Top

Gepubliceerd in:

12-03-2019 | Original Article

The effects of early schema acquisition on mathematical problem solving

Gepubliceerd in: Psychological Research | Uitgave 6/2020

Abstract

The current paper explores the effects of providing people with schema training at the outset of learning (compared to at later stages) on mathematical word problems modeled after problems from the Graduate Record Examination. Additionally, the ratio of worked examples to problem-solving practice was manipulated. Participants were randomly assigned to one of four conditions and were tested on near and far transfer problems. Participants provided schema training at the outset of learning outperformed those provided schema training after problem-solving practice, particularly on far transfer problems. Likewise, participants provided with a higher ratio of worked examples to problem-solving practice demonstrated better performance during testing than those provided with more problem-solving practice and fewer worked examples. These findings extend the worked example effect to far transfer problems and suggest that providing schema training prior to learning solution strategies may be effective in improving mathematical problem solving.

vorige artikel Deaf signers outperform hearing non-signers in recognizing happy facial expressions

volgende artikel Silent shapes and shapeless sounds: the robustness of the diminished crossmodal correspondences effect in autism spectrum conditions

Alleen toegankelijk voor geautoriseerde gebruikers

The pattern of results did not change if this covariate was excluded.

Balota, D. A., & Neely, J. H. (1980). Test-expectancy and word-frequency effects in recall and recognition. Journal of Experimental Psychology: Human Learning and Memory, 6, 576–587. https://doi.org/10.1037/0278-7393.6.5.576.CrossRef

Brenner, M., Mayer, R., Moseley, B., Brar, T., Durán, R., Reed, B., et al. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34, 663–689. https://doi.org/10.3102/00028312034004663.CrossRef

Chechile, R., & Soraci, S. (1999). Evidence for a multiple-process account of the generation effect. Memory, 7, 483–508. https://doi.org/10.1080/741944921.CrossRef

Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79, 347–362. https://doi.org/10.1037/0022-0663.79.4.347.CrossRef

Corral, D., & Jones, M. (2014). The effects of relational structure on analogical learning. Cognition, 132, 280–300. https://doi.org/10.1016/j.cognition.2014.04.007.CrossRefPubMed

Doumas, L. A. A., Hummel, J. E., & Sandhofer, C. M. (2008). A theory of the discovery and predication of relational concepts. Psychological Review, 115, 1–43. https://doi.org/10.1037/0033-295x.115.1.1.CrossRefPubMed

Dweck, C. S. (1986). Motivational processes affecting learning. American Psychologist, 41, 1040–1048. https://doi.org/10.1037//0003-066x.41.10.1040.CrossRef

Educational Testing Service (1996). GRE: Practicing to take the general test: Big book. New Jersey: Educational Testing Service.

Educational Testing Service (2001). GRE: Practicing to take the GRE general test 10th ed. New Jersey: Educational Testing Service.

Educational Testing Service (2010). The Official Guide to the GRE Revised General Test. New Jersey: Educational Testing Service.

Ericsson, K. A., Chase, W., & Faloon, S. (1980). Acquisition of a memory skill. Science, 208, 1181–1182. https://doi.org/10.1126/science.7375930.CrossRef

Evans, J. (1999). Building bridges: Reflections on the problem of transfer of learning in mathematics. Educational Studies in Mathematics, 39, 23–44. https://doi.org/10.1023/a:1003755611058.CrossRef

Fyfe, E. R., DeCaro, M. S., & Rittle-Johnson, B. (2014). An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge. British Journal of Educational Psychology, 84, 502–519. https://doi.org/10.1111/bjep.12035.CrossRefPubMed

Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, 155–170. https://doi.org/10.1207/s15516709cog0702_3.CrossRef

Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38. https://doi.org/10.1016/0010-0285(83)90002-6.CrossRef

Healy, A. F., Wohldmann, E. L., Sutton, E. M., & Bourne, L. E. Jr. (2006). Specificity effects in training and transfer of speeded responses. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32, 534–546. https://doi.org/10.1037/0278-7393.32.3.534.CrossRefPubMed

Holyoak, K. J., & Koh, K. (1987). Surface and structural similarity in analogical transfer. Memory and Cognition, 15, 332–340. https://doi.org/10.3758/bf03197035.CrossRefPubMed

Kalyuga, S., Chandler, P., Tuovinen, J., & Sweller, J. (2001). When problem solving is superior to studying worked examples. Journal of Educational Psychology, 93, 579–588. https://doi.org/10.1037//0022-0663.93.3.579.CrossRef

Keating, D. P., & Crane, L. L. (1990). Domain-general and domain-specific processes in proportional reasoning: A commentary on the merrill-palmer quarterly special issue on cognitive development. Merrill-Palmer Quarterly, 36, 411–424.

