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## Developing a Meaningful Understanding of the MEAN

### Using a Journal Article as a Professional Development ExperienceFOY 2007-2008 Data Analysis & Probability

 Title:Author:Journal:Issue: Developing a Meaningful Understanding of the MEANElizabeth George BremiganMathematics Teaching in the Middle SchoolSeptember 2003, volume 9, issue 1, pp. 22-26

Rationale/Suggestions for Use

The concept of arithmetic mean is typically taught as a procedure rarely answering the question, “What does it mean to understand the mean?”  This article provides participants with two tasks to build their understanding of measures of central tendency using the research of Strauss and Bichler (1988). This article may be used with pre-service teachers or in-service teachers interested in exploring ways to incorporate the study of single-variable statistics in their classroom.

Procedures/Discussion Questions

• Ask participants to brainstorm characteristics of the arithmetic mean with individual think time (Think-Ink), followed by share time with a partner (Pair) and finally share with the whole group (Share). Chart the whole group responses. Distribute a copy of the “Properties of the Mean” from the Strauss and Bichler research on page 23 of the article. Compare the properties listed in the article to the whole group’s list. Add any other properties the group may have overlooked or that may arise in the discussion.
• Do the math! Ask participants, in small groups, to complete the “Fund-Raising Contest” task on page 23 of the article. Invite each small group to chart its solution to the task indicating where members encountered the various “Properties of the Mean.” Select one small group to present the findings to the whole group and ask other groups to add any different solutions or results.
• Possible questions for the facilitator:
• How did your group decide which of the five groups in the fund raising task was most successful? How did your group justify that decision?
• Which of the properties from “Properties of the Mean” became important or visible as your group completed the task?
• How did the discussion in your group help you better understand the “Properties of the Mean?”
• Request that participants read the section titled, “The Fund-Raising Contest” beginning at the bottom of page 23 and continuing through page 24. Compare participants’ solutions and insights to the problem to those presented by the students in the article (chart these).
• Ask participants to return to small groups to complete the “What Happens If…? task on page 25 of the article. Use the questions from the task to prompt discussions in small groups. Assign specific questions from the task to different small groups to present to the whole group. Remind groups to refer to the “Properties of the Mean” as appropriate.
• Request participants return to the article to read the section titled, “What Happens If…?” beginning at the bottom of page 24 and continuing through page 26. Compare participants’ solutions and insights to the problem to those presented by the students in the article (chart these).
• Discuss ways to incorporate the two tasks in the article into your classroom instruction/curriculum materials.
• Ask participants to use the two tasks with at least one class of students and bring student work samples to share at the next meeting.

Extensions

• Find or create other data sets that would allow for discussion of the “Properties of the Mean.”
• Create parallel documents to the “Properties of the Mean” for the other measures of central tendency (median and mode).
• Create parallel tasks that would allow investigation of the median and mode.
• Investigate the Data Analysis and Probability Strand in the PSSM for middle school and high school participants to better understand the trajectory of single-variable statistics in the secondary school curriculum.

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