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Formulating Measures: Toward Modeling in the K-12 Science and Mathematics Curriculum


"Models are ways of relating the behavior of different measures to one another. Measures are constructs that we devise to quantify the amount or degree of a property of interest. It follows that to devise models one first needs to be able to formulate measures. We explore the sorts of measures that are all too often taken for granted in the K-12 mathematics and science curriculum, with particular attention to quotient measures and product measures. In particular, we propose a problem type that explicitly parses the act of modeling into 1) a initial stage in which measures are formulated, 2) a next stage in which relationship among these measures are postulated. There is, of course a final stage, which will not be discussed, in which measurements are made and decisions made as to whether the model is sufficient for the purpose for which it is formulated or needs to be revised."