Keppel, G., & Underwood, B. J. (1962). Proactive inhibition in short-term retention of single items. Journal of Verbal Learning & Verbal Behavior, 1, 153–161. https://doi.org/10.1016/s0022-5371(62)80023-1.CrossRef

Lewandowsky, S., Kalish, M., & Griffiths, T. L. (2000). Competing strategies in categorization: expediency and resistance to knowledge restructuring. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 1666–1684. https://doi.org/10.1037/0278-7393.26.6.1666.CrossRefPubMed

Lewandowsky, S., Kalish, M., & Ngang, S. K. (2002). Simplified learning in complex situations: Knowledge partitioning in function learning. Journal of Experimental Psychology: General, 131, 163–193. https://doi.org/10.1037//0096-3445.131.2.163.CrossRef

Lewandowsky, S., & Kirsner, K. (2000). Knowledge partitioning: Context-dependent use of expertise. Memory and Cognition, 28, 295–305. https://doi.org/10.3758/bf03213807.CrossRefPubMed

Lewis, A., & Mayer, R. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79, 363–371. https://doi.org/10.1037/0022-0663.79.4.363.CrossRef

Mayer, R. (1974). Acquisition processes and resilience under varying testing conditions for structurally different problem-solving procedures. Journal of Educational Psychology, 66, 644–656. https://doi.org/10.1037/h0037482.CrossRef

Mayer, R. (1975). Information processing variables in learning to solve problems. Review of Educational Research, 45, 525–541. https://doi.org/10.3102/00346543045004525.CrossRef

Mayer, R. (1976a). Integration of information during problem solving due to a meaningful context of learning. Memory and Cognition, 4, 603–608. https://doi.org/10.3758/bf03213224.CrossRefPubMed

Mayer, R. (1976b). Comprehension as affected by structure of problem representation. Memory and Cognition, 4, 249–255. https://doi.org/10.3758/bf03213171.CrossRefPubMed

Mayer, R. (1982a). Memory for algebra story problems. Journal of Educational Psychology, 74, 199–216. https://doi.org/10.1037/0022-0663.74.2.199.CrossRef

Mayer, R. (1982b). Different problem-solving strategies for algebra word and equation problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8, 448–462. https://doi.org/10.1037/0278-7393.8.5.448.CrossRef

Mayer, R. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26, 49–63. https://doi.org/10.1023/a:1003088013286.CrossRef

Mayer, R., & Greeno, J. (1975). Effects of meaningfulness and organization on problem solving and computability judgments. Memory and Cognition, 3, 356–362. https://doi.org/10.3758/bf03212924.CrossRefPubMed

Melby-Lervåg, M., & Hulme, C. (2013). Is working memory training effective? A meta-analytic review. Developmental Psychology, 49, 270–291. https://doi.org/10.1037/a0028228.CrossRefPubMed

Novick, L. R. (1988). Analogical transfer, problem similarity, and expertise. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 510–520. https://doi.org/10.1037//0278-7393.14.3.510.CrossRefPubMed

Penn, D. C., Holyoak, K. J., & Povinelli, D. J. (2008). Darwin’s mistake: Explaining the discontinuity between human and nonhuman minds. Behavioral and Brain Sciences, 31, 109–178. https://doi.org/10.1017/s0140525x08003543.CrossRefPubMed

Quilici, J., & Mayer, R. (2002). Teaching students to recognize structural similarities between statistics word problems. Applied Cognitive Psychology, 16, 325–342. https://doi.org/10.1002/acp.796.CrossRef

Rebello, S., & Cui, L. (2008). Retention and transfer of learning from math to physics to engineering. Paper presented at 2008 Annual Conference and Exposition, Pittsburgh, Pennsylvania.

