How People Learn Brain, Mind, Experience, and School: Expanded Edition (2000) / Chapter Skim
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7 Effective Teaching: Examples in History, Mathematics, and Science
7 Effective Teaching: Examples in History, Mathematics, and Science
Pages 155-189
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From page 155... ...
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.
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From page 156... ...
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.
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From page 157... ...
that underlie expert teaching. They should help to clarify why effective teaching requires much more than a set of "general teaching skills." HISTORY Most people have had quite similar experiences with history courses: they learned the facts and dates that the teacher and the text deemed relevant.
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From page 158... ...
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.
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From page 159... ...
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.
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From page 160... ...
'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.
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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.
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162 HOW PEOPLE LEARN, EXPANDED EDITION 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.
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From page 163... ...
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.
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From page 164... ...
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, 19921.
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From page 165... ...
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, 1986:3161. 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.
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From page 166... ...
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 t~vo-digit multiplication.
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From page 167... ...
Students defend the reasonableness of their procedures by using drawings and stories. Eventually, students explore more traditional as well as alternative algorithms for two-digit multiplication, using only written symbols.
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From page 168... ...
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 indi
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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., 19971. 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.
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From page 170... ...
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.
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From page 171... ...
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 171
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From page 172... ...
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. SCIENCE Two recent examples in physics illustrate how research findings can be used to design instructional strategies that promote the sort of problemsolving behavior observed in experts.
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. 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., 19961.
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From page 174... ...
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.
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From page 175... ...
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 175
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From page 176... ...
Now set the initial energy equal to the final energy that is made up of the kinetic energy of the disk plus the mass M and any potential energy left in the system with respect to the chosen coordinate system. Strategy 2: I would use conservation of mechanical energy to solve this problem.
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From page 177... ...
. One instructional strategy, termed "bridging," has been successful in helping students overcome persistent misconceptions (Brown, 1992; Brown and Clement, 1989; Clement, 19931.
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From page 178... ...
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
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From page 179... ...
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, 19971.
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From page 180... ...
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.
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From page 181... ...
Interactive Instruction in Large CLasses 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?
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From page 182... ...
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. Science for AU Children The examples above present some effective strategies for teaching and learning science for high school and college students.
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From page 183... ...
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.
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From page 184... ...
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.
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From page 185... ...
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)
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From page 186... ...
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 an hypothesis "How would you find out?
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From page 187... ...
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 (see Chapter 3)
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From page 188... ...
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.
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From page 189... ...
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., 19911; 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., 19971.
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