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

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## Akihiko Takahashi

on 3 February 2014

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#### 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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