Reed, S. (1989). Constraints on the abstraction of solutions. Journal of Educational Psychology, 81, 532–540. https://doi.org/10.1037//0022-0663.81.4.532.CrossRef

Rittle-Johnson, B. (2006). Promoting transfer: Effects of self-explanation and direct instruction. Child Development, 77, 1–15. https://doi.org/10.1111/j.1467-8624.2006.00852.x.CrossRefPubMed

Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91, 175–189. https://doi.org/10.1037//0022-0663.91.1.175.CrossRef

Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346–362. https://doi.org/10.1037//0022-0663.93.2.346.CrossRef

Rittle-Johnson, B., Star, J., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101, 836–852. https://doi.org/10.1037/a0016026.CrossRef

Simon, R. (1970). Encoding effects on complex problem solving. Journal of Experimental Psychology, 83, 227–231. https://doi.org/10.1037/h0028574.CrossRef

Stigler, J. W., & Hiebert, J. (1997). Understanding and improving classroom mathematics instruction: an overview of the TIMSS video study. Phi Delta Kappan, 79, 14–21.

Stigler, J. W., & Hiebert, J. (2009). Closing the teaching gap. Phi Delta Kappan, 91, 32–37. https://doi.org/10.1177/003172170909100307.CrossRef

Sweller, J., & Cooper, G. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59–89. https://doi.org/10.1207/s1532690xci0201_3.CrossRef

Sweller, J., Mawer, R., & Ward, M. (1983). Development of expertise in mathematical problem solving. Journal of Experimental Psychology: General, 112, 639–661. https://doi.org/10.1037//0096-3445.112.4.639.CrossRef

Sweller, J., & Sweller, S. (2006). Natural information processing systems. Evolutionary Psychology, 4, 4434–4458. https://doi.org/10.1177/147470490600400135.CrossRef

Tomlinson, T. D., Huber, D. E., Rieth, C. A., & Davelaar, E. J. (2009). An interference account of cue-independent forgetting in the no-think paradigm. PNAS Proceedings of the National Academy of Sciences of the United States of America, 106, 15588–15593. https://doi.org/10.1073/pnas.0813370106.CrossRef

Tuovinen, J., & Sweller, J. (1999). A comparison of cognitive load associated with discovery learning and worked examples. Journal of Educational Psychology, 91, 334–341. https://doi.org/10.1037//0022-0663.91.2.334.CrossRef

Ward, M., & Sweller, J. (1990). Structuring effective worked examples. Cognition and Instruction, 7, 1–39. https://doi.org/10.1207/s1532690xci0701_1.CrossRef

Weaver, C., & Kintsch, W. (1992). Enhancing students’ comprehension of the conceptual structure of algebra word problems. Journal of Educational Psychology, 84, 419–428. https://doi.org/10.1037/0022-0663.84.4.419.CrossRef

Yamauchi, T., & Markman, A. B. (2000). Inference using categories. Journal of Experimental Psychology Learning, Memory, and Cognition. 26. 776–795. https://doi.org/10.1037//0278-7393.26.3.776.CrossRefPubMed

Titel: The effects of early schema acquisition on mathematical problem solving
Publicatiedatum: 12-03-2019
Gepubliceerd in: Psychological Research / Uitgave 6/2020
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-019-01164-8

Bohn Stafleu van Loghum

Deel dit onderdeel of sectie (kopieer de link)

Abstract

Log in om toegang te krijgen

Andere artikelen Uitgave 6/2020

Effects of neurofeedback and working memory-combined training on executive functions in healthy young adults

Are model parameters linked to processing stages? An empirical investigation for the ex-Gaussian, ex-Wald, and EZ diffusion models

Wikipedia outperforms individuals when it comes to hindsight bias

Silent shapes and shapeless sounds: the robustness of the diminished crossmodal correspondences effect in autism spectrum conditions

Embodied cognition in multitasking: increased hand-specific task shielding when stimuli are presented near the hand

Test of a dynamic neural field model: spatial working memory is biased away from distractors