## Representations in Teaching and Learning Fractions

In this article from the NCTM journal, Teaching Children Mathematics, author Tad Watanabe presents various issues related to the use of representations in the teaching and learning of fractions. The three most common fraction models are considered and examples of student misconceptions are provided.

Related content 1:
http://www.nctm.org/publications/article.aspx?id=21293

## Creating, Naming, and Justifying Fractions

This article is from the NCTM journal, Teaching Children Mathematics. For students to develop meaningful conceptions of fractions and fraction operations, they need to think of fractions in terms other than as just whole-number combinations. The authors, Daniel Siebert and Nicole Gaskin, suggest two powerful images for thinking about fractions that move beyond whole-number reasoning and can be used in the classroom to help support the teaching of fractions.

Related content 1:
http://www.nctm.org/publications/article.aspx?id=21961

## PoW Membership: Resources & Strategies for Effective Implementation

After completing this online course, current subscribers of the Math Forum's Problems of the Week (PoWs) will be familiar with all the resources associated with their PoW membership access. During rounds 2 and 5 of the six-week course, attention is focused on strategies to encourage students to develop their communication skills, both verbal and written. Participants will be able to make an informed decision about how to start implementing PoWs with their students, and they will have an idea of further steps to try when they are ready.

Related content 2:
http://mathforum.org/pd/membership/

## Problem Solving in Geometry and Measurement

This course will provide teachers an opportunity to deepen their understanding of topics and student learning in geometry and measurement and the problem solving process. Teachers will discuss their own solutions to problems about perimeter, area, volume, and properties of triangles. Exploration will include the use of interactive applets and dynamic geometry software. Teachers will analyze student work to discover strengths and weaknesses in order to make more effective instructional decisions. The course is available from the Math Forum for a reasonable fee.

Related content 2:
http://mathforum.org/pd/geometry/

## PoW Membership: Resources & Strategies for Effective Implementation

After completing this online course, current subscribers of the Math Forum’s Problems of the Week (PoWs) will be familiar with all the resources associated with their PoW membership access. They will be able to make an informed decision about how to start implementing PoWs with their students, and they will have an idea of further steps to try when they are ready. Both PoW membership and this course are available from the Math Forum for a reasonable fee.

Related content 2:
http://mathforum.org/pd/membership/

## Math Conversation Starters

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Use the resources in this collection to encourage your students to talk about the math they use to play the game or solve the problem. Encourage them to share their thoughts and describe their strategies to one another as they figure out the best moves or steps in a process. Provide students with opportunities to demonstrate their work and explain their reasoning using the language of mathematics. Listen carefully as your students interact with one another to exchange ideas, organize their thoughts, present their arguments and consider the suggestions of their classmates. These resources provide you with starting points that engage students in mathematical thinking and communication.

Resources list:
MATH-PATH-000-000-000-466~Coloured Squares
MATH-PATH-000-000-000-339~Calculation Nation
MATH-PATH-000-000-000-408~Making Trains
MATH-PATH-000-000-001-091~Exploring Number Sequences
MATH-PATH-000-000-000-934~Venn Diagrams
MATH-PATH-000-000-000-363~GOT IT
MATH-PATH-000-000-000-875~Patterns in Mathematics-Number Patterns
MATH-PATH-000-000-000-572~Junior Frogs
MATH-PATH-000-000-000-431~Chairs
MATH-PATH-000-000-000-311~Coloring Remainders in Pascal
MATH-PATH-000-000-000-099~Coloring Multiples in Pascal

## Why Math Blogs?

In this action-research study, published in the NCTM journal Teaching Children Mathematics, a third-grade teacher explores the impact of student blogs on the quality of their mathematical discussions. The teacher introduced math blogs to facilitate a productive online discussion focused on multistep story problems. This study is for teachers who want to develop student understanding through writing using technology. The article has a helpful hint section that focuses on how to set up blogs.

Related content 1:
http://www.nctm.org/publications/article.aspx?id=22159

## Promoting Mathematical Discourse through Children's Literature

Four examples of children's books that can be used to facilitate mathematical discussions in teaching and learning are suggested in this article, from the NCTM journal Teaching Children Mathematics. The authors summarize each story, indicate the standards that are addressed by each book, suggest the appropriate grade levels, and provide discussion prompts and questions.

Related content 1:
http://www.nctm.org/publications/article.aspx?id=21389

## Promoting Communication in the Mathematics Classroom

This article, from the NCTM journal Teaching Children Mathematics, describes the importance of children representing their mathematical understanding in many different ways. These modes of communication include building, writing, drawing, and talking. Using the classic story “One Hundred Hungry Ants” the authors provide discussion questions and samples of students’ journal entries as they communicate their mathematical ideas and explanations.

Related content 1: