Skip to main content
Mijn bibliotheek
Shop
Nieuws Boeken Tijdschriften Toetsvragen Web-tv Video Audio
Tips voor Mijn BSL
Inloggen

Welkom bij Scalda & Bohn Stafleu van Loghum

Scalda heeft ervoor gezorgd dat je Mijn BSL eenvoudig en snel kunt raadplegen.Je kunt de producten hieronder links aanschaffen en rechts inloggen.

» Andere revante producten voor Scalda studenten en medewerkers.

Registreer

Schaf de BSL Academy aan: 

BSL Academy mbo AG

Eenmaal aangeschaft kun je thuis, of waar ook ter wereld toegang krijgen tot Mijn BSL.

Heb je een vraag, neem dan contact op met Jan van der Velden.

Login

Als u al geregistreerd bent, hoeft u alleen maar in te loggen om onbeperkt toegang te krijgen tot Mijn BSL.

Inloggen
Top
Psychological Research
Gepubliceerd in:

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

Log in om toegang te krijgen
share
DELEN

Deel dit onderdeel of sectie (kopieer de link)

  • Optie A:
    Klik op de rechtermuisknop op de link en selecteer de optie “linkadres kopiëren”
  • Optie B:
    Deel de link per e-mail
    Link delen
publish
Publiceer nu

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.
vorige artikel Response inhibition under task switching: its strength depends on the amount of task-irrelevant response activation
volgende artikel An egocentric frame of reference in implicit motor sequence learning
Voetnoten
1
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.
 
2
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).
 
3
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.
 
4
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.
 
5
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.
 
