ABSTRACT

Offering voices from the field – the first of its kind outside of Japan – this guide to teaching and learning elementary mathematics highlights real case examples from teachers and educators who share what they have learned through Lesson Study.

The teachers’ reports provide vivid examples of new insights and ideas about mathematics, about pedagogy and lesson design, about student learning, and about professional collaboration gained through Lesson Study. Each report includes an abbreviated plan of the specific research lesson that led to the new insights, which readers can draw from to replicate the powerful learning in their own community. The case examples of this book are from Lesson Study in mathematics, elementary to lower secondary grade levels, focused on what teachers and educators have learned about improving mathematics teaching and learning; but many ideas from each report can be applied to other subjects and different grade levels.

This unique book will be an excellent resource for mathematics teachers in training and practice who seek to improve mathematics teaching and learning in their own and others’ classrooms, including researchers and school administrators who lead professional development.

part I|25 pages

How we expect Lesson Study to contribute to the quality of teaching and learning

part II|49 pages

What we learned about the contents we teach

chapter |8 pages

"Doing the math"

Word problems in the primary grades — solve "take-from with change unknown" story problems with grade 1 (6- and 7-year-old) students

chapter |14 pages

To add or subtract, that is the question

A compare-type problem with the smaller quantity unknown, grade 2 (7- and 8-year-old) students

chapter |8 pages

Expanding the meaning of multiplication

Understanding multiplication of a whole number by a decimal, grade 5 (10- and 11-year-old) students

chapter |8 pages

Conceptualizing equivalent expressions through problem-solving

Combining like terms, for grade 7 (12- to 13-year-old) students

chapter |7 pages

Expanding my conception of place value

Three-digit subtraction with regrouping, for grade 3 (8- and 9-year-old) students

chapter |2 pages

Summary of Chapter II

What we learned about the contents we teach

part III|27 pages

What we learned about lesson design and pedagogy

chapter |8 pages

Designing lessons students lead

Numbers greater than 1,000, for grade 2 (7- and 8-year-old) students

chapter |7 pages

Creating meaning with data and graphing

Collecting, graphing, and interpreting data, for grade 2 (7- and 8-year-old) students

chapter |8 pages

Boardwork as a roadmap

Introducing subtraction, for Kindergarten (5- and 6-year-old) students

chapter |2 pages

Summary of Chapter III

What we learned about lesson design and pedagogy

part IV|48 pages

What we learned about student

chapter |11 pages

An upper elementary teacher learns about making ten in first grade

Making a new ten, first grade (6- and 7-year-old) students

chapter |10 pages

Discovering numbers greater than 1000

Making meaning of numbers above 1000, for second grade (7- and 8-year-old) students

chapter |8 pages

Student learning: addition with fractions

Adding fractions with like denominators, grade 3 (8- and 9-year-old) students

chapter |7 pages

Student learning: division with remainders

Division with remainders, for grade 4 (9- and 10-year-old) students

chapter |8 pages

Student learning: multi-digit multiplication algorithm

Multiplying a two-digit number by another two-digit number, for grade 4 (9-year-old) students

chapter |2 pages

Summary of Chapter IV

What we learned about student learning

part V|38 pages

What we learned about teacher collaboration and leadership

chapter |7 pages

Teacher collaboration: the growth of Lesson Study in one school

How the development of Lesson Study can be seen through decimals

chapter |8 pages

Teachers solving their own problems of practice

Quotative division for grade 3 (8- and 9-year-old) students

chapter |11 pages

Lesson Study and the new teacher

Adding fractions with unlike denominators, for grade 4 (8- and 9-year-old) students

chapter |7 pages

Building district infrastructure for Lesson Study: designing educator support centering our students at the margins

The San Francisco Unified School District (SFUSD) Teacher Leader Fellowship (TLF) and Lesson Study support programming

chapter |3 pages

Summary of Chapter V

What we learned about teacher collaboration and leadership

part VI|9 pages

Ideas for establishing sustainable Lesson Study – what we learned from US schools