Doing “Measurement”

I like to introduce measurement by doing it. My class on measurement starts with a wide collection of fruit lined up on the chalkboard ledge. I ask students to select three items from the collection and compare them on three dimensions. (I often provide a matrix of appropriate size on a handout or project one on the screen to give students a framework for their work.) We usually briefly discuss what some of the dimensions are that they could compare on: color, taste, size, weight, water content or density, sweetness, etc. After giving students about 5 minutes to complete their measurement matrix, we compare some of the measurements they made and discuss what measurement is: the systematic comparison, evaluation and assignment of values to objects or phenomena. They have just engaged in ‘measuring’ the fruit, even though no tape measures or scales were involved.

We then usually move on to a discussion of precision and accuracy in measurement, usually by discussing the ways in which they measured weight and color. Replicability looms large in this part of the discussion, with a focus on ways to reduce the subjectivity of measurement so that other student or researchers would obtain the same values that they did. How would we obtain reliable measurements of color? Color comparison charts (an external reference) are one option, but how would that handle the bicolored apple? Are there uses of the variable ‘color’ where the coarse measurement of red, yellow, green, etc., is sufficient? In some terms, I’ve numbered the items; we then discuss how the simple act of naming (classifying) the object as an apple or mango or whatever constitutes a form of measurement.

Just to complicate the comparison and discussion, I usually include at least one bicolored apple (red and green), one can of juice (often pineapple), some type of dried fruit, a tomato, a bell pepper, and an eggplant. (The latter three are technically fruit since they have seeds on the inside, even though most Americans think of them as vegetables.) A can of fruit cocktail is also a good ‘wrench’ to throw into the mix. Whether the dried fruit or the juice “count” as fruit is always a good discussion. If I can get unusual fruit like starfruit, kiwi, persimmon, or plantain, I like to include those alongside the usual suspects of apples, oranges, bananas, grapes, plums and the like. I typically spend no more than about $15-20 on fruit for the activity, and frequently far less in the summer.

When we’re done with the class, I usually invite them to take whatever fruit they want from the collection for snacking. I take home the rest and use it myself, or leave it in the department lounge for others.

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