Ch 5

Problem
Solving

Concepts

Processes

Tools

Context

Way of Being

This activity requires students to carefully walk through a Case Study of the Problem Solving Methodology. It is a complex example and students will need some time to understand how and why each step and calculation is necessary. If your students do not have strong math skills, it would be most appropriate for them to complete this activity in teams or groups.

1. Why do the students have to make assumptions rather than finding out all information?
   It is important that students appreciate that the students in the Case Study are solving a theoretical problem. That is, they are working with square footage, a floor plan, a dollar amount, and potential future conditions, rather than standing in the apartment itself right now, with money-in-hand. As such, the problem solving in the case study is a kind of planning.

2. How did the students determine the values for each of the following? Where was the information obtained?

• Cost per square foot:
  This is calculated in the "Model cost of each room" section. The necessary information was given in the problem (total square footage, floor plan with dimensions, monthly cost of rent, $50 premium for a private bedroom)

• Cost for common area:
  Once cost-per-square-foot has been calculated, this figure ($0.3779) can be applied to any room to determine the value of that room. Common area is defined and the cost calculated in the "Integration" section (common area = total house area – total bedroom area; cost of common area = common area × cost per square foot)

• Cost for each student:


The student in the private room (student #1) pays for that room + $50 per month premium. The students sharing a room (#2, #3) split that cost in half. And all three students will share equally (thirds) in paying for the common area. Student #1: bedroom #1 + $50 + 1/3 common area. Student #2: 1/2 bedroom #2 + 1/3 common area. Student #3 is the same as student #2.

3. What assumptions made by the students do you question? Why? What assumptions were never used in solving the problem?
   The assumption that every square foot of space has the same value is one that the students even come to question, along with the private room being worth $50 more per month. The students never considered a rent deposit or possible additional costs (i.e. what if only one bedroom had a phone line?).

4. Why is it important to build and use models when problem solving? Do you agree with the models the students created? Why or why not?


Students should work with the idea of a model as a way to plan.

5. What are some other key issues that the students could have considered for this problem? Which key issues were never used in solving the problem?
   They never dealt with whether or not each student could afford the $50 premium for a private room, or whether or not any two students (all three possible combinations) were willing to share a room. Additional potential key issues not considered might be things like: What about the students' schedules (what if one with early morning classes was supposed to share a room with one who had a late-night part-time job)? Encourage your students to brainstorm other potential issues.

6. Do you feel the students made the correct decision? Why or why not? If not, describe an alternative model.
   Encourage students to consider other possible ways of modeling the problem.

In this activity, students are given two options and must decide, through application of the Problem Solving Methodology which option they would select. There is space provided for them to complete each step. Note that you, as the instructor, have a great deal of latitude in how you want students to complete this activity. If you do not task students with doing additional research (i.e. finding out the cost of a Caribbean cruise), they will be forced to make assumptions and personal preferences will almost certainly be the determiner for their 'solution.' And that's fine; students must still note those assumptions and plan how they would find the information they need (i.e. Step 3, Collect data and information). You may want to assign costs to the two options. If you do this, consider making the costs somewhat complex (e.g. The cruise option might be a cruise cost of X and airfare cost of Y, with a booking fee of Z). This is just an example; depending upon how involved you want the problem to be, you may a) insist that students work the problem as stated, b) provide additional information, or c) ask that they actually collect minimal data and information (the cost of the two options).

Notes on the Critical Thinking Questions

Appreciate that students will struggle with some of the steps because of the nature of the problem. Not all problems are straightforward and we must often 'solve' problems where we do not have all the information we might like. When we do this, we make assumptions. There should be a correlation between available information and assumptions. This topic alone is worthy of a class-level discussion. The Critical Thinking Questions for this activity are focused upon helping students become aware of the process of problem-solving. They are also tasked with assessing their problem solving work. Be sure that students are truly assessing and not evaluating their performance.

1. What step in this process was the most difficult? Why?

2. Were there steps in this process that you found less useful than others? Explain.

3. Provide three insights you have about the Problem Solving Methodology after completing this activity.

4. Assess your work on this activity. What did you do well? What could you improve for future problem-solving situations?

5. If you worked as part of a team, do you feel the students on your team made the correct decision? Why or why not? If not, describe an alternative model.