasks by students—whether manual or intellectual—is unlikely to lead to improved skills or keener insights. Learning often takes place best when students have opportunities to express ideas and get feedback from their peers. But for feedback to be most helpful to learners, it must consist of more than the provision of correct answers. Feedback ought to be analytical, to be suggestive, and to come at a time when students are interested in it. And then there must be time for students to reflect on the feedback they receive, to make adjustments and to try again—a requirement that is neglected, it is worth noting, by most examinations—especially finals.

Expectations Affect Performance

Students respond to their own expectations of what they can and cannot learn. If they believe they are able to learn something, whether solving equations or riding a bicycle, they usually make headway. But when they lack confidence, learning eludes them. Students grow in self-confidence as they experience success in learning, just as they lose confidence in the face of repeated failure. Thus, teachers need to provide students with challenging but attainable learning tasks and help them succeed.

What is more, students are quick to pick up the expectations of success or failure that others have for them. The positive and negative expectations shown by parents, counselors, principals, peers, and—more generally—by the news media affect students’ expectations and hence their learning behavior. When, for instance, a teacher signals his or her lack of confidence in the ability of students to understand certain subjects, the students may lose confidence in their ability and may perform more poorly than they otherwise might. If this apparent failure reinforces the teacher’s original judgment, a disheartening spiral of decreasing confidence and performance can result.

TEACHING SCIENCE, MATHEMATICS, AND TECHNOLOGY

Teaching Should Be Consistent With the Nature of Scientific Inquiry

Science, mathematics, and technology are defined as much by what they do and how they do it as they are by the results they achieve. To understand them as ways of thinking and doing, as well as bodies of knowledge, requires that students have some experience with the kinds of thought and action that are typical of those fields. Teachers, therefore, should do the following:

Start With Questions about Nature

Sound teaching usually begins with questions and phenomena that are interesting and familiar to students, not with abstractions or phenomena outside their range of perception, understanding, or knowledge. Students need to get acquainted with the things around them—including devices, organisms, materials, shapes, and numbers—and to observe them, collect them, handle them, describe them, become puzzled by them, ask questions about them, argue about them, and then to try to find answers to their questions.

Engage Students Actively

Students need to have many and varied opportunities for collecting, sorting and cataloging; observing, note taking and sketching; interviewing, polling, and surveying; and using hand lenses, microscopes, thermometers, cameras, and other common instruments. They should dissect; measure, count, graph, and compute; explore the chemical properties of common substances; plant and cultivate; and systematically observe the social behavior of humans and other animals. Among these activities, none is more important than measurement, in that figuring out what to measure, what instruments to use, how to check the correctness of measurements, and how to configure and make sense out of the results are at the heart of much of science and engineering.

Concentrate on the Collection and Use of Evidence

Students should be given problems—at levels appropriate to their maturity—that require them to decide what evidence is relevant and to offer their own interpretations of what the evidence means. This puts a premium, just as science does, on careful observation and thoughtful analysis. Students need guidance, encouragement, and practice in collecting, sorting, and analyzing evidence, and in building arguments based on it. However, if such activities are not to be destructively boring, they must lead to some intellectually satisfying payoff that students care about.

Provide Historical Perspectives

During their school years, students should encounter many scientific ideas presented in historical context. It matters less which particular episodes teachers select (in addition to the few key episodes presented in Chapter 10) than that the selection represent the scope and diversity of the scientific enterprise. Students can develop a sense of how science really happens by learning something of the growth of scientific ideas, of the twists and turns on the way to our current understanding of such ideas, of the roles played by different investigators and commentators, and of the interplay between evidence and theory over time.

History is important for the effective teaching of science, mathematics, and technology also because it can lead to social perspectives—the influence of society on the development of science and technology, and the impact of science and technology on society. It is important, for example, for students to become aware that women and minorities have made significant contributions in spite of the barriers put in their way by society; that the roots of science, mathematics, and technology go back to the early Egyptian, Greek, Arabic, and Chinese cultures; and that scientists bring to their work the values and prejudices of the cultures in which they live.

Insist on Clear Expression

Effective oral and written communication is so important in every facet of life that teachers of every subject and at every level should place a high priority on it for all students. In addition, science teachers should emphasize clear expression, because the role of evidence and the unambiguous replication of evidence cannot be understood without some struggle to express one’s own procedures, findings, and ideas rigorously, and to decode the accounts of others.

Use a Team Approach

The collaborative nature of scientific and technological work should be strongly reinforced by frequent group activity in the classroom. Scientists and engineers work mostly in groups and less often as isolated investigators. Similarly, students should gain experience sharing responsibility for learning with each other. In the process of coming to common understandings, students in a group must frequently inform each other about procedures and meanings, argue over findings, and assess how the task is progressing. In the context of team responsibility, feedback and communication become more realistic and of a character very different from the usual individualistic textbook-homework-recitation approach.

Do Not Separate Knowing From Finding Out

In science, conclusions and the methods that lead to them are tightly coupled. The nature of inquiry depends on what is being investigated, and what is learned depends on the methods used. Science teaching that attempts solely to impart to students the accumulated knowledge of a field leads to very little understanding and certainly not to the development of intellectual independence and facility. But then, to teach scientific reasoning as a set of procedures separate from any particular substance—”the scientific method,” for instance—is equally futile. Science teachers should help students to acquire both scientific knowledge of the world and scientific habits of mind at the same time.

