1. Upper Elementary Math Three Things to Keep in Mind: US Teaching Culture and Practice Problem Solving as an Instructional Tool Big Math Concepts Need Time and Exploration

2. US Math Texts and Teaching Tend toward procedural instruction (TIMSS) Give more worksheets than most other countries (TIMSS) Cover too many topics in a given year (breadth rather than depth) Teachers may be less mathematically versed than in other countries (Ma)

3. Problem Solving as an Instructional Method Teaching Problems and the Problems of Teaching, Magdalene Lampert Automatically differentiated, if the problem is rich enough Requires mathematical proof, reasoning, and communication Ways to do this: word problems (daily book); rich problems (NCTM)

4. Problem Solving Example from Lesson Study at Highlands Quick demo on this problem: 01/10 X

5. Big Math Concepts that Need Deep Exploration in Early Elementary School Zero/ place markers in base systems Equals and Equivalence The Many Names for a Number Properties: associative, commutative, distributive, zero Representations for amounts: number line, pie graphs, hundred charts, sets, etc. Many more I am sure I have not explored/discovered

6. My Favorite Places to Go for More Information Teaching Problems and the Problems of Teaching, Magdalene Lampert Teaching Problems and the Problems of Teaching, Magdalene Lampert Knowing and Teaching Elementary Mathematics, Liping Ma Knowing and Teaching Elementary Mathematics, Liping Ma NCTM Illuminations National Library of Virtual Manipulatives National Library of Virtual Manipulatives