Literatuur
Anderson, J. R. (1993). Rules of the mind. Hillsdale, NJ: Erlbaum.
Ashcraft, M. H. (1982). The development of mental arithmetic: A chronometric approach. Developmental Review, 2, 213–236.CrossRef
Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75–106.PubMedCrossRef
Baroody, A. J. (1983). The development of procedural knowledge: An alternative explanation for chronometric trends of mental arithmetic. Developmental Review, 3, 225–230.CrossRef
Baroody, A. J. (1984). A re-examination of mental arithmetic models and data: A reply to Ashcraft. Developmental Review, 4, 148–156.CrossRef
Baroody, A. J. (1985). Mastery of the basic number combinations: Internalization of relationships or facts? Journal of Research in Mathematics Education, 16, 83–98.CrossRef
Brigman, S., & Cherry, K. E. (2002). Age and skilled performance: Contributions of working memory and processing speed. Brain and Cognition, 50, 242–256.PubMedCrossRef
Butterworth B. (1999). The mathematical brain. London: Macmillan.
Campbell J. I. D. (1987). Network interference and mental multiplication. Journal of Experimental Psychology: Learning, Memory, & Cognition, 13, 109–123.CrossRef
Campbell J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121–164.
Campbell J. I. D. (1997). On the relation between skilled performance of simple division and multiplication. Journal of Experimental Psychology: Learning, Memory, & Cognition, 23, 1140–1159.CrossRef
Campbell J. I. D., & Austin, S. (2002). Effects of response time deadlines on adults’ strategy choices for simple addition. Memory & Cognition, 30, 988–994.
Campbell J. I. D., & Graham, D. J. (1985). Mental multiplication skill: Structure, process and acquisition. Canadian Journal of Psychology, 39, 338–366.
Campbell J. I. D., Gunter R. (2002). Calculation, culture, and the repeated operand effect. Cognition, 86, 71–96.PubMedCrossRef
Campbell J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299–315.CrossRef
Campbell J. I. D., Fuchs-Lacelle, S., & Phenix, T. L. (2006). Identical elements model of arithmetic memory: Extension to addition and subtraction. Memory & Cognition, 34, 633–647.
Compton B. J., & Logan, G. D. (1991). The transition from algorithm to retrieval in memory-based theories of automaticity. Memory & Cognition, 19, 151–158.
Dehaene S. (1997). The number sense. New York: Oxford University Press.
Delaney, P. F., Reder, L. M., Staszewski, J. J., & Ritter, F. E. (1998). The strategy-specific nature of improvement: The power law applies by strategy within task. Psychological Science, 9, 1–7.CrossRef
Delazer, M., Ischebeck, A., Domahs, F., Zamarian, L., Koppelstaetter, F., Siedentopf, C. M., Kaufmann, L., Benke, T., & Felber, S. (2005). Learning by strategies and learning by drill—Evidence from an fMRI study. Neuroimage, 25, 838–849.PubMedCrossRef
Fendrich, D. W., Healy, A. F., & Bourne, L. E. (1993). Mental arithmetic: Training and retention of multiplication skill. In C. Izawa (Ed.), Applied Cognitive Psychology: Applications of Cognitive Theories and Concepts (pp. 111–133). Hillsdale, NJ: Erlbaum.
French J. W., Ekstrom R. B., & Price, I. A. (1963). Kit of reference tests for cognitive factors. Princeton, NJ: Educational Testing Service.
Fuson, K. C. (1982). An analysis of the counting-on procedure in addition. In T. H. Carpenter, J. M. Moser, & T. H. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 67–78). Hillsdale NJ: Lawrence Erlbaum.
Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.
Geary, D. C. (1996). The problem-size effect in mental addition: Developmental and cross-national trends. Mathematical Cognition, 2, 63–93.CrossRef
Geary, D. C., Salthouse, T. A., Chen, G. -P., & Fan, L. (1996). Are East Asian versus American differences in arithmetic ability a recent phenomenon? Developmental Psychology, 32, 254–262.CrossRef
Geary, D. C., Hamson, C. O., Chen, G. -P., Fan, L., Hoard, M. K., & Salthouse, T. A. (1997). Computational and reasoning in arithmetic: Cross-generational change in China and the United States. Psychonomic Bulletin and Review, 4, 254–263.
Gelman R., & Gallistel, R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.
Hoyer, W. J., Cerella, J., & Onyper, S. V. (2003). Item learning in cognitive skill training: Effects of item difficulty. Memory & Cognition, 31, 1260–1270.
Imbo, I., & Vandierendonck, A. (in press a). The role of phonological and executive working-memory resources in simple-arithmetic strategies. European Journal of Cognitive Psychology.
Imbo, I., & Vandierendonck, A. (in press b). Do multiplication and division strategies rely on executive and phonological working-memory resources? Memory & Cognition.
Imbo, I., Vandierendonck, A., & Rosseel, Y. (2007). The influence of problem features and individual differences on strategic performance in simple arithmetic. Memory & Cognition, 35, 454–463.
Kirk, E. P., & Ashcraft, M. H. (2001). Telling stories: The perils and promise of using verbal reports to study math strategies. Journal of Experimental Psychology: Learning, Memory, & Cognition, 27, 157–175.CrossRef
Klapp, S. T., Boches, C. A., Trabert, M. L., Logan, G. D. (1991). Automatizing alphabet arithmetic: II. Are there practice effects after automaticity is achieved? Journal of Experimental Psychology: Learning, Memory, & Cognition, 17, 196–209.CrossRef
Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs: A meta-analysis. Remedial and Special Education, 24, 97–114.CrossRef
LeFevre, J. -A., & Liu, J. (1997). The role of experience in numerical skill: Multiplication performance in adults from Canada and China. Mathematical Cognition, 3, 31–62.CrossRef
LeFevre, J.-A., Bisanz, J., Daley, K. E., Buffone, L., Greenham, S. L., & Sadesky, G. S. (1996). Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology: General, 125, 284–306.CrossRef
LeFevre, J. -A., Sadesky, G. S., & Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem size effect in adults. Journal of Experimental Psychology: Learning, Memory, & Cognition, 22, 216–230.CrossRef
