1. Mathematics For Elementary Teachers MA201 – Dr. Byrne Instructional Laboratory 0410

2. Today We Will 1.Go over course syllabus. 2.Preview the kinds of things we’ll be learning: “Knowing and teaching elementary mathematics” by Liping Ma 3. Homework Assignment: Paragraph #1

3. Kinds of Things We’ll Be Learning

4. Knowing and teaching elementary mathematics by Liping Ma, 1999

5. Exercise (will not be collected, but save results)

6. Results for 21 Teachers

7. Fractions But teachers don’t just need to KNOW how to do the calculation correctly…

8. Exercise (will not be collected) But teachers don’t just need to KNOW how to do the calculation correctly… … they need to TEACH a student how to do that calculation. (so the student really understands how to do it, and won’t be confused 15 years later by.)

9. Can you think of a story that models this?

10. Some Results of Ma’s Research Subtraction –The concept of borrowing is confusing and misleading. –Better to teach the concept of regrouping. Multiplication –U.S. teachers tend to have a more procedural than conceptual understanding of the algorithm. Fractions –U.S. teachers had difficulty coming up with a story to describe the problem because they lacked a clear conceptual understanding of it. –Chinese teachers understood several different representations of the problem.

11. Different Representations Measurement model: How many units of ½ can be found in 1¾? Partitive model: If half of something is 1¾, what is the whole? Product and factors: If a rectangle has area 1¾ and one side of the rectangle is ½ feet, how long is the other side?

12. Next time: Pre-Test and Why The Elementary Education Curriculum Needs This Course