# Reasoning & explaining (MP2, MP3)

## Multiple Problem-Solving Strategies in Instruction

Mark Driscoll explains how use of multiple strategies contributes to student learning by letting students see problems in new ways. He stresses the importance of worked examples and comparing and contrasting strategies.

FEATURING: Mark J. Driscoll, Education Development Center

SOURCE: Doing What Works

## Effective Problem-Solving Instruction

This summary describes a wide range of research-based recommendations for guiding instruction in problem solving. Three important strategies that apply at all grade levels and in all areas of math are: use of visual representations, encouragement of multiple approaches to solving problems, and linking mathematical and algebraic notation to intuitive approaches.

SOURCE: Doing What Works

## Problems

In the media piece, Connecting Mathematical Ideas to Notation, Sybilla Beckmann presents two examples of problems showing how students can connect mathematical concepts and notation. This sample material has the problem statements along with the solution ideas given by Beckmann.

SOURCE: Doing What Works

## Connecting Mathematical Ideas to Notation

Sybilla Beckmann uses two different problems to demonstrate how to develop mathematical concepts and present mathematical notation in problem-solving situations.

FEATURING: Sybilla Beckmann, University of Georgia

SOURCE: Doing What Works

## Pre-Conference Planning Form

Elementary math coaches in the Papillion-La Vista School District use a lesson pre-conference planning form with teachers. Coaches work with teachers to consider goals and students’ experience and interests as they prepare problems and incorporate problem-solving activities into lessons.

SOURCE: Doing What Works

## Coach Talk

Listen in as two mathematics coaches discuss being strategic in the selection of problems and planning for classroom discussions including use of the Pre-Conference Planning Form.

FEATURING: Jane McGill & Danielle Inserra, Papillion Junior High School (NE)

SOURCE: Doing What Works

This sample question list is organized to go along with tasks in problem solving. Teachers can use this list to prepare prompts and to help students monitor and reflect during the problem-solving process.

SOURCE: Doing What Works

## Coach Talk

Listen to two mathematics coaches from the Papillion-La Vista School District share the concepts they emphasize when working with teachers, including the importance of comparing multiple approaches to solving a problem and debriefing the strategies students have used.

FEATURING: Jane McGill & Danielle Inserra, Papillion Junior High School (NE)

SOURCE: Doing What Works

## The Conceptual Basis for Fractions

This multimedia overview introduces how children’s intuitive understandings of sharing and proportion can serve as a foundation on which to build formal instruction of fraction concepts.

SOURCE: Doing What Works

## The Concepts Behind Operations

David C. Geary describes how to build students’ understanding of the concepts underlying operations with fractions, common misconceptions that children have, and what can be learned from their errors.

FEATURING: David C. Geary, University of Missouri

SOURCE: Doing What Works