Enhancing arithmetic and word-problem solving skills efficiently by individualized computer-assisted practice

Journal of Educational Research

Volumn 103, Issue 4, 2010, Pages 239-252

  Schoppek, Wolfgang ^a   Tulis, Maria ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Computer assisted instruction; Individualized instruction; Mathematics education; Skill acquisition

Indexed keywords

EID: 77951088033     PISSN: 00220671     EISSN: None     Source Type: Journal    
DOI: 10.1080/00220670903382962     Document Type: Article

References (63)

1. Ackerman, P. L. (1987). Individual differences in skill learning: An integration of psychometric and information processing perspectives. Psychological Bulletin, 102, 3-27.
2. Anderson, J. R. (1982). Acquisition of cognitive skill. Psychological Review, 89, 369-406.
3. Anderson, J. R., Fincham, J.M.,&Douglass, S. (1997).The role of examples and rules in the acquisition of a cognitive skill. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 932-945.
4. Anderson, J. R., Reder, L. M., & Simon, H. A. (2000). Applications and misapplications of cognitive psychology tomathematics education. Texas Educational Review, 1, 29-49.
5. Atkins, J. (2005). The association between the use of Accelerated math and students' math achievement. Unpublished doctoral dissertation, East Tennessee State University. Retrieved March 12, 2010, from http://etdsubmit. etsu.edu/etd/theses/available/etd-0504105-1130335
6. Atkinson, R. C., & Fletcher, J. (1972). Teaching children to read with a computer. Reading Teacher, 25, 319-327.
7. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Ed.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1-33). Mahwah, NJ: Erlbaum.
8. Bassoe, C. F. (1995). Automated diagnoses from clinical narratives: A medical system based on computerized medical records, natural language processing, and neural network technology. Neural Networks, 8, 313-319.
9. Baumert, J., Schmitz, B., Roeder, P., & Sang, F. (1989). Zur Optimierung von Leistungsforderung und Chancenausgleich in Schulklassen: Explorative Untersuchungen mittels HYPAG [Maximizing achievement and equal opportunity in the classroom: Explorative studies with HYPAG]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 21, 201-222.
10. Blöte, A. W., Klein, A. S., & Beishuizen, M. (2000). Mental computation and conceptual understanding. Learning and Instruction, 10, 221-247.
11. Brophy, J. (1986). Teacher influences on student achievement. American Psychologist, 41, 1069-1077.
12. Brown, J. S., & VanLehn, K. (1981). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4, 379-426.
13. Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. (1999). Children's mathematics: Cognitively guided instruction. Portmouth, NH: Heinemann.
14. Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. (1997). A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 29, 3-20.
15. Carstensen, C., & Rost, J. (2003). MULTIRA: A software system for multidimensional Rasch models. Kiel, Germany: IPN.
16. Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.
17. Desoete, A., & Roeyers, H. (2006). Metacognitive macroevaluations in mathematical problem solving. Learning and Instruction, 16, 12-25.
18. Desoete, A., Roeyers, H., & