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How Students Learn: History, Mathematics, and Science in the Classroom
be changed but changing a model for them means (typical of high-school students) adding new information or (typical of middle-school students) replaing a part that was made wrong (p. 26).
Interpretation of Data: Students of all ages show a tendency to uncritically infer cause from correlations.18 Some students think even a single co-occurance of antecedent and outcome is always sufficient to infer causality. Rarely do middle-school students realize the indeterminacy of single instances, although high-school students may readily realize it. Despite that, as covariant data accumulate, even high-school students will infer a causal relation based on correlations. Further, students of all ages will make a causal inference even when no variation occurs in one of the variables. For example, if students are told that light-colored balls are used successfully in a game, they seem willing to infer that the color of the balls will make some difference in the outcome even without any evidence about dark-colored balls.
Inadequacies in Arguments: Most high-school students will accept arguments based on inadequate sample size, accept causality from contiguous events, and accept conclusions based on statistically insignificant differences.19 More students can recognize these inadequacies in arguments after prompting (for example, after being told that the conclusions drawn from the data were invalid and asked to state why).20
PRINCIPLE #2:KNOWLEDGE OF WHAT IT MEANS TO “DO SCIENCE”
Feynman characterized the scientific method in three words: observation, reason, and experiment.21 Einstein emphasized the importance of imagination to scientific advancement, making it possible for the reasoning that follows observation to go beyond current understanding. This view of science extolled by some of its greatest minds is often not recognizable in classroom efforts to teach students how to do science.
We have noted that in the past, teaching the processes, not just the outcomes, of science often involved no more than memorizing and reproducing the steps of an experiment. However, even when science instruction