Academic journal article Psychonomic Bulletin & Review

Spacing and the Transition from Calculation to Retrieval

Academic journal article Psychonomic Bulletin & Review

Spacing and the Transition from Calculation to Retrieval

Article excerpt

Many arithmetic problems can be solved in two ways-by a calculation involving several steps and by direct retrieval of the answer. With practice on particular problems, memory retrieval tends to supplant calculation-an important aspect of skill learning. We asked how the distribution of practice on particular problems affects this kind of learning. In two experiments, subjects repeatedly worked through sets of multiple-digit multiplication problems. The size of the trained problem set was varied. Using a smaller set size (with shorter average time between problem repetitions) showed faster responses and an earlier transition to retrieval during training. However, in a test session presented days later, the pattern reversed, with faster responses and more retrieval for the large set size. Evidently, maximizing the occurrence of direct retrieval within training is not the best way to promote learning to retrieve the answer. Practical implications are discussed.

It has long been clear that spacing of explicit learning (distributing a fixed amount of study time for certain materials over a longer period) can powerfully increase the probability that these materials can be recalled. Less well known are the inconsistent effects of spacing on other kinds of learning, in particular those related to skill acquisition. In the present study, we examine the effects of temporal spacing on a particular form of skill learningthe performance improvement that occurs as people repeatedly do arithmetic calculations. This form of learning differs from that considered in the "standard" studies of spacing in the episodic memory literature in at least two respects. First, the information recalled is not taught to the learner by the experimenter, but is self-produced. second, the most conspicuous change is in speed of response, rather than accuracy. For reasons we discuss, effects of spacing in this situation might not parallel those found with episodic memory designs.

Spacing Effects

Evidence that spacing can enhance recall probability goes back to Ebbinghaus (1885/1964). Spacing has been shown to be quite robust in a variety of tasks involving verbal episodic recall (see Cepeda, Pashler, VuI, Wixted, & Rohrer, 2006, for a recent review). Various studies have documented the fact that spacing increases the probability of success in cued recall and paired associate tasks with long retention intervals (e.g., Glenberg, 1976; Glenberg & Lehmann, 1980; Pashler, Rohrer, Cepeda, & Carpenter, 2007; Rumelhart, 1967). Spacing can also help children recall newly taught mathematical facts (Rea & Modigliani, 1985).

However, when one looks across the broad category of "skill learning" or "implicit memory," tasks where the repsponse does not typically involve explicit recollection, the beneficial effects of spacing are far less clear. For example, spacing effects do not seem to be robust for perceptual identification and word fragment completion tasks (Greene, 1990; Perruchet, 1989). In our lab, we did not find substantial spacing effects for tasks involving visuospatial categorization learning (Pashler et al., 2007).

Transitions From Calculation to Retrieval

A particularly prominent consequence of arithmetic skill learning is a gradual increase in the occurrence of direct memory retrieval-directly recollecting the answer in one step, rather than relying on calculation using an explicit algorithm. There has been debate about whether retrieval occurs simultaneously with calculation on any given trial (as suggested by Logan, 1988; Palmeri, 1997) or merely supplants calculation (Rickard, 1997, 2004). There is little doubt, however, that with repeated exposure to a given arithmetic problem, retrieval becomes more frequent.

The Present Experiments

The present study poses a fairly straightforward question that bridges the topics of spacing and the algorithmto-retrieval transition. We ask how spacing of training on specific problems affects this transition. …

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