Deemphasize the Memorization of Technical Vocabulary

Understanding rather than vocabulary should be the main purpose of science teaching. However, unambiguous terminology is also important in scientific communication and—ultimately—for understanding. Some technical terms are therefore helpful for everyone, but the number of essential ones is relatively small. If teachers introduce technical terms only as needed to clarify thinking and promote effective communication, then students will gradually build a functional vocabulary that will survive beyond the next test. For teachers to concentrate on vocabulary, however, is to detract from science as a process, to put learning for understanding in jeopardy, and to risk being misled about what students have learned.

Science Teaching Should Reflect Scientific Values

Science is more than a body of knowledge and a way of accumulating and validating that knowledge. It is also a social activity that incorporates certain human values. Holding curiosity, creativity, imagination, and beauty in high esteem is certainly not confined to science, mathematics, and engineering—any more than skepticism and a distaste for dogmatism are. However, they are all highly characteristic of the scientific endeavor. In learning science, students should encounter such values as part of their experience, not as empty claims. This suggests that teachers should strive to do the following:

Welcome Curiosity

Science, mathematics, and technology do not create curiosity. They accept it, foster it, incorporate it, reward it, and discipline it—and so does good science teaching. Thus, science teachers should encourage students to raise questions about the material being studied, help them learn to frame their questions clearly enough to begin to search for answers, suggest to them productive ways for finding answers, and reward those who raise and then pursue unusual but relevant questions. In the science classroom, wondering should be as highly valued as knowing.

Reward Creativity

Scientists, mathematicians, and engineers prize the creative use of imagination. The science classroom ought to be a place where creativity and invention—as qualities distinct from academic excellence—are recognized and encouraged. Indeed, teachers can express their own creativity by inventing activities in which students’ creativity and imagination will pay off.

Encourage a Spirit of Healthy Questioning

Science, mathematics, and engineering prosper because of the institutionalized skepticism of their practitioners. Their central tenet is that one’s evidence, logic, and claims will be questioned, and one’s experiments will be subjected to replication. In science classrooms, it should be the normal practice for teachers to raise such questions as: How do we know? What is the evidence? What is the argument that interprets the evidence? Are there alternative explanations or other ways of solving the problem that could be better? The aim should be to get students into the habit of posing such questions and framing answers.

Avoid Dogmatism

Students should experience science as a process for extending understanding, not as unalterable truth. This means that teachers must take care not to convey the impression that they themselves or the textbooks are absolute authorities whose conclusions are always correct. By dealing with the credibility of scientific claims, the overturn of accepted scientific beliefs, and what to make out of disagreements among scientists, science teachers can help students to balance the necessity for accepting a great deal of science on faith against the importance of keeping an open mind.

Promote Aesthetic Responses

Many people regard science as cold and uninteresting. However, a scientific understanding of, say, the formation of stars, the blue of the sky, or the construction of the human heart need not displace the romantic and spiritual meanings of such phenomena. Moreover, scientific knowledge makes additional aesthetic responses possible—such as to the diffracted pattern of street lights seen through a curtain, the pulse of life in a microscopic organism, the cantilevered sweep of a bridge, the efficiency of combustion in living cells, the history in a rock or a tree, an elegant mathematical proof. Teachers of science, mathematics, and technology should establish a learning environment in which students are able to broaden and deepen their response to the beauty of ideas, methods, tools, structures, objects, and living organisms.

Science Teaching Should Aim to Counteract Learning Anxieties

Teachers should recognize that for many students, the learning of mathematics and science involves feelings of severe anxiety and fear of failure. No doubt this results partly from what is taught and the way it is taught, and partly from attitudes picked up incidentally very early in schooling from parents and teachers who are themselves ill at ease with science and mathematics. Far from dismissing math and science anxiety as groundless, though, teachers should assure students that they understand the problem and will work with them to overcome it. Teachers can take such measures as the following:

Build on Success

Teachers should make sure that students have some sense of success in learning science and mathematics, and they should deemphasize getting all the right answers as being the main criterion of success. After all, science itself, as Alfred North Whitehead said, is never quite right. Understanding anything is never absolute, and it takes many forms. Accordingly, teachers should strive to make all students—particularly the less-confident ones—aware of their progress and should encourage them to continue studying.

Provide Abundant Experience in Using Tools

Many students are fearful of using laboratory instruments and other tools. This fear may result primarily from the lack of opportunity many of them have to become familiar with tools in safe circumstances. Girls in particular suffer from the mistaken notion that boys are naturally more adept at using tools. Starting in the earliest grades, all students should gradually gain familiarity with tools and the proper use of tools. By the time they finish school, all students should have had supervised experience with common hand tools, soldering irons, electrical meters, drafting tools, optical and sound equipment, calculators, and computers.

Support the Roles of Girls and Minorities in Science

Because the scientific and engineering professions have been predominantly male and white, female and minority students could easily get the impression that these fields are beyond them or are otherwise unsuited to them. This debilitating perception—all too often reinforced by the environment outside the school—will persist unless teachers actively work to turn it around. Teachers should select learning materials that illustrate the contributions of women and minorities, bring in role models, and make it clear to female and minority students that they are expected to study the same subjects at the same level as everyone else and to perform as well.

