## Teaching Through Problem-Solving

Teaching Through Problem-Solving is used as a general lesson structure throughout the SFUSD Math Core Curriculum, as well as more formally at schools that are using Lesson Study to deepen teaching practice.

The following description of Teaching Through Problem-Solving is from the Mills College Lesson Study Group:

Japanese lessons center on “Teaching Through Problem-solving.” Students grapple with a mathematical task they have not previously learned to solve that embodies the new mathematical ideas or procedures to be learned. Teaching Through Problem-solving is very similar to the 5 Practices for Orchestrating Mathematical Discussions by Margaret Smith and Mary Kay Stein that is widely used in the U.S.

In a typical Teaching Through Problem-Solving lesson, the teacher starts the class by presenting a mathematics problem and making sure students understand what is being asked. Students write or glue a copy of the problem into their journals and begin solving it. As students work on the problem, the teacher walks around to see their work (often using a clipboard with a seating chart to note down each student’s strategy). Having thought through in advance the “line-up” of work at the board that will build the major mathematical ideas of the lesson, the teacher selects several students to present their work and share their thinking at the board, in a sequence designed to build the key mathematical ideas. As each student shares their work and the class discusses it, the teacher makes sure each student strategy and important discussion points are recorded on the board in a way that is easy to read and follow. From comparing and synthesizing the various strategies, the lesson’s new mathematical ideas emerge, and they are summarized on the board. So by the end of the lesson, the board provides a coherent story of the mathematics developed during the lesson.

More information about Teaching Through Problem-Solving is available from the

The following description of Teaching Through Problem-Solving is from the Mills College Lesson Study Group:

Japanese lessons center on “Teaching Through Problem-solving.” Students grapple with a mathematical task they have not previously learned to solve that embodies the new mathematical ideas or procedures to be learned. Teaching Through Problem-solving is very similar to the 5 Practices for Orchestrating Mathematical Discussions by Margaret Smith and Mary Kay Stein that is widely used in the U.S.

In a typical Teaching Through Problem-Solving lesson, the teacher starts the class by presenting a mathematics problem and making sure students understand what is being asked. Students write or glue a copy of the problem into their journals and begin solving it. As students work on the problem, the teacher walks around to see their work (often using a clipboard with a seating chart to note down each student’s strategy). Having thought through in advance the “line-up” of work at the board that will build the major mathematical ideas of the lesson, the teacher selects several students to present their work and share their thinking at the board, in a sequence designed to build the key mathematical ideas. As each student shares their work and the class discusses it, the teacher makes sure each student strategy and important discussion points are recorded on the board in a way that is easy to read and follow. From comparing and synthesizing the various strategies, the lesson’s new mathematical ideas emerge, and they are summarized on the board. So by the end of the lesson, the board provides a coherent story of the mathematics developed during the lesson.

More information about Teaching Through Problem-Solving is available from the

**Mills College Lesson Study Group**.