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01-09-2008 | Original Article

Practice effects on strategy selection and strategy efficiency in simple mental arithmetic

Auteurs: Ineke Imbo, André Vandierendonck

Gepubliceerd in: Psychological Research | Uitgave 5/2008

Abstract

Two experiments were conducted to investigate the effects of practice on strategy selection and strategy efficiency in mental arithmetic. Participants had to solve simple addition or multiplication problems, after having received 0, 3, or 6 practice sessions (Experiment 1), and before and after having received 3 practice sessions (Experiment 2). Strategy selection was measured by means of trial-by-trial strategy reports, whereas strategy efficiency was measured by means of response latencies. Results showed significant practice effects on retrieval frequency, procedural frequency, retrieval efficiency, and procedural efficiency. However, practice effects on strategy efficiency appeared to be both strategy-specific (i.e., only for procedural strategies) and operation-specific (i.e., only for multiplication problems). Implications of the present results for mathematic cognition and its modeling are discussed.

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In the present paper, the term ‘training’ is seen as the explicit training of a particular strategy, whereas the term ‘practice’ is seen as exercising through repetition, without enforcing a particular strategy.

There exist several recent adaptations of the ASCM, such as the strategy choice and discovery simulation (SCADS) model (Shrager & Siegler, 1998), which incorporates the ASCM but also models metacognitive processes to allow for the discovery of new strategies; and the SCADS* model (Siegler & Araya, 2005), which adds six new mechanisms to the SCADS model (i.e., controlled attention, interruption of procedures, verbalization, priming, forgetting, and dynamic feature detection).

Note that the design used in this first experiment (i.e., without a pretest but with different practice groups) has been used earlier (e.g., Rickard et al., 1994; Rickard & Bourne, 1996). We acknowledge that the absence of a pretest is a drawback of the first experiment. Therefore, a pretest has been included in the second experiment.

As the amount of counting strategy use is very low (cf. Tables 1, 3), we decided to put counting RTs and transformation RTs together. These procedural RTs are then contrasted with the retrieval RTs. Although, since (a) not all strategies were used across all the practice sessions, and (b) only RTs of the correctly solved problems were analyzed, for some subjects empty cells occurred in the practice level × operation × size × strategy ANOVA. We replaced these empty cells for each participant with the correct RT of the corresponding cell [i.e., the mean RT (over participants) of the practice level × operation × size × strategy cell]. Obviously, this procedure was only needed in the ANOVAs on strategy efficiency and not in the ANOVAs on strategy selection. The number of cells replaced was 10 (out of 240) in Experiment 1 and 34 (out of 320) in Experiment 2.

T = BN ^−α in which T represents the performance time, B is the time taken to perform the first trial, N is the trial number, and α represents the rate at which performance time changes.

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Titel: Practice effects on strategy selection and strategy efficiency in simple mental arithmetic
Auteurs: Ineke Imbo
André Vandierendonck
Publicatiedatum: 01-09-2008
Uitgeverij: Springer-Verlag
Gepubliceerd in: Psychological Research / Uitgave 5/2008
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-007-0128-0

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