chadwick school monday, january 31, 2011. megan holmstrom, chadwick school: elementary math coach -...
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Chadwick School
Monday, January 31, 2011
CAIS Professional Day in Mathematics:
Changes in Math Education
Megan Holmstrom, Chadwick School: Elementary Math Coach - Elements of a vigorous math program- Changes in math [email protected]
Yasuko Morihara, Chadwick School: Middle School Mathematics- Middle School [email protected]
• Patrick Kimani, Assistant Professor of Mathematics – CSUF- Teaching Mathematics via Cooperative Problem Solving
Kathy Clemmer, CMAST Executive Director and Founder – LMU - Goal-Oriented and Vision-Driven Teacher Leadership in Math Education
Overview
Mathematics Education: What Research is Telling Us
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)
National Math Advisory Panel Final Report
A mathematically proficientstudent balances:
conceptual understandingprocedural fluency
strategic competenceadaptive reasoning
productive disposition(active learner)
Adding it Up by National Research Council
Meaningful Mathematics: Leading Students Toward Understanding and Application
Principles of Learning:
1.Prior understandings must be engaged 2.Factual knowledge needs to be integrated into
conceptual frameworks3.Metacognition is key
National Research Council of the NationalAcademy of Sciences
How Children Learn Mathematics
A Comprehensive Math Program:What it Looks Like
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 SmarterCathy L. Seeley
21st Century View of a Balanced Math Program: Balance is Basic
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.
Create Students Who:
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
A Framework for Instruction:
Current News in Math Education:Changes, Looking Ahead…
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
National Council of Teachers of Mathematics and National Math Panel Report
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.
The Test Chinese Schools Still Fail Program for International Student Assessment (PISA)
A mathematically proficientstudent balances:
conceptual understandingprocedural fluency
strategic competenceadaptive reasoning
productive disposition(active learner)
Adding it Up by National Research Council
Meaningful Mathematics: Leading Students Toward Understanding and Application
Faster Isn’t Smarter, Cathy L. SeeleyThinking Mathematically, Carpenter / Franke / LeviChildren’s Mathematics, Carpenter, et. al.About Teaching Mathematics, Marilyn BurnsMarcy Cook MathGuided Math, Laney SammonsMath Knowledge for Teaching (MKT), Deborah Ball
University of MichiganNCTM www.nctm.orgCommon Core State Standards http://
www.corestandards.org/
Resources /References