Emphasize Group Learning

A group approach has motivational value apart from the need to use team learning (as noted earlier) to promote an understanding of how science and engineering work. Overemphasis on competition among students for high grades distorts what ought to be the prime motive for studying science: to find things out. Competition among students in the science classroom may also result in many of them developing a dislike of science and losing their confidence in their ability to learn science. Group approaches, the norm in science, have many advantages in education; for instance, they help youngsters see that everyone can contribute to the attainment of common goals and that progress does not depend on everyone’s having the same abilities.

Science Teaching Should Extend Beyond the School

Children learn from their parents, siblings, other relatives, peers, and adult authority figures, as well as from teachers. They learn from movies, television, radio, records, trade books and magazines, and home computers, and from going to museums and zoos, parties, club meetings, rock concerts, and sports events, as well as from schoolbooks and the school environment in general. Science teachers should exploit the rich resources of the larger community and involve parents and other concerned adults in useful ways. It is also important for teachers to recognize that some of what their students learn informally is wrong, incomplete, poorly understood, or misunderstood, but that formal education can help students to restructure that knowledge and acquire new knowledge.

Teaching Should Take Its Time

In learning science, students need time for exploring, for making observations, for taking wrong turns, for testing ideas, for doing things over again; time for building things, calibrating instruments, collecting things, constructing physical and mathematical models for testing ideas; time for learning whatever mathematics, technology, and science they may need to deal with the questions at hand; time for asking around, reading, and arguing; time for wrestling with unfamiliar and counterintuitive ideas and for coming to see the advantage in thinking in a different way. Moreover, any topic in science, mathematics, or technology that is taught only in a single lesson or unit is unlikely to leave a trace by the end of schooling. To take hold and mature, concepts must not just be presented to students from time to time but must be offered to them periodically in different contexts and at increasing levels of sophistication.

 

 

 

“Effective teaching goes beyond the mere transmission of subject matter. It involves gaining the students’ attention and convincing them of the importance of what is being taught and learned. Such teaching, communicates both information and concepts as well as develops powers of analysis, synthesis, judgment, and evaluation, all in the context of considered values. When teaching has truly succeeded, students leave with an ability to learn, question, evaluate and commit on their own. Enthusiastic teachers convey to students that they are confident, enjoy what they are doing, and they trust and respect students, and that the subject they teach is valuable and enjoyable (Carusso, 1982). Effective teachers are also believed by their students to be credible and worthy of trust (Rosnow & Robinson, 1967).”

The Effective Teaching Methodology Unit was set up for this very purpose of promoting excellence in teaching and learning in MMU. It aims to improve the academics’ pedagogical and andragogical skills. It aims to maximize teacher effectiveness by providing relevant trainings and workshops in order for academics to be guides in learning motivators, organizers assessors, evaluators etc. An induction program that focuses on enhancing pedagogical skills of academics is incorporated as one of the trainings.

 

 

 

Effective Teaching

One of the most important goals of The Ohio State University is to offer effective instruction to the students who study here. The university strives to recruit the best faculty and teaching associates possible and to support them in their teaching, research, and service endeavors. As part of the support for teaching, this handbook provides an overview of some basic information on instructional strategies. To situate this information within the general context of effective teaching, this chapter discusses what is meant by effective teaching, how teachers can continue to develop their instructional strengths through seeking and using feedback and how, given the pressures on instructors to perform well in several roles, they can “balance it all.”

 

Traits of Effective Teachers

 

 

Although many people believe that good teaching is impossible to define in any general way, a large body of research suggests that certain characteristics are consistently associated with good college teaching as viewed by students, other teachers, and administrators. In a study of winners of the Alumni Distinguished Teaching Award at Ohio State (Ebro, 1977), observation of classes identified the following characteristics of effective teaching, which strongly parallel those found in other studies:

The teachers got right down to business. They began class promptly and were well organized.

They taught at an appropriately fast pace, but stopped regularly to check student comprehension and engagement.

They used a variety of instructional strategies rather than lecture alone.

They focused on the topic and their instructional objectives and did not get sidetracked.

Their explanations were clear.

They used humor that was in keeping with their individual styles.

They practiced good classroom management techniques, holding the attention and respect of the group.

They interacted with students by providing immediate answers to questions or comments and corrective feedback when needed. They praised student answers and used probing questions to extend the answers.

They provided a warm classroom climate by allowing students to speak freely and by including personal humor or other attempts to relate to students as people.

They used nonverbal behavior, such as gestures, walking around, and eye contact, to reinforce their comments.

Joseph Lowman (1996) describes two main dimensions of effective college teaching that emerge in his studies: intellectual excitement (enthusiasm, knowledge, inspiration, humor, interesting viewpoint, clarity, and organization) and interpersonal concern/effective motivation (concern, caring, availability, friendliness, accessibility, helpfulness, encouragement, challenge). Other studies (see, for example, Chickering and Gamson, 1991) consistently identify knowledge of subject matter, organizational skills, enthusiasm, clarity, and interpersonal skills as marks of the effective teacher.

The amount of agreement across studies suggests that the characteristics of good teaching are not mysterious or extremely discipline-specific. They can, and have been, identified by researchers, students, and professionals alike.

