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Representation as a Vehicle for Solving and Communicating

Using a Journal Article as a Professional
Development Experience


Representation as a Vehicle for Solving and Communicating 
Ronald V. Preston & Amanda S. Garner  
Mathematics Teaching in the Middle School 
September 2003, Volume 9, Number 1   

Rationale for Use

This article provides mathematics teachers an activity that explores use of multiple representations in their classroom, but also builds teachers’ understanding of representations as “tools that are vital for recording, analyzing, solving, and communicating mathematical data, problems, and ideas (p. 39).”

Suggestions for Use

This activity may be used with groups of middle school teachers or individuals who are interested in a careful examination of middle school students’ use of representations.


  1. Participants should solve The Class Party Problem individually.
  2. Have participants discuss their problem-solving approaches in small groups and post all group members’ solutions on white paper.
  3. In whole-group discussion, have small groups share their approaches to solving the problem that they posted on white paper. The facilitator should allow each group to share one strategy until all strategies have been shared.
  4. Have participants brainstorm other possible representations students might use. Display the ideas generated during brainstorming.
  5. Have participants individually read the article.
  6. Engage the participants in discussing the following questions:

    a. How do you help students understand which style of graph works best in a certain situation? Refer to Figure 5 after this question has been discussed.

    b. How do you help students in your class, like the student in Figure 2, move beyond the guess and check approach?

    c. What do you think the author means by “Note that a lot of action is depicted in this Standard (p.40)”?
  7. Ask participants to generate a list of questions that they will use in their classroom when implementing this activity with anticipated student responses to each question. Suggest that they include questions to ask students who are struggling as well as students who understand the concept. Additionally, as participants to generate reflection questions they can ask themselves after the activity.
  8. If there is a follow-up session scheduled, ask participants to collect (and bring) samples of student work, and to reflect on the student work using the reflection questions they generated before coming to the session. Use the session to discuss what they learned about their students’ use of representations and any discoveries they made about their teaching or their students’ understanding after taking time to reflect.


  • Participants should use the Representation Standard to create an action plan that outlines the incremental steps that document student growth.
  • Have participants create a rubric to score the use of representations.

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