Spring 2008

How Children and Adults Think About Data

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Children’s and adults’ understanding and use of data characteristics

In addition to considering the interplay between theory and data in the context of simple science experiments, another related line of work I have pursued (in collaboration with Dr. Brad Morris at Grand Valley State University) involves exploring the specific characteristics of data children and adults use. Although many researchers have demonstrated that theoretical background knowledge influences data interpretation (e.g., Chinn & Malhotra, 2002; Koslowski, 1996; Kuhn & Dean, 2004; Schauble, 1996), few have looked directly at how characteristics of data influence theoretical knowledge.

In a forthcoming paper, we describe work in which we asked third graders, sixth graders and college students to reason about sets of data (Masnick & Morris, in press). The data were presented as paired comparisons of outcomes (i.e., distance traveled) from either a robot or athlete using different sports balls (such as golf balls, baseballs and basketballs). On each trial, participants saw two columns of data. The data sets varied by sample size (number of data points) and by how much the data varied (for example, in some data sets, all the numbers in one column were larger than the numbers in the other column, while in other data sets, many of the numbers overlapped). Participants were asked to state their confidence that the two columns of data were the same or different from one another.

We found that although college students are much more likely to base their confidence ratings on data characteristics, even in the third grade, many students used sample size and variation (i.e., the differences between the numbers in each column) when rating how confident they were that there was a difference between sets. In addition, with age, they improved their ability to discuss the reasons for their confidence in terms of characteristics in the data. Interestingly, despite the fact that participants were deliberately given very little contextual background from which to draw conclusions, approximately half the participants in each age group came up with reasons for the data outcomes that relied on issues other than the data – factors that focused on theoretical background knowledge they inferred to explain the patterns of data. For example, many inferred that a robot would be less variable than a person, and suggested a reason for a difference in outcomes might be due to how much each ball was inflated or how aerodynamic each ball was.

In some follow-up work, we have been exploring other ways of looking at how people represent number sets in the brain. One strategy for assessing such representations involves looking at reaction times and accuracy in choosing which set has higher numbers. We have asked people to quickly compare number sets with varying characteristics, including sample size, difference between means, and range of the numbers. If reaction times and accuracy vary based on multiple data characteristics, it might suggest that cognitive representations of number sets include information about these characteristics, and that these characteristics may be considered either implicitly or deliberately in making judgments about the data.

Summary

Even without formal statistics training, many children and adults recognize and use data characteristics such as variation and sample size when drawing conclusions. However, context matters. Reasoning when data generally match prior expectations does not lead to belief revision, though even in these situations children do exhibit some beginning understanding of different sources of errors and variation in the data. Also, when children and adults use these data characteristics, they cannot always clearly articulate their reasoning. With age and experience, they talk more explicitly about how these characteristics play a role, but their reasoning is not always linked directly to their conclusions. There is still much to learn about how we learn and use data, and what factors lead to change over time. Understanding more about the cognitive representations we create of data may be one important step toward improving our understanding of this topic.

*Many of the issues discussed in this essay are described in greater detail in: Masnick, A.M., Klahr, D., & Morris, B.J. (2007). Separating signal from noise: Children's understanding of error and variability in experimental outcomes. In M. Lovett & P. Shah (Eds.), Thinking With Data (pp. 3-26). New York: Lawrence Erlbaum Associates.

Acknowlegdements

Funding for the research described here was supported in part by NIMH training grant T32 MH19102, NICHHD (HD25211) to David Klahr, and NSF (HD25211) to David Klahr and partially subcontracted to Hofstra University.

References

Chen, Z., & Klahr, D. (1999). All other things being equal: Acquisition and transfer of the Control of Variables Strategy. Child Development, 70, 1098, 1120.

Chinn, C.A., & Brewer, W.F. (2001). Models of data: A theory of how people evaluate data. Cognition and Instruction, 19, 323-393.

Chinn, C A., & Malhotra, B. A. (2002). Children’s responses to anomalous scientific data: How is conceptual change impeded? Journal of Educational Psychology, 94, 327-343.

Klahr, D. & Nigam, M. (2004). The equivalence of learning paths in early science instruction: Effects of direct instruction and discovery learning. Psychological Science, 15, 661-667.

Koslowski, B. (1996). Theory and Evidence: The Development of Scientific Reasoning. Cambridge, MA: MIT Press.

Kuhn, D., & Dean, D., Jr. (2004). Connecting scientific reasoning and causal inference. Journal of Cognition and Development, 5, 261-288.

Masnick, A.M., & Klahr, D. (2003). Error matters: An initial exploration of elementary school children’s understanding of experimental error. Journal of Cognition and Development, 4, 67-98.

Masnick, A.M., & Morris, B.J. (in press). Investigating the development of data evaluation: The role of data characteristics. Child Development.

Schauble, L. (1996). The development of scientific reasoning in knowledge-rich contexts. Developmental Psychology, 32, 102-119.