Inspection of these characteristics fails to support another commonly held belief about teaching:

“Good teachers are born, not made.” While certain characteristics, such as humor and interpersonal skills, seem to come easily to some people and not others, people are not born with knowledge of a given discipline or competency in the use of instructional strategies. Furthermore, those who exhibit these qualities most consistently state that they work hard at attaining them and are very conscious of their actions and their effects.

These highly conscious teachers are examples of what Donald Schön (1983) has termed the “reflective practitioner,” the professional who acquires expertise by learning in the action environment. In a study of Ohio State faculty

(Chism, 1988), a model of faculty growth in teaching emerged that suggested that effective teachers develop by maximizing what they learn through experience. They engage in cycles of learning during which they try a practice, observe its effects, and decide how and when they will use a similar practice. The process is often carried on without a great deal of conscious attention and rather unsystematically by most teachers. What distinguishes those who learn best, however, is the very level of conscious reflection and the quality of information they bring to bear in determining the effects of a practice in a particular context. The best teachers know not only what they are doing, but why it is working and why it is likely to work in one kind of environment and not in another.

Although they may have some natural personality characteristics that support their success, they also work very hard at their teaching and continually try to improve.

 

 

Teaching Styles

 

A number of writers have observed differences in style among teachers. They classify them according to a number of dimensions that represent how the teachers approach their students, the ways in which they think learning takes place, and personal strengths and preferences. Lowman (1996), for example, observes that exemplary college teachers “appear to be those who are highly proficient in either one of two fundamental sets of skills: the ability to offer presentations in clearly organized and interesting ways [intellectual excitement] or to relate to students in ways that communicate positive regard and motivate them to work hard to meet academic challenges [interpersonal rapport]. All are probably at least completely competent in both sets of skills but outstanding in one or, occasionally, even both of them” (p. 38). Grasha (1996) delineates five teaching styles: Expert—is concerned with transmitting information from an expert status; challenges students to enhance their competence.

Formal Authority—is concerned with the acceptable ways to do things and providing students with the structure they need to learn

Personal Model—believes in teaching by personal example; oversees and guides students to emulate

Facilitator—emphasizes the personal nature of teacher-student interactions; guides students toward developing their capacity for independent action

Delegator—is concerned with developing students’ capacity to function autonomously; encourages independent projects

Grasha advocates an “integrated model” of teaching and learning styles, recognizing that individual teachers will naturally exhibit different styles, but stressing that teachers must cultivate certain styles so that they can use approaches that are appropriate to the instructional situations and kind of learners they encounter. For example, he observes that a blend of the Expert-Formal

Authority styles works best with learners who are dependent and less capable with the content.

Grasha advocates that teachers reflect on their stylistic approaches and make conscious decisions about these. His book, Teaching with Style, provides many exercises for faculty to use in thinking about styles of teaching.

 

Starting Well and Developing Teaching Skills

 

After studying new faculty at different institutions over several years, Robert Boice (1991, 1992) identified several characteristics of new faculty members he calls “quick starters,” those who adjust easily and make steady progress in their work. According to Boice, quick starters:

are concerned about students’ active involvement in the learning process

avoid feelings of isolation by developing social and professional networks with colleagues and others

seek advice on teaching from colleagues and consultants

avoid being critical and negative about under graduate students

learn to balance time across teaching, research, and service

are highly energetic, curious, and humorous

Eison (1990) stresses the importance of confidence for new teachers. Confidence is built upon good planning, clear goals, and a cultivation of relaxation and self-esteem. Eison advises new teachers to avoid perfectionism, to recognize their limitations, and to view admitting that they do not have all the answers as scholarly, rather than a sign of failure.

Sustaining growth in teaching involves continuing to learn. Chism (1993), using a model of teaching development rooted in experiential learning, suggests that experienced teachers can avoid burnout and continue to improve through:

stimulating their own thinking by taking advantage of opportunities to learn new approaches to teaching through reading, attending workshops and conferences, observing colleagues, and joining book groups or seminars on teaching topics

relying on colleagues and teaching consultants to try new things and to provide them with support as they experiment with teaching

obtaining regular, systematic feedback on their teaching

reflecting on their teaching continually and making changes based on those reflections

Stephen Brookfield, in Becoming a Critically

Reflective Teacher (1995), offers a variety of practical and insightful methods for promoting reflection on one’s teaching. He stresses understanding how students learn as a way to approach teaching improvement. Chapter 9 will highlight additional opportunitiesfor growth and development. Strategies for documenting teaching performance will also be discussed.

 

The Role and Types of Feedback

 

A key element in the process of teacher development is feedback. As with all learning, getting information on one’s actions is essential to continuing improvement. Most teachers get feedback on their teaching by scanning faces in class for signs of interest or confusion. While these are important strategies, they are highly inferential. The most effective teachers employ more systematic ways of obtaining feedback. Several ways are described below.

Written Evaluations from Students

There are a variety of ways in which instructors can obtain written information on their teaching from students. They may use one of several standard teaching evaluation forms with rating items that have been tested for their validity and reliability. Since the items on these forms are often very global and students frequently are asked to provide a rating without an explanation, standard forms serve mainly as gross performance indicators. They can alert instructors to areas that differ from average ratings.

