Comparing Two Airlines

This activity has the following goals for students:

1. Expose students to a real-world problem with data.
2. Expose students to ideas of central tendency and variability.
3. Provide students with an informal conceptual understanding for comparing groups.
4. Engage students in statistical thinking and working as a team.

This activity:

• Is appropriate for use at any time in an introductory statistics course.
• May be adapted for junior high, high school, and college‐level instruction.
• Is most effective when students work in groups of 3‐4.
• Lasts 50 ‐ 75 minutes. The reading and individual student responses can take place prior to class and comparison of student reports can take place at a subsequent class or via an online class management system.

1. Media article: Students individually read the media article to become familiar with the context of the problem. Comparing-Airlines-Media-Article (Acrobat (PDF) 155kB Sep15 10)
2. Readiness questions: Students individually answer these reading comprehension questions about the media article to become even more familiar with the context and begin thinking about the problem. Comparing-Airlines-Questions (Acrobat (PDF) 70kB Sep15 10)
3. Problem statement: In teams of three or four, students are given the problem statement and work on the problem in a group for 30 ‐ 45 minutes. Comparing-Airlines-Problem-Statement (Acrobat (PDF) 98kB Sep15 10) This time range depends on the amount of self‐reflection and revision you want the students to do. Students are given an initial set of graphs Comparing-Airlines-First-Graph (Acrobat (PDF) 68kB Sep15 10) to develop measures and rules. After they develop their initial method, students are then given an additional set of graphs to modify their method Comparing-Airlines-Second-Graphs (Acrobat (PDF) 167kB Sep15 10)(Note: The actual data used to produce the graphs is provided in the Excel file Comparing-Airlines (Excel 16kB Sep15 10) if the instructor wants students to analyze the data themselves.)
4. Process of sharing solutions: Each team writes their solution in a letter or memo to the client. Then, each team presents their solution to the class. Whole class discussion is integrated with these presentations to discuss the different solutions, the statistics involved, and the effectiveness of the different solutions in meeting the needs of the client.

The following supplies and materials are recommended for this activity.

• Computers with word‐processing programs to write up their reports.
• Optional: Computers with programs such as Fathom and Excel
• Optional: Calculators
• Optional: Materials for students to create posters to share their solutions.

1. The purpose of the media article and the readiness questions is to introduce the students to the context of the problem. Depending on the grade level and/or your instructional purposes, you may want to use a more teacher‐directed format or a more student‐directed format for going through the article and the questions.
2. Place the students in teams of three or four. If you already use teams in your classroom, it is best if you continue with these same teams since results for MEAs are better when the students have already developed a working relationship.
3. Encourage (but don't require or assign) the students to select roles such as timer, collector of supplies, writer of letter, etc.
4. Remind the students that they should share the work of solving the problem.
5. As students work in groups, the teacher's role should be one of a facilitator and observer. Avoid questions or comments that steer the students toward a particular solution. Try to answer student questions with questions so that the student teams come to their own solutions.
6. Watch the time and try to urge groups on if they are falling behind.
7. If students seem to get off task and are not focusing on the data provided, direct them back to the actual data and task. Students become very engaged in this activity and it is easy for them to get off track. When students get off track (e.g., spending a lot of time telling their own airline stories), remind them of the task for that part of the activity (e.g., "Have you come up with 5 numerical measures?" "Have you come up with a rule?").
8. If more follow‐up is desired, after presentations and discussion, allow students to resume their groups and modify their models.

Assessment is an integral part of a model‐eliciting activity. Each group is required to write a report to a "client" that describes their model, the reasoning that led to the model, and a justification of all decisions that are made based on the model. Group reports may be assessed for their clarity, completeness and the soundness of the explanations and justifications. In addition, instructors can decide if they wish to evaluate the students' presentations. Example rubric and scoring methods for student reports and presentations can be found at:

https://engineering.purdue.edu/ENE/Research/SGMM/Problems/CASESTUDIESKIDSWEB /casestudies/airport/tools.htm

Follow‐up questions to the MEA may be used to assess student learning outcomes. For example,

• What do you think you learned from this activity?
• What questions do you have as a result of completing this activity?

Additional assessment items may be used depending on the purpose for using the activity and the nature of the course.

• CAUSEweb includes other interesting activities for developing student understanding of related statistical content: http://www.causeweb.org/repository/StarLibrary/activities/
• More examples of model‐eliciting activities can be found at: https://engineering.purdue.edu/ENE/Research/SGMM/Problems/MEAs_html