Measuring Up Prototypes for Mathematics Assessment (1993) / Chapter Skim
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The Hog Game
The Hog Game
Pages 141-156
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background: This task uses a game callecl Hog to pose questions that require students to use two areas of mathematics to answer. On the first day the questions concern combinatorics and reasoning about the possibility or impossibility of certain outcomes.
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Presenting the task: The teacher should pass out the first student sheet and several number cubes (cubes numbered from 1 to 6) to each pair of students being assessed.
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r -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ___________________~ |Names and Datel l l l l 1 1 ,This is a game called HOG. You will need number cubes, a cup,, I and pencil and paper.
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Names Part 1 and 1. Tsao-lim said he wanted put 8 number cubes in the cup.
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l l 4. Johann said he wanted to put ~ number cubes in the cup.
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; i ! ; Here are some more questions about the game called HOG.
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7. Suppose you want to find the best strategy for playing HOG.
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In this case, some of the questions about the game involve relatively simple numerical concepts, while other questions involve more sophisticated ideas from probability. Even the simplest numerical questions are non-routine, however, and are presented in a format that requires the child to explain his or her reasoning carefully.
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There are many variants of the simple numerical questions that can be posed along the lines suggested in question 4. A more substantial variant is to ask how many number
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Part 2. This task provides a good example of how the inc~usion of intermediate questions can provide a "scaffolding" to help students approach the problem of deciding whether : ~ v ~ .
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The second a~ternative simply exacerbates the problem of making unambiguous judgments, since it is possible that many children will do better on one part of the task than on the other. Hence two protorubrics are provided below, one for each component of the task.
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High ri~ 9' A Question 6 (Part 2) There is evidence in questions 1 and 2 that the student forgets or ignores the fundamental rule of the Hog Game.
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The final strategy chosen should be based on the empirical evidence gathered. No fourth-grade child should be expected to choose a strategy on any basis more sophisticated than the successive approximation method outlined above.
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In question 6, the response is empirically based on playing the game repeatedly, but using a small number of trials, or based on trials that are not clearly organizecl. Or the claim is that Roberto's strategy is better because he rolls more and hence has more of a chance to get more points (i.e., not taking into account that Roberto also has a bigger chance of rol l i ng a 1, and thus getting a score of 0~.
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