#### Transcript of Teaching through problem solving to address CCSS-M mathematical practice

**Teaching through problem solving to address **

CCSS-M mathematical practice

Three Levels of Teaching Mathematics

Level 1 teaching

teachers tell students important basics, such as facts, concepts, procedures, and ways of thinking in mathematics.

Level 2 teaching,

teachers explain the meanings and reasons of the important basics in order for students to understand them.

Level 3 Teaching

Teachers provide students opportunities to understand the basics, and support their learning so that the students become independent learners.

In order to develop mathematical practice, student should develop those practice by doing mathematics rather than passively listening to the teachers' explanations. Thus it is important for teachers to have classrooms based on Level 3 teaching as often as possible.

Standards for Mathematical Practice

Mathematically proficient students..........

1 Make sense of problems and persevere in solving them.

2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

4 Model with mathematics.

5 Use appropriate tools strategically.

6 Attend to precision.

7 Look for and make use of structure.

8 Look for and express regularity in repeated reasoning.

Look back

Provide students the opportunity to look back at the solutions the class discussed and summarize the mathematical ideas and procedures

An Example

After students learn single digit multiplication, teacher may pose the following problem to the students.

Teaching through Problem Solving

Based on Polya’s four phases of problem solving work (1945), the structure of the teaching through problem solving lessons as follows.

The teacher Presents a problem to the students without first demonstrating how to solve the problem.

The students solve the problems individually or by working with other students.

The class discuss the solution by comparing multiple approaches to the problem.

The students look back the solutions the class discussed and summarize the mathematical ideas and procedures.

Tokyo Shoseki Mathematics International Grade 2 p. B42

www.globaledresources.com

Tokyo Shoseki Mathematics International Grade 2 p. B45

www.globaledresources.com

Model with mathematics

Construct viable arguments and critique the reasoning of others

Make sense of problems and persevere in solving them

Use appropriate tools strategically.

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