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Presentation 7F2. Technology, Statistics, and Subtleties of Measurement: Bridging the Gap between Science and Mathematics

Tim Erickson (USA)


Presentation Abstract
In an ideal world, science students would act as scientists do: investigating their own questions, designing experiments, and so forth. This paper reports on curriculum development and field testing that takes a step in this open-ended direction. To make this work, we have to make sure that science students have the mathematics background they need.

What mathematics is that? Data analysis and statistics, of course. But here we will focus on a narrower field: measurement. In the USA, "measurement" includes using rulers in elementary school and doing unit conversions in middle school. But by secondary school, measurement topics such as dimensionality are most often folded into geometry.

We can profitably and properly extend the study of measurement to include topics such as error in physical measurements. This connects directly to statistics topics such as measures of spread and standard error.

We can go further, however: we can also ask students to use mathematical reasoning to better choose what to measure and to evaluate the consequences of that choice. This begins with indirect measurement, for example, measuring angles and using trigonometry to find a long distance instead of employing a more direct (and perhaps less accurate) technique. Here students use technology both to perform the calculations and to simulate (without calculus) how measurement error propagates into the result.

A look at the physical science curriculum shows us that there are a number of places where this kind of thinking - and where this student skill - is useful. This talk will describe what else we can explore beyond simply estimating measurement error.

Thus science students can have a bigger role in choosing what they measure and how - as scientists do. We hope these ideas and technologies give teachers and students the tools they need to be responsibly more open-ended.


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