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Welcome• Enjoy breakfast• Use three post-its to answer these
questions:– What does it mean to DO mathematics?– What does it mean to LEARN mathematics?– What does it mean to UNDERSTAND mathematics?
• Post answers on appropriate poster• Discover patterns within the Banner
Numbers
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Success In Algebra
March 22, 2013Leitchfield, KY
Facilitated by the P12 Math and Science Outreach Unit of PIMSER, UKFunding provided by Council on Post Secondary Ed
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Reflection and Feedback
Agenda !/? Card
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Survey
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One UpOne Down
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Math Practice Standards1. Make sense of problems and persevere in solving
them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the
reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated
reasoning
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Exploring What It Means to Know and Do Mathematics
Chapter 2“… about the learning theory of teaching
developmentally and the knowledge necessary for students to learn mathematics with
understanding.” (p 13 Van de Walle)
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• What does it mean to DO mathematics?– Pages 13 – 15
• What does it mean to LEARN mathematics?– Pages 19 – 23
• What does it mean to UNDERSTAND mathematics?– Pages 23 – 29
• An invitation to DO mathematics– Pages 15 – 19
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Verbs of Math
Compare Explain Predict
Conjecture Explore Represent
Construct Formulate Solve
Describe Investigate Use
Develop Justify Verify
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Classroom Environment for Doing Mathematics
1. Persistence, effort and concentration are important in learning mathematics
2. Students share their ideas3. Students listen to each other4. Errors or strategies that didn’t work are
opportunities for learning5. Students look for and discuss connections
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Implications for Teaching Mathematics
• Provide opportunities to talk about mathematics
• Build in opportunities for reflective thought• Encourage multiple approaches• Engage students in productive struggle• Treat errors as opportunities for learning• Scaffold new content• Honor diversity
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Intertwined Strands of Proficiency
• Conceptual understanding: comprehension of mathematical concepts, operations, and relations
• Procedural fluency: skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• Strategic competence: ability to formulate, represent, and solve mathematics problems
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• Adaptive reasoning: capacity for logical thought, reflection, explanation and justification
• Productive disposition: habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
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Connecting the Dots
• Between theory and practice…• Students develop their own
networks of blue dots…
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• “As you … design instruction, you should constantly reflect on how to elicit prior knowledge by designing tasks that reflect the social and cultural backgrounds of students, to challenge students to think critically and creatively, and to include a comprehensive treatment of mathematics.” (p 29 Van de Walle)
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© 2012, EDC
Math Accessibility Framework
17
Align StrategiesPlan and Implement Evaluate and Revise as Needed
Identify Barriers
Consider theMath Student
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Student Engagement Strategies
Chapter 9Discussion
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Games to Build Fluency
• Revisit–Bowl-a-Fact– Salute–War
• New– MangaHigh– Integer Capture
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Feedback and Homework• Turn in !/? Card• Accessibility Framework (by April 30, 2013)– Plan an accessible lesson for your focal student– Implement lesson– Reflect on lesson– Email Karen a copy of completed Accessibility
Framework and your reflection on the lesson• Set Coaching Date via email