# When to Block versus Interleave Practice? Evidence Against Teaching Fraction Addition before Fraction Multiplication

- Rony Patel,
*Carnegie Mellon University*
- Ran Liu,
*Carnegie Mellon University*
- Kenneth Koedinger,
*Carnegie Mellon University*

## Abstract

In practice, mathematics education is blocked (i.e., teaching one
topic at a time; CCSS, 2010), but research generally promotes interleaving (i.e.,
teaching multiple topics together; Rohrer & Taylor, 2007). For example, fraction
arithmetic is blocked with students being taught fraction addition before
fraction multiplication. Since students often confuse fraction operations to
produce arithmetic errors, interleaved fraction arithmetic instruction might be
more productive than blocked instruction to teach students to discriminate
between the operations. Additionally, a cognitive task analysis suggests that
fraction multiplication may be a prerequisite to fraction addition and thus
reversing the blocking order may enhance learning. Two experiments with fraction
addition and fraction multiplication were run. Experiments 1 and 2 show that
interleaved instruction is generally better than the current blocked instruction.
Experiment 2 provides evidence that blocking that reverses the standard order --
providing practice on fraction multiplication before fraction addition --
produces better learning.

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