The Student Evaluation of Instruction (SEI)

One student rating form that is available at Ohio State is the Student Evaluation of Instruction (SEI). A 10-item form, the SEI is designed primarily to monitor teaching performance for personnel decision-making processes. The items tap into global ratings of instruction, such as “The subject matter of this course was well organized,” “The course was intellectually stimulating,” and “The instructor was generally interested in teaching.” Forms are sent automatically to all instructors, who may use them and return them to the University Registrar for tabulation, using a process designed to preserve confidentiality and validity. Instructors then receive reports that display their scores, their college’s or schools mean scores, and university mean scores for all items, along with interpretive graphs.

Feedback on Your Instruction (FYI)

A second optional method for collecting student feedback is the FYI. This is a web-based tool that instructors can use anytime to generate customized questionnaires containing items that solicit student opinion about particular things that the instructor wishes to check. It can be used for early or final feedback, depending on the instructor’s preferences. It should not be used for documenting teaching effectiveness since it is intended specifically for teaching and course improvement.

 

Discussion Mapping

Instructors often wonder why some class discussions are more productive than others or how they can better keep discussions on track. The discussion mapping technique can help answer these and other questions regarding class discussions. This technique leaves the instructor free to continue his or her role as facilitator while a colleague or teaching consultant observes various aspects of the discussion, including (a) how participation is distributed (Are there patterns associated with age, gender, or cultural differences?); (b) the nature of teacher comments (Are they supportive, argumentative, topical, or discursive?); (c) the listening skills of students; (d) how content is addressed (e.g., Do students concentrate on theoretical or practical implications? When appropriate do they engage in synthesis, analysis, and evaluation techniques?); and (e) the role of the facilitator (e.g., Does the facilitator mainly guide the discussion, monitor participation, or handle problems that arise?).Discussion mapping services are available throughthe Office of Faculty and TA Development.

In-Class Observation

Inviting a colleague or teaching consultant from Faculty and TA Development to observe class is yet another way in which instructors can receive helpful feedback on teaching. It is useful to try to identify in advance of the observation some specific things that the observer should be noting. For example, an instructor concerned about whether he or she creates enough opportunities for participation might ask the observer to pay close attention to this question as the class is observed. Depending on the particular focus of the observation, observers may use a pre-established rating or frequency count form for recording information or they may use a narrative format. The more skilled the observer, the better the feedback the instructor is likely to receive. Observation is also improved if multiple observations are used to establish a representative information base and if multiple observers are used to corroborate findings. Following an observation, it is important for the instructor and observer to meet to exchange information and to discuss specific ways for improving the instruction that was observed. Specific ideas for classroom observation are in Peer Review of Teaching: A Sourcebook (Chism, 1999).

Videotaping

Videotapes recorded either in the actual class setting or in a simulated environment, are a very powerful means of feedback for assessing presentational skills. The videotape can be analyzed by the instructor with or without assistance from a consultant or colleague to explore a variety of teaching skills ranging from nonverbal behavior, voice tone, and diction to clarity of presentation, classroom management, and organizational quality. Often, viewing one provides an immediate message that creates a strong awareness of one’s strengths and weaknesses as a teacher. Videotaping only services are available through Classroom Services (see Appendix). Videotaping and analysis are available through Faculty and TA Development.

These services are free of charge.

Class Interviews

Usually conducted by a person other than the instructor, class interviews can serve as another good source of feedback for the improvement of teaching. According to a procedure described as a Small Group Instructional Diagnosis (SGID) by Joseph Clark, a former instructional developer at the University of Washington, the interview is conducted by a teaching consultant who works with students in groups to answer three questions: What do you like best about this course? What do you like least? And what suggestions do you have for the instructor? The consultant tries to probe when there are areas of uncertainty or disagreement and tries to get the class to arrive at a consensus on each topic which is brought up. Following the class, the consultant reports back to the instructor and the two discuss relative teaching strengths identified and implications for change. Other ways of conducting class interviews are also available to instructors who might want to identify some specific areas of concern or might want a student or colleague to conduct the interview. Instructors may also want to interview specific students themselves to get feedback. Consultants at Faculty and TA Development are available to conduct class interviews at the request of the instructor.

 

Syllabus and Materials Review

When instructors would like information and opinions about the goals of the course, the way in which it is structured, the appropriateness of the activities and examinations, and the accuracy and quality of the printed materials that are distributed, they can ask colleagues who have knowledge of the discipline to review course documents. While students or a teaching consultant may offer some feedback on examination items or the clarity of explanations in printed notes, often the best judge of content accuracy will be the colleague who has disciplinary expertise. A review of materials is followed by a conversation during which the reviewer provides feedback to the instructor. Specific ideas for reviewing syllabi or course materials are in Chism (1999).

Students’ Exams, Written Work, and Other Products

Although instructors generally keep a careful record of grades, very few devote a lot of attention   results. In order to learn more about the effects of specific teaching practices, instructors can do such things as examine a set of graded papers for common error patterns (see the section “Procedures for Computing Difficulty and Discrimination Indexes”, talk with students about how prepared they felt for a given examination (individually or in the form of a “minute paper,” or look to see if certain key concepts or skills they tried to convey are reflected in the students’ tests, papers, or other work.

