The Perfect Principal

Overview

This activity is meant to be used as a quick assessment tool at the beginning of the year or before entering a mathematics unit on Data Management and Probability. It should be noted, however that before evaluating students' academic progress a number of assessment tools must be used. During this activity students are required to examine survey data on the desired attributes of a perfect principal, describe the information that can be extracted from the given data and calculate the mean, median and mode for the set of data provided.

Contributor: Irini Clelland, Statistics Canada Support Teacher.

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Objectives

Before students are able to satisfy the demands of the Mathematics curriculum in Canada for the intermediate level, they must understand the concepts taught in previous years. The goal of this activity is to assist teachers in assessing students' data management skills.

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Suggested grade level and subject area

Intermediate
Mathematics: Data Management

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Outcomes

Students will:

• calculate the mean, median and mode for a given set of data;
• use the given data to construct tally charts and graphs;
• read and report information about data presented in graphs and use the information to solve problems;
• understand the impact that statistical methods have on decision making; and
• make inferences and convincing arguments that are based on calculations of mean, median and mode.

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Materials

1. Writing utensils
2. Calculators and/or computers
3. Student worksheet

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Resources

Statistics: Power from data!

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Classroom instruction

The average length of time for completing this activity is estimated to be two hours, but it may vary depending on the level of students' data management skills. Students may work in small groups or individually.

If you are working in small groups at school:

• Divide students into groups of four or five.
• Assign each student a number or color that corresponds to a specific position that they will have within the group (e.g., record keeper, timekeeper, maintenance, equipment manager). These roles are usually used as a classroom management tool during group-work. Student role cards can be made and laminated for greater durability.
• Give students worksheets and instruct them to work cooperatively while completing them. During this time you should circulate to help students and/or evaluate their progress.
• At the end of the activity ask students to present their findings to the class and engage students in a meaningful conversation about their results.

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Evaluation

The students' responses to your questions and the quality of discussions generated will give you a good idea of their Data Management related skills. A checklist may be useful in evaluating students' classroom participation and group involvement. Marking their worksheets is another way of collecting information about your students' understanding of the concepts presented in this activity.

Here's one possible scoring guide for this activity:

Application
Constructed bar graphs
Level 1: All or several graphs are incomplete
Level 2: Some graphs are incomplete
Level 3: Majority of graphs are complete and appropriately labeled
Level 4: All bar graphs are completed and appropriately labeled

Application
Constructed circle graphs
Level 1: Incorrect circle graphs
Level 2: Some circle graphs are incomplete
Level 3: Most circle graphs are complete.
Level 4: All circle graphs are correctly labeled and well presented

Application
Understanding the mean, median and mode
Level 1: Incorrect interpretation of the mean, median and mode
Level 2: Some of the interpretations are incorrect
Level 3: Most interpretations are correct, but there are still errors in distinction.
Level 4: There is a clear understanding between the three measures of central tendency.

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Enrichment

Other activities students could do using the Questionnaire in this lesson are the following:

• answer the questionnaire as a class and after collecting and organizing the data write a report (supported by tables, graphs and concluding arguments) about the type of principal the class would prefer.
• compare your class' results with those from the Unidentified Grade 7 Class and discuss the similarities and differences between the two sets of students.
• critique the validity of the questions and discuss any biases that may be contaminating the quality of this project.
• conduct a similar inquiry about the perfect teacher, student or parent. Students can share their results with the school's principal or their parents and offer suggestions of how perfection can be reached.
• explore with students the changes that their children will face as a result of technological advancements.
• a philosophical conversation can be initiated about the pros and cons of perfection. Students could also create a portrait of what the perfect principal might look like after consulting the results of their data-calculations.

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Please e-mail comments or examples of how you used this exercise in your class.