Improving Mathematics Education Resources for Decision Making (2001) / Chapter Skim
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3 How Should We Teach?
3 How Should We Teach?
Pages 10-18
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From page 10... ...
What is the nature of teaching practice supported by research in cognitive science? RESOURCES AVAILABLE Adding It Up: Helping Children Learn Mathematics, developed by the National Research Council's Mathematics Learning Study Committee, 2001.
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From page 11... ...
In particular, it describes how skill and understanding in key subjects are acquired and discusses our growing knowledge about complex reasoning and problem solving. Adding It Up: Helping Children Learn Mathematics Adding It Up is a research-based examination of pre-K-8 mathematics that focuses on what the mathematical content is with which students must develop proficiency, how instruction can help students develop this proficiency, and, most significant, the research that undergirds why these positions are taken.
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From page 12... ...
Thoughtful discussion about these and similar controversial questions is provided in this report, which considers the mathematical knowledge children bring to school and how students develop proficiency with numbers and in other mathematical areas. The report also discusses teaching for mathematical proficiency, describes instruction as "interactions among teachers and students around content" (p.
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From page 13... ...
· Additional research should be undertaken on the nature, development, and assessment of mathematical proficiency." Among the 58 specific recommendations made to help move the nation toward the change needed in school mathematics, Adding It Up urges the following with respect to student learning and its relation to curriculum: "Mathematics programs in the early grades should make extensive use of appropriate objects, diagrams, and other aids to ensure that all children understand and are able to use number words and the base-10 properties of numerals, that all children can use the language of How Should We Teach?
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From page 14... ...
in solving problems, and that all children can explain their reasoning in obtaining solutions." (p 412) "Instructional materials and classroom teaching should help students learn increasingly abbreviated procedures for producing number combinations rapidly and accurately without always having to refer to tables or other aids." (p.413)
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From page 15... ...
134. Learning research suggests a need to change current practice; "there are new ways to introduce students to traditional subjects...and that these new approaches make it possible for the majority of individuals to develop a deep understanding of important subject matter" (p.
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From page 16... ...
In lieu of specific recommendations, How People Learn concludes with a detailed set of summary findings and conclusions and 23 categories of recommended research and development for future research. Recommendations for practice include the following: 16 Improving Mathematics Education
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From page 17... ...
236) Teachers need expertise in both subject-matter content and in teaching; need to develop an understanding of the theories of knowledge that guide the subject-matter disciplines in which they work; need to develop an understanding of pedagogy as an intellectual discipline that reflects theories of learning, including knowledge of how cultural beliefs and the personal characteristics of learners influence learning; and need to develop models of their own professional development that are based on lifelong learning, rather than on an "updating" model of learning (p.
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From page 18... ...
Support additional research along the lines proposed in Chapter 11 of How People Learn, forming teams that combine the expertise of researchers and the wisdom of practitioners. This research should focus on curriculum materials, formative assessment, the use of technology, and on the alignment and effectiveness of professional development programs.
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