#### Transcript of Providing Textbook Supports for Teaching Math

**Providing Textbook Supports for Teaching Mathematics through Problem Solving**

Textbook page designed for teaching through problem solving

The same problem in the the 2011 edition

**Akihiko Takahashi, Ph.D.**

CURRENT ISSUES IN TEACHING MATHEMATICS IN JAPAN

In order to implement the new COS, Japanese teachers, especially those who have had less than 10 years of experience, need to consider not only how the amount of content has changed but also how to design lessons that will push all students to think mathematically and to communicate their ideas in such a way as to learn multiple ways of thinking mathematically.

The problems are typical of those found in Japanese mathematics textbooks for 4th grade; they are presented to students who have just learned the formulas for finding the area of rectangles and squares.

The objective is for students to understand how they might use formulas, which they have learned previously, to find the area of unfamiliar shapes. In order to use their prior knowledge to find the area of these new shapes, the students should use strategies like area-preserving transformations (cutting and re-arranging) or area-doubling transformations (copying and re-arranging).

Thus, the teachers should be able to use this problem to help students learn general strategies for using previously-learned area formulas to find the area of unfamiliar shapes (Watanabe, Takahashi, & Yoshida, 2008).

Japanese mathematics educators and teachers identify three levels of expertise between

“teaching the textbook” and “using the textbook to teach mathematics” (Sugiyama, 2008):

Level 1: The teacher can tell students important basic ideas of mathematics such as facts, concepts, and procedures.

Level 2: The teacher can explain the meanings and reasons of the important basic ideas of mathematics in order for students to understand them.

Level 3: The teacher can provide students opportunities to understand these basic ideas, and support their learning so that the students become independent learners.

Full transcript