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.
