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# TERC Staff Published in NCTM Yearbook

## July 3, 2006

Thinking and Reasoning with Data and Chance, the 68th yearbook of the National Council of Teachers of Mathematics (NCTM), includes two chapters by TERC staff members. Excerpts of these articles follow.

What Does It Mean That “5 Has a Lot”? From the World to Data and Back
by Susan Jo Russell

This article describes how elementary students conduct data investigations by deciding on a question, refining the data collection process, and making sense of their data.

These second graders are focused on defining their questions in a way that will be clear to those they survey and will provide information they can interpret accurately. Later in the conversation, students consider the connection between their data collection and their results:
Susannah: Everyone has to understand your question. If they don’t understand your question, everyone will be answering just any old way.
Thomas: I wouldn’t trust your data very much then!
Teacher: Why not?
Thomas: Well, people wouldn’t be thinking very hard about their answers.
Keith: If I came along and I asked the same question, then I might get different answers than Susannah because people might not really understand what we are asking. If we ask the same question and we ask the same people at the same time, then our answers should be the same.

Already these students are developing a notion of “good data”—data that are collected in such a way that they reasonably represent the events they are investigating.

Understanding Data through New Software Representations
by Andee Rubin and James K. Hammerman

This article is based on the work of the VISOR project at TERC and describes the type of classroom work made possible by data visualization software tools such as TinkerPlots.

Using proportions in the form of percents to equalize groups of unequal size is a powerful and sometimes new idea for students in middle school. In a sixth-grade teaching experiment conducted by one of the authors, several students were excited when they realized that by using percents to compare groups of different sizes, they could “make it seem like they’re even.” They much preferred this to other ideas they had been considering to deal with unequal group sizes—primarily removing points from the larger group to equalize group sizes. But they didn’t like this solution for good reasons: students couldn’t figure out which points to cut without introducing bias. …

In all these examples, we see a tension for both students and teachers between recognizing the power of “making groups even” by putting everything on a common scale of 100 and a desire for the solidity of absolute numbers. This tension between additive, count-based thinking and multiplicative, proportional thinking is difficult for students and important for data analysis. By supporting representations of both these ideas, software tools can help bring these types of reasoning out into the open to be discussed and debated.