Classroom Research

Instructors with particular questions related to student learning or teaching strategies can use the classroom as a natural laboratory for descriptive or experimental studies. Often, these may be very informal, such as to assign one paper with a given format and to assign another with a different format to see which format is associated with better achievement of objectives. Studies may involve such things as having students take learning style inventories so that the instructor knows more about the range of learning preferences in the class. The studies must be conducted in a way which does not jeopardize student learning, but which can provide solid information for making good teaching choices. Classroom research is a more systematic way of conducting the ongoing inquiry into teaching practice that is so essential to teacher growth. For a more in-depth look at the subject, see Classroom Research: Implementing the Scholarship of Teaching by Cross and Steadman (1996).

Balancing It All

The challenging task of being the kind of teacher who continually strives to improve instructional technique is faced by instructors who are simultaneously conducting their own studies or research program as well as engaging in service activities and maintaining a personal life. Often, instructors feel caught among all these roles and have the sense that they are not performing up to their personal standards. Severe stress can result. Experts in the field suggest several ways in which stress can be controlled. Psychology professor Anthony Grasha (1987) lists the following solutions:

1. be more assertive about refusing requests. He suggests that instructors avoid feeling that they must please others at personal expense to themselves. He notes that it is not necessary to provide a reason for refusing requests.

2. Set priorities. Grasha advises that instructors look at their calendars before each week begins with the following questions in mind: (a) Does the task have to be completed as scheduled?, (b)

Is the task something that can be delegated to others?, (c) Can completion of the task be delayed for a period of time?, and (d) Is it really necessary to do this task at all? After using the questions to eliminate some tasks, the instructor should schedule social and recreational time as well as uninterrupted “work” time for writing or extended projects and take these “appointments” as seriously as scheduled meetings.

3. Use quick relaxation techniques. Grasha suggests that tensing the body for a count of 10 and then breathing deeply in and out to a count of four for a period of three to five minutes is especially effective after a tension-producing event. He also suggests that writing, such as keeping a personal journal or writing angry letters that are not mailed, can help during extremely stressful periods.

4. Think Positively. Citing William James, Grasha points out that stress often occurs when people feel that they cannot perform to self-expectations. He advises that people reevaluate their expectations, seek small victories, focus on achievements rather than deficiencies, and seek social support.

Summary

Teaching is, as a recent report (Higher Education Research Program, 1989) terms it, “the business of the business,” the main purpose for institutions of higher education. Instructors who take this responsibility seriously strive continually to be more reflective about their practice and to improve as their careers progress. Good teaching involves more than the simple transmission of information and includes motivating students and creating a positive classroom environment as well. When coupled with the many other responsibilities a university instructor has, however, efforts to teach well can lead to stress and burnout. Maintaining realistic expectations and exercising time management are ways in which instructors can help avoid unproductive stress.

 

h1

SPECIFICATIONS ABOUT BLOOM’S TAXONOMY

February 23, 2008

Major Categories in the Taxonomy of Educational Objectives

Categories in the Cognitive Domain: (with Outcome-Illustrating Verbs)

1.      Knowledge of terminology; specific facts; ways and means of dealing with specifics (conventions, trends and sequences, classifications and categories, criteria, methodology); universals and abstractions in a field (principles and generalizations, theories and structures):
Knowledge is (here) defined as the remembering (recalling) of appropriate, previously learned information.

o        defines; describes; enumerates; identifies; labels; lists; matches; names; reads; records; reproduces; selects; states; views.

2.      Comprehension: Grasping (understanding) the meaning of informational materials.

o        classifies; cites; converts; describes; discusses; estimates; explains; generalizes; gives examples; makes sense out of; paraphrases; restates (in own words); summarizes; traces; understands.

3.      Application: The use of previously learned information in new and concrete situations to solve problems that have single or best answers.

o        acts; administers; articulates; assesses; charts; collects; computes; constructs; contributes; controls; determines; develops; discovers; establishes; extends; implements; includes; informs; instructs; operationalizes; participates; predicts; prepares; preserves; produces; projects; provides; relates; reports; shows; solves; teaches; transfers; uses; utilizes.

4.      Analysis: The breaking down of informational materials into their component parts, examining (and trying to understand the organizational structure of) such information to develop divergent conclusions by identifying motives or causes, making inferences, and/or finding evidence to support generalizations.

o        breaks down; correlates; diagrams; differentiates; discriminates; distinguishes; focuses; illustrates; infers; limits; outlines; points out; prioritizes; recognizes; separates; subdivides.

5.      Synthesis: Creatively or divergently applying prior knowledge and skills to produce a new or original whole.

o        adapts; anticipates; categorizes; collaborates; combines; communicates; compares; compiles; composes; contrasts; creates; designs; devises; expresses; facilitates; formulates; generates; incorporates; individualizes; initiates; integrates; intervenes; models; modifies; negotiates; plans; progresses; rearranges; reconstructs; reinforces; reorganizes; revises; structures; substitutes; validates.

6.      Evaluation: Judging the value of material based on personal values/opinions, resulting in an end product, with a given purpose, without real right or wrong answers.

o        appraises; compares & contrasts; concludes; criticizes; critiques; decides; defends; interprets; judges; justifies; reframes; supports.

Bloom’s Taxonomy

Bloom’s Taxonomy is a way to classify instructional activities or questions as they progress in difficulty.  The lower levels require less in the way of thinking skills.  As one moves down the hierarchy, the activities require higher level thinking skills.

