best practices in mathematics · essentially, we want all students to: 1. make sense of math:...
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Best Practices in Mathematics
“No matter how lucidly and patiently teachers (parents) explain to their students, they cannot understand for their students.”
Best Practices: Mathematically Rich Tasks Elements of a Comprehensive Math Program Pedagogy & Content Embedded Research: Growth Mindset Questions, Answers, Discussion
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Essentially, we want all students to: 1. make sense of math: understand mathematical
concepts and ideas so they can make sense of the mathematics they do;
2. do math: know mathematical facts and perform mathematical skills; and
3. use math: solve a wide range of problems in various contexts by reasoning, thinking, and applying the mathematics they have learned.
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Shift to now…
deep transferable skills for application – problem solving, decision-making, reasoning, research, critical thinking, communication, innovation / creativity, collaboration
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Lesson Study
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Developing Mathematical Literacy
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Meaningful Mathematics: Leading Students Toward Understanding and Application
A mathematically proficient student balances:
conceptual understanding procedural fluency
strategic competence adaptive reasoning
productive disposition
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Answer-Getting vs. Learning Mathematics
United States: How can I teach my students to get the answer to this problem?
Japan: How can I use this problem to teach the mathematics of this unit?
- devised methods for slowing down, postponing answer-getting
Phil Daro, 2012
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Solve problems across a wide variety of situations using multiple 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
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Assessment Contexts for Balanced Assessment
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Growth Mindset Task Framework
Look for opportunities for growth and learning Openness Different Ways of Seeing Multiple Entry Points Multiple Paths / Strategies
Math Tasks
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Jo Boaler ~ Math Anxiety
“Math anxiety is an important and widespread phenomenon, it impacts the performance of the working memory (one of the building blocks of IQ), and it interferes with the brain’s ability to process information needed to succeed in school.”
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Growth Mindset
Grouping = Fixed Mindset Tracking Messages Connections to Carol Dweck: Growth Mindset
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Timed Tests
One of the clearest and most significant causes of the early onset of math anxiety is the use of timed math tests.
There are many known causes of math anxiety, including the presence of math anxious elementary school teachers, an effect that is known to particularly impact girls, and the use of classroom strategies that exert pressure upon students.
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21st century skills. Deeper learning. Global competence.
Report found that teaching for global competence: supports students’ achievement of the Math Standards adds priority for students’ application of skills and knowledge to address important, real-world problems
Standards / Practices go beyond basic academic skills and include 21st century goals and global competencies:
critical thinking, non-routine problem solving, and constructing and evaluating evidence-based arguments = key parts of standards
Educating for Life and Work: Developing Transferrable Knowledge and Skills in the 21st Century