Comparing Grizzly Bears and Black Bears | Measuring Up: Prototypes for Mathematics Assessment |The National Academies Press
Rationale for the mathematics education community
The task requires students to analyze a fairly complex set of measurements obtained from a “real world” context that is appealing to children of this age group. Rather than simply reading individual values on a graph or from a table, they must view the data set as a whole. More specifically, the problem reveals students’ ability to create a representation that shows these data on a reasonable scale in a way that allows comparison of the two groups. (Some students may also find ways to show males and females within each group, thereby coping with one numerical and two categorical variables.)
A second reason for including the task in this collection is that it pushes the curriculum to include work in data analysis, specifically:
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organizing unordered data in a representation that reveals the overall shape and characteristics of the data set;
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describing data sets;
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summarizing data in a way that enables one to compare two data sets.
As with the other tasks in the collection, it requires students to communicate their thinking verbally and graphically.
Task design considerations: Note that there are not the same number of bears of each type, which forces the student to consider more than just the total weights. In fact, the data have been adjusted so that the sums of the weights are the same. This will serve as a subtle hint to the child who adds the two columns of figures and is tempted to stop at that point.
The heaviest bear in the entire set is a grizzly, which is the heaviest kind of bear. When looking at student responses, one must be careful to distinguish reasoning that relies on the difference between the central values of the weights from reasoning that simply cites the heaviest bear.
Even though many of the difficulties associated with performing computations on data have been obviated by the advent of inexpensive hand-held calculators, finding suitable “real world” data is still tricky. Of course children should have
