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The Development of Mathematical Proficiency

The Development of Mathematical Proficiency. Presented by the Math Coaches of LAUSD, District K Based on: Adding It Up: Helping Children Learn Mathematics , National Research Council, National Academy Press, Washington D.C., 2001. Adding It Up: Helping Children Learn Mathematics.

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The Development of Mathematical Proficiency

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  1. The Development of Mathematical Proficiency Presented by the Math Coaches of LAUSD, District K Based on: Adding It Up: Helping Children Learn Mathematics, National Research Council, National Academy Press, Washington D.C., 2001

  2. Adding It Up: Helping Children Learn Mathematics • The research evidence is consistent and compellingshowing the following weaknesses: • US students have limited basic understanding of mathematical concepts • They are notably deficient in their ability to solve even simple problems • And, overall, are not given educational opportunity they need to achieve at high levels • In short, the authors tell us that US teachers focus primarily on one area, computation.

  3. Mathematical Proficiency • Conceptual Understanding • Strategic Competence • Procedural Fluency • Adaptive Reasoning • Productive Disposition Let’s give kids something they can hold on to!

  4. Conceptual Understanding “When knowledge is learned withunderstanding it provides a basis forgenerating new knowledge.” • It is comprehension of concepts, operations and relationships • It helps students avoid critical errors in problem solving • It is being able to represent mathematical situations in different ways

  5. What do these say about the student’s Conceptual Understanding? 16 - 8 12 1/3 + 2/5 = 3/8 9.83 x 7.65 = 7,519.95

  6. Discussion Questions • What is Conceptual Understanding? • How do we teach forConceptual Understanding? • What does it look like when students have Conceptual Understanding?

  7. Procedural Fluency • Skill in carrying out mathematical steps and computations • Understanding concepts makes learning skills easier, less susceptible to common errors, andless prone to forgetting • Using procedures can help to strengthen and develop understanding

  8. Does Practice Make Perfect? • Understanding concepts helps recallprocedures correctly • Mastering concepts fosters the ability to choose appropriate math tools and strategies

  9. How Do You Know They Got It? • What are some successful strategiesyou use to develop procedural fluency? • How are procedural fluency and conceptual understanding related?

  10. How would you solve this problem? • A cycle shop has a total of 36 bicycles and tricycles in stock. Collectively there are 80 wheels. How many bicycles and how many tricycles are there?* *Adding It Up, National Research Council, 2001, p.126

  11. Questions to Consider • What is the problem? • What do you need to know to solve this problem? • Describe more than one way to solve this problem?

  12. Strategic CompetenceThe ability to formulate, represent and solve mathematical problems. • Formulate problems • Multiple strategies • Flexibility • Nonroutine problems vs. routine problems Allow nonroutine problems to be the vehicle to build Strategic Competence.

  13. Adaptive Reasoning“…the glue that holds everything together.” • Adaptive Reasoning is the capacity for: • Logical thought • Reflection • Explanation • Justification

  14. Conditions Needed • Real-world, motivating tasks • Utilizes the knowledge-base and experience that children bring to school • Rigorous questioning • Students justify their work on a regular basis

  15. Questions • How do you promote adaptive reasoning in your classroom? • What is the evidence that your students are regularly using adaptive reasoning? • What are the long-term benefits of students utilizing adaptive reasoning?

  16. Productive Disposition • Mathematics makes sense • Mathematics is useful and worthwhile • Steady effort • Effective learners and doers

  17. Key Points • Emotional development • Self-efficacy and self-image • Stereotype threat • Peer pressure to under-achieve • “Wise educational environments” • Affective filter - math as a “second” language

  18. Application • How do teachers’ feelings/perceptions toward math affect productive disposition? • How can SDAIE teaching strategies increase productive disposition in math?

  19. Mathematical Proficiency Conceptual Understanding • Comprehension of mathematical concepts Strategic Competence • Ability to solve mathematical problems Procedural Fluency • Knowledge of algorithms Adaptive Reasoning Productive Disposition • Capacity for logical thought, reflection, explanation and justification • Views mathematics as sensible, useful, & worthwhile, coupled with a belief of ability

  20. Bringing It All Together • How do the five strands of mathematical proficiency relate to standards-based instruction? • How will you incorporate mathematical proficiency into daily teaching practice?

  21. In Conclusion • The goal of instruction should be mathematical proficiency • It takes time for mathematical proficiency to be fully developed • Mathematical proficiency spans number sense, algebra & functions, measurement & geometry, SDAP, and mathematical reasoning “All young Americans must learn to think mathematically and must think mathematically to learn.”

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