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Summarizing

Explore the importance of teachers learning mathematical concepts and connecting them to everyday life, focusing on problem-solving, making conjectures, and effective communication. Gain insights on longitudinal coherence, representations, and abstract algebra in teaching mathematics.

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Summarizing

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  1. Summarizing • “Teachers need to learn concepts.” • Mike Maxon • “Teachers need to be able to connect and see mathematics in their everyday lives.” • Personal communication with a SDSU Prof. • “There are a lot of holes in the dam.” • Larry Sowder

  2. Content • Conceptual understanding • Problem solving • Think mathematically • Make conjectures • Communicate math ideas • Concrete to the abstract • Reason Deductively

  3. Content part 2 • Make connections - “the connections are essential”–Mariam Clifford • Concepts and procedures • Math ideas to students’ lives • Longitudinal Coherence • Representations • Equations, Tables, Graphs, Diagrams, Contexts • Content Knowledge in math and content appropriate for students • Abstract Algebra and M.S. Algebra

  4. Disposition • What is math? • Is math a fixed field of facts and procedures or is there more to it than that? • Like mathematics • Developing stick-to-itiveness

  5. Implementation • Percentages of how often types of problems were presented. • Proceduralizing good problems

  6. Implementation • Percentages of How Problems are Worked on During the Lesson. • Proceduralizing good problems

  7. Implementation • Good use of manipulatives • Using technology in the classroom • Getting students to communicate about math ideas • Modeling the way we want them to teach • Being explicit about the pedagogy we are using • Covering content • “If you cover the content then students can’t see the math.” – Kate Masarik

  8. College Course vs. Professional Development What content or ideas are students not ready to grapple with until they are in the classroom?

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