Lewis, A. B. (1989). Training students to represent arithmetic word problems. Journal of Educational Psychology, 81, 521–531.CrossRef
Logan, G. D. (1988). Toward an instance theory of automatization. Psychological Review, 95, 492–527.CrossRef
Logan, G. D., & Klapp, S. T. (1991). Automatizing alphabet arithmetic: I. Is extended practice necessary to produce automaticity? Journal of Experimental Psychology: Learning, Memory, & Cognition, 17, 179–195.CrossRef
McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Brain and Cognition, 4, 171–196.CrossRef
Mulhern, G., & Wylie, J. (2004). Changing levels of numeracy and other core mathematical skills among psychology undergraduates between 1992 and 2002. British Journal of Psychology, 95, 355–370.PubMedCrossRef
Newell, A., & Rosenbloom, P. S. (1981). Mechanisms of skill acquisition and the law of practice. In J. R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 1–55). Hillsdale, NJ: Erlbaum.
Onyper, S. V., Hoyer, W. J., & Cerella, J. (2006). Determinants of retrieval solutions during cognitive skill training: Source confusions. Memory & Cognition, 34, 538–549.
Pauli, P., Lutzenberger, W., Rau, H., Birbaumer, N., Rickard, T. C., Yaroush, R. A., & Bourne, L. E. (1994). Brain potentials during mental arithmetic—Effects of extensive practice and problem difficulty. Cognitive Brain Research, 2, 21–29.PubMedCrossRef
Pauli, P., Lutzenberger, W., Birbaumer, N., Rickard, T. C., & Bourne, L. E. (1996). Neurophysiological correlates of mental arithmetic. Psychophysiology, 33, 522–529.PubMedCrossRef
Pauli, P., Bourne, L. E., & Birbaumer, N. (1998). Extensive practice in mental arithmetic and practice transfer over a ten-month retention interval. Mathematical Cognition, 4, 21–46.CrossRef
Rickard, T. C. (1997). Bending the power law: A CMPL theory of strategy shifts and the automatization of cognitive skills. Journal of Experimental Psychology: General, 126, 288–311.CrossRef
Rickard, T. C. (2004). Strategy execution in cognitive skill learning: An item-level test of candidate models. Journal of Experimental Psychology, 30, 65–82.PubMed
Rickard, T. C. (2005). A revised identical elements model of arithmetic fact representation. Journal of Experimental Psychology: Learning, Memory, & Cognition, 31, 250–257.CrossRef
Rickard, T. C., & Bourne, L. E. (1996). Some tests of an identical elements model of basic arithmetic skills. Journal of Experimental Psychology: Learning, Memory, & Cognition, 22, 1281–1295.CrossRef
Rickard, T. C., Healy, A. F., & Bourne, L. E. (1994). On the cognitive structure of basic arithmetic skills: Operation, order, and symbol transfer effects. Journal of Experimental Psychology: Learning, Memory, & Cognition, 20, 1139–1153.CrossRef
Royer, J. M., Tronsky, L. N., Chan, Y., Jackson, S. J., & Marchant, H. III. (1999). Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance. Contemporary Educational Psychology, 24, 181–266.PubMedCrossRef
Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary subtraction. Journal of Experimental Psychology: Learning, Memory, & Cognition, 29, 1339–1352.CrossRef
Shrager, J., & Siegler, R. S. (1998). SCADS: A model of children’s strategy choices and strategy discoveries. Psychological Science, 9, 405–410.CrossRef
Siegler, R. S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258–275.CrossRef
Siegler, R. S., & Araya, R. (2005). A computational model of conscious and unconscious strategy discovery. Advances in Child Development and Behavior, 33, 1–42.PubMed
Siegler, R. S., & Shipley, C. (1995). Variation, selection, and cognitive change. In G. Halford, &T. Simon (Eds.), Developing cognitive competence: New approaches to process modeling (pp. 31–76). Hillsdale, NJ: Erlbaum.
Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition, subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229–294). Hillsdale, NJ: Erlbaum.
Spelke, E., & Dehaene, S. (1999). Biological foundations of numerical thinking: response to T.J. Simon. Trends in Cognitive Science, 3, 365–366.CrossRef
Steel, S., & Funnell, E. (2001). Learning multiplication facts: A study of children taught by discovery methods in England. Journal of Experimental Child Psychology, 79, 37–55.PubMedCrossRef
Touron, D. R., Hoyer, W. J., & Cerella, J. (2004). Cognitive skill learning: Age-related differences in strategy shifts and speed of component operations. Psychology and Aging, 19, 565–580.PubMedCrossRef
Van der Goten, K., & Vandierendonck, A. (1997). Software to calculate measures of sensitivity and response bias based on detection theory and threshold theory. Behavior Research Methods, Instruments, & Computers, 29, 461–463.
Verguts, T., & Fias, W. (2005). Interacting neighbors: A connectionist model of retrieval in single-digit multiplication. Memory & Cognition, 33, 1–16.
Whetstone, T. (1998). The representation of arithmetic facts in memory: Results from retraining a brain-damaged patient. Brain and Cognition, 36, 290–309.PubMedCrossRef
Zbrodoff, N. J. (1995). Why is 9 + 7 harder than 2 + 3? Strength and interference as explanations of the problem-size effect. Memory & Cognition, 23, 689–700.
Zbrodoff, N. J. (1999). Effects of counting in alphabet arithmetic: Opportunistic stopping and priming of intermediate steps. Journal of Experimental Psychology: Learning, Memory, & Cognition, 25, 299–317.CrossRef
Metagegevens
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

Andere artikelen Uitgave 5/2008

On the interplay between familiarity and emotional expression in face perception

  • Original Article

Response inhibition under task switching: its strength depends on the amount of task-irrelevant response activation

  • Original Article

Control by action representation and input selection (CARIS): a theoretical framework for task switching

  • Original Article

The dynamic-stimulus advantage of visual symmetry perception

  • Original Article

An egocentric frame of reference in implicit motor sequence learning

  • Original Article

Task switching based on externally presented versus internally generated information

  • Original Article