Level

Type of Activity
or Question

Verbs Used for Objectives

Lowest level

Knowledge

define, memorize, repeat, record, list, recall, name, relate, collect, label, specify, cite, enumerate, tell, recount

 

Comprehension

restate, summarize, discuss, describe, recognize, explain, express, identify, locate, report, retell, review, translate

 

Application

exhibit, solve, interview, simulate, apply, employ, use, demonstrate, dramatize, practice, illustrate, operate, calculate, show, experiment

Higher levels

Analysis

interpret, classify, analyze, arrange, differentiate, group, compare, organize, contrast, examine, scrutinize, survey, categorize, dissect, probe, inventory, investigate, question, discover, text, inquire, distinguish, detect, diagram, inspect

 

Synthesis

compose, setup, plan, prepare, propose, imagine, produce, hypothesize, invent, incorporate, develop, generalize, design, originate, formulate, predict, arrange, contrive, assemble, concoct, construct, systematize, create

 

Evaluation

judge, assess, decide, measure, appraise, estimate, evaluate, infer, rate, deduce, compare, score, value, predict, revise, choose, conclude, recommend, select, determine, criticize


Example Product list:

Advertisement
Annotated bibliography
Art gallery
Biography
Blueprint
Board game
Book Cover
Bulletin board
Card game
Chart
Collage
Collection with illustration
Collection with narrative
Comic Strip
Computer program
Crossword puzzle

Debate
Detailed illustration
Diary
Diorama
Display
Drama
Dramatic monologue
Editorial
Essay
Experiment
Experiment Log
Fable
Fact file
Fairy tale
Family tree
Glossary

Graph
Graphic design
Greeting card
Illustrated story
Journal
Labeled diagram
Large scale drawing
Lecture
Letter
Letter to the editor
Lesson
Line drawing
Magazine article
Map
Map with legend
Mobile

Monograph
Museum exhibit
Musical composition
News report
Pamphlet
Pattern with instructions
Photo essay
Picture dictionary
Poem
Poster
Reference file
Powerpoint Presentation
Survey
Transparency of overhead
Vocabulary List
Written report

Example of taking an objective and creating questions and activities from each of the different levels:

Objective:  The student will write a compound sentence using conjunctions.

Questions and Activities that might follow:

Knowledge
    1.  What is a compound sentence?
2.  List the conjunctions that you could use to combine sentences into a compound sentence.

Comprehension
1.  What is the difference between a compound and a simple sentence?
2.  Create a compound sentence from two given simple sentences.

Application
1.  Write one example of a compound sentence.
2.  Use the conjunction “and” to form a compound sentence.

Analysis
1.  Identify reasons for using conjunctions to form compound sentences.
2.  Compare the three conjunctions “and”, “or”, and “but” and explain the differences between each.

Synthesis
1.  Write a paragraph that uses each of the three conjunctions to form a compound sentence.

Evaluation
1.  Trade paragraphs with a partner and look for 3 compound sentences using “and”, “or”, and “but”.
2.  Determine whether or not your partner understands writing with compound sentences and be prepared to defend your answers.

Bloom’s Taxonomy

Benjamin Bloom created this taxonomy for categorizing level of abstraction of questions that commonly occur in educational settings. The taxonomy provides a useful structure in which to categorize test questions, since professors will characteristically ask questions within particular levels, and if you can determine the levels of questions that will appear on your exams, you will be able to study using appropriate strategies.

Competence

Skills Demonstrated

Knowledge

  • observation and recall of information
  • knowledge of dates, events, places
  • knowledge of major ideas
  • mastery of subject matter
  • Question Cues:
    list, define, tell, describe, identify, show, label, collect, examine, tabulate, quote, name, who, when, where, etc.

Comprehension

  • understanding information
  • grasp meaning
  • translate knowledge into new context
  • interpret facts, compare, contrast
  • order, group, infer causes
  • predict consequences
  • Question Cues:
    summarize, describe, interpret, contrast, predict, associate, distinguish, estimate, differentiate, discuss, extend

Application

  • use information
  • use methods, concepts, theories in new situations
  • solve problems using required skills or knowledge
  • Questions Cues:
    apply, demonstrate, calculate, complete, illustrate, show, solve, examine, modify, relate, change, classify, experiment, discover

Analysis

  • seeing patterns
  • organization of parts
  • recognition of hidden meanings
  • identification of components
  • Question Cues:
    analyze, separate, order, explain, connect, classify, arrange, divide, compare, select, explain, infer

Synthesis

  • use old ideas to create new ones
  • generalize from given facts
  • relate knowledge from several areas
  • predict, draw conclusions
  • Question Cues:
    combine, integrate, modify, rearrange, substitute, plan, create, design, invent, what if?, compose, formulate, prepare, generalize, rewrite

Evaluation

  • compare and discriminate between ideas
  • assess value of theories, presentations
  • make choices based on reasoned argument
  • verify value of evidence
  • recognize subjectivity
  • Question Cues
    assess, decide, rank, grade, test, measure, recommend, convince, select, judge, explain, discriminate, support, conclude, compare, summarize

 

 

 

C1 Bloom’s Taxonomy

Following the 1948 Convention of the American Psychological Association, B S Bloom took a lead in formulating a classification of “the goals of the educational process”. Three “domains” of educational activities were identified. The first of these, named the Cognitive Domain, involves knowledge and the development of intellectual attitudes and skills. (The other domains are the Affective Domain and the Psychomotor Domain, and need not concern us here).

Eventually, Bloom and his co-workers established a hierarchy of educational objectives, which is generally referred to as Bloom’s Taxonomy, and which attempts to divide cognitive objectives into subdivisions ranging from the simplest behaviour to the most complex.

It is important to realise that the divisions outlined above are not absolutes and that other systems or hierarchies have been devised. However, Bloom’s taxonomy is easily understood and widely applied.

C1.1. Knowledge.

Knowledge is defined as the remembering of previously learned material. This may involve the recall of a wide range of material, from specific facts to complete theories, but all that is required is the bringing to mind of the appropriate information. Knowledge represents the lowest level of learning outcomes in the cognitive domain.

Examples of learning objectives at this level are: know common terms, know specific facts, know methods and procedures, know basic concepts, know principles.

C.1.2. Comprehension.

Comprehension is defined as the ability to grasp the meaning of material. This may be shown by translating material from one form to another (words to numbers), by interpreting material (explaining or summarizing), and by estimating future trends (predicting consequences or effects). These learning outcomes go one step beyond the simple remembering of material, and represent the lowest level of understanding.

Examples of learning objectives at this level are: understand facts and principles, interpret verbal material, interpret charts and graphs, translate verbal material to mathematical formulae, estimate the future consequences implied in data, justify methods and procedures.

C.1.3. Application.

Application refers to the ability to use learned material in new and concrete situations. This may include the application of such things as rules, methods, concepts, principles, laws, and theories. Learning outcomes in this area require a higher level of understanding than those under comprehension.

Examples of learning objectives at this level are: apply concepts and principles to new situations, apply laws and theories to practical situations, solve mathematical problems, construct graphs and charts, demonstrate the correct usage of a method or procedure.

C.1.4. Analysis.

Analysis refers to the ability to break down material into its component parts so that its organizational structure may be understood. This may include the identification of parts, analysis of the relationship between parts, and recognition of the organizational principles involved. Learning outcomes here represent a higher intellectual level than comprehension and application because they require an understanding of both the content and the structural form of the material.

Examples of learning objectives at this level are: recognize unstated assumptions, recognises logical fallacies in reasoning, distinguish between facts and inferences, evaluate the relevancy of data, analyse the organizational structure of a work (art, music, writing).

C.1.5. Synthesis.

Synthesis refers to the ability to put parts together to form a new whole. This may involve the production of a unique communication (theme or speech), a plan of operations (research proposal), or a set of abstract relations (scheme for classifying information). Learning outcomes in this area stress creative behaviours, with major emphasis on the formulation of new patterns or structure.

Examples of learning objectives at this level are: write a well organized theme, gives a well organized speech writes a creative short story (or poem or music), propose a plan for an experiment, integrate learning from different areas into a plan for solving a problem, formulates a new scheme for classifying objects (or events, or ideas).

C.1.6. Evaluation.

Evaluation is concerned with the ability to judge the value of material (statement, novel, poem, research report) for a given purpose. The judgments are to be based on definite criteria. These may be internal criteria (organization) or external criteria (relevance to the purpose) and the student may determine the criteria or be given them. Learning outcomes in this area are highest in the cognitive hierarchy because they contain elements of all the other categories, plus conscious value judgments based on clearly defined criteria.

Examples of learning objectives at this level are: judge the logical consistency of written material, judge the adequacy with which conclusions are supported by data, judge the value of a work (art, music, writing) by the use of internal criteria, judge the value of a work (art, music, writing) by use of external standards of excellence.

 

Bloom’s Taxonomy: An Overview

Asking students to think at higher levels, beyond simple recall, is an excellent way to stimulate students’ thought processes. Different types of questions require us to use different kinds or levels of thinking.

See a list of verbs for use in lesson plans and discussion questions that correlates to Bloom’s levels of thinking.

According to Bloom’s Taxonomy, human thinking skills can be broken down into the following six categories.

1.   Knowledge: remembering or recalling appropriate, previously learned information to draw out factual (usually right or wrong) answers. Use words and phrases such as: how many, when, where, list, define, tell, describe, identify, etc., to draw out factual answers, testing students’ recall and recognition.

2.   Comprehension: grasping or understanding the meaning of informational materials. Use words such as: describe, explain, estimate, predict, identify, differentiate, etc., to encourage students to translate, interpret, and extrapolate.

3.   Application: applying previously learned information (or knowledge) to new and unfamiliar situations. Use words such as: demonstrate, apply, illustrate, show, solve, examine, classify, experiment, etc., to encourage students to apply knowledge to situations that are new and unfamiliar.

4.   Analysis: breaking down information into parts, or examining (and trying to understand the organizational structure of) information. Use words and phrases such as: what are the differences, analyze, explain, compare, separate, classify, arrange, etc., to encourage students to break information down into parts.

5.   Synthesis: applying prior knowledge and skills to combine elements into a pattern not clearly there before. Use words and phrases such as: combine, rearrange, substitute, create, design, invent, what if, etc., to encourage students to combine elements into a pattern that’s new.

6.   Evaluation: judging or deciding according to some set of criteria, without real right or wrong answers. Use words such as: assess, decide, measure, select, explain, conclude, compare, summarize, etc., to encourage students to make judgements according to a set of criteria.