# Transitivity is Not Obvious: Probing Prerequisites for Learning

- Eliane Wiese,
*Carnegie Mellon University*
- Rony Patel,
*Carnegie Mellon University*
- Jennifer Olsen,
*Carnegie Mellon University*
- Ken Koedinger,
*Carnegie Mellon University*

## Abstract

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.

Back to Table of Contents