Minutes of meeting 02.09.2001

Present: Tom Moher, Alex Hill, Yongjoo Cho

We went through step-by-step procedures how to teach comparison of distributions

1. Motivating comparison of distribution.

How are we going to motivate students to compare distributions from one to another. We need at least three distributions to motivate students to compare one another. Students can do the actual survey of likes or dislikes of broccoli in different classes. Then we can change the numbers a little to make them have the same total population for every class so we don’t have to deal with normalization until later.

2. Representing distributions

With the numerical values we got from the survey, we are going to provide students a table with numeric values. Then, we can ask students what alternative representations they can think of? Students may come up with pie charts, bar graphs, and so on. We can then ask again what would be the features of those different representations. Depends on students’ answers, we may have to guide them to talk about at least pie charts and bar graphs at this stage.

3. Using representations to qualitatively compare distributions

We’ll probably provide the pie charts and bar graphs for the survey data to students. Then, we can ask how are they different from one another. We are not trying to come up with any numeric metrics for the difference at this stage. If students can say this is more similar to the other or totally different from the other. Pie chart might be more appropriate for this than bar graphs.

4. Quantitative comparisons: developing metrics

After students compare the distributions qualitatively, now we have to bridge them to compare the same distributions quantitatively. The question we have for this is whether students need to do this as a whole class activity or in small groups. We are leaning toward to small group activity. We are probably going to ask students to come up with their own group’s metrics for comparing two distributions shown in bar graphs. We are trying to stick with bar graphs to get the metrics but we can probably ask students to do the same thing again with pie charts to show them how hard it would be doing it with pie charts. The metrics we are trying to get from the students is overlaying two bar graphs and measure the actual difference between them. They would sum up the differences of each bar.

5. Normalization issues

At this stage, students are expected to have their own metrics to compare distributions with the same total population. Now we are trying to bridge them to the comparison among distributions that have different populations. Let’s say comparing Ms. Rothstein and Peterson’s class to motivate students. We can ask questions like “Which class likes broccoli more?” Since Ms. Peterson’s class has smaller number of students than Ms. Rothstein’s class, we cannot really compare the raw numbers with our own metrics developed in step 4. We can provide them bar graphs with raw number of students and pre-calculated percentages in each class. Then, we can ask them to calculate the differences with the metrics with the percentiles instead of raw numbers. We are not going to ask students to calculate the difference for the raw numbers because it may confuse them. Again, we are not going to show them how to calculate the percentages yet not to confuse them with the fractions and calculating algorithms. First, we’ll show a bar graph from both classes (i.e, the percentages of students who like broccoli). Then, we are going to help the students learn how to compare multiple bars based on the comparison of single bar. After they understand how to compare the differences between two distributions that have different number of total populations, then we can go through the steps of calculating percentages a little more detail.