1. Chadwick School Monday, January 31, 2011

2. 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

4. A balanced math program should encompass: the mutually 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. 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. Principles of Learning: 1. Prior understandings must be engaged 2. Factual knowledge needs to be integrated into conceptual frameworks 3. Metacognition is key National Research Council of the National Academy of Sciences

8. 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 Math 2. Do Math 3. Use Math Faster Isn’t Smarter Cathy L. Seeley

9. 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. Cognitive Guided Instruction - Critical Junctures: Teacher as Facilitator vs. Teacher as Director Questioning Strategies Discussions Drive Planning, Next Moves - Communication: ideas, solutions, problems, proofs, conjectures - Active Engagement: thinking while doing, discussing Guide Students – Multiple Perspectives

12. 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 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. 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. 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.orgwww.nctm.org Common Core State Standards http://www.corestandards.org/http://www.corestandards.org/