Transitivity is Not Obvious: Probing Prerequisites for Learning


Empirical results from a fraction addition task reveal a surprising gap in prior knowledge: difficulty applying the transitive property of equality in a symbolic context. 13 out of the 182 4th and 5th graders (7%) correctly applied the transitive property of equality to identify the sum of two fractions in a step-by-step worked example. This difficulty was robust to brief instruction on transitivity (after which performance rose to 11%). Students’ demonstrated difficulty with transitivity is surprising, especially because common instructional techniques, such as worked examples, assume that the learner understands this concept and where it applies.

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