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

Content

Conceptual understanding

Problem solving

Think mathematically

Make conjectures

Communicate math ideas

Concrete to the abstract

Reason Deductively

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

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

Implementation

Proceduralizing good problems

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Japan U.S. HongKong

UsingProcedures

Makingconnections

Percentages of how often types of problems were presented.

Implementation

Proceduralizing good problems

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40

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Japan U.S. HongKong

UsingProcedures

Makingconnections

Percentages of How Problems are Worked on During the Lesson.

Implementation

Good use of manipulativesUsing technology in the classroomGetting students to communicate about math ideasModeling 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

College Course vs. Professional Development

What content or ideas are students not ready to grapple with until they are in the classroom?