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CAIS Professional Day in Mathematics: Changes in Math Education

CAIS Professional Day in Mathematics: Changes in Math Education. Chadwick School Monday, January 31, 2011. Overview. Megan Holmstrom, Chadwick School: Elementary Math Coach Elements of a vigorous math program Changes in math education m egan.holmstrom@chadwickschool.org

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CAIS Professional Day in Mathematics: Changes in Math Education

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  1. CAIS Professional Day in Mathematics:Changes in Math Education Chadwick School Monday, January 31, 2011

  2. Overview • Megan Holmstrom, Chadwick School: Elementary Math Coach • Elements of a vigorous math program • Changes in math education megan.holmstrom@chadwickschool.org • Yasuko Morihara, Chadwick School: Middle School Mathematics • Middle School Problem-Solving yasuko.morihara@chadwickschool.org • Patrick Kimani, Assistant Professor of Mathematics – CSUF • Teaching Mathematics via Cooperative Problem Solving pkimani@exchange.fullerton.edu • Kathy Clemmer, CMAST Executive Director and Founder – LMU • Goal-Oriented and Vision-Driven Teacher Leadership in Math Education katharine.clemmer@lmu.edu

  3. Mathematics Education: What Research is Telling Us

  4. National Math Advisory Panel Final Report A balanced math program should encompass: • themutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic recall of facts (instructional strategies) • high-quality research does not support the contention that instruction should be either entirely ‘student-centered’ or ‘teacher-directed’ (curriculum choice) • effort, not just inherent talent, counts in mathematical achievement (developmentally appropriate)

  5. Meaningful Mathematics: Leading Students Toward Understanding and Application A mathematically proficient student balances: conceptual understanding procedural fluency strategic competence adaptive reasoning productive disposition (active learner) Adding it Up by National Research Council

  6. How Children Learn Mathematics Principles of Learning: • Prior understandings must be engaged • Factual knowledge needs to be integrated into conceptual frameworks • Metacognition is key National Research Council of the National Academy of Sciences

  7. A Comprehensive Math Program:What it Looks Like

  8. 21st Century View of a Balanced Math Program: Balance is Basic • The nature of mathematics students need and the depth of mathematical thinking called for today has changed • The fundamentals of a mathematics program remain the same Essentially, we all want students to: 1. Make Sense of Math2. Do Math 3. Use Math Faster Isn’t Smarter Cathy L. Seeley

  9. Create Students Who: • Effectively solve problems across a wide variety of situations using multiple mathematical strategies, techniques, and tools. • Create numeric, algebraic, graphical, and verbal representations of mathematical concepts. • Analyze and evaluate the mathematical thinking and strategies of others. • Use the language of mathematics to precisely express ideas and conclusions.

  10. A Framework for Instruction: Cognitive Guided Instruction • Critical Junctures: Teacher as Facilitator vs. Teacher as DirectorQuestioning StrategiesDiscussions Drive Planning, Next Moves • Communication: ideas, solutions, problems, proofs, conjectures • Active Engagement: thinking while doing, discussing Guide Students – Multiple Perspectives

  11. Current News in Math Education:Changes, Looking Ahead…

  12. National Council of Teachers of Mathematics and National Math Panel Report • Mental math need not depend on rote memorization: - students engaging in purposeful experiences with concrete objects and number patterns- teachers play a vital role: making sure the experiences are connected in meaningful ways to the mathematics we ask students to learn • Automaticity of basic facts: - practice allows students to achieve automaticity of basic skills - frees up working memory and for more complex aspects of problem-solving

  13. The Test Chinese Schools Still Fail Program for International Student Assessment (PISA) • The failings of a rote-memorization system are well-known; Chinese students burn themselves out testing into university • Using tests to structure schooling is a mistake • Tests are less relevant to concrete life and work skills than "critical thinking" skills; these are what Chinese students need to learn if they are to become globally competitive.

  14. Meaningful Mathematics: Leading Students Toward Understanding and Application A mathematically proficient student balances: conceptual understanding procedural fluency strategic competence adaptive reasoning productive disposition (active learner) Adding it Up by National Research Council

  15. Resources /References Faster Isn’t Smarter, Cathy L. Seeley Thinking Mathematically, Carpenter / Franke / Levi Children’s Mathematics, Carpenter, et. al. About Teaching Mathematics, Marilyn Burns Marcy Cook Math Guided Math, Laney Sammons Math Knowledge for Teaching (MKT), Deborah Ball University of Michigan NCTM www.nctm.org Common Core State Standards http://www.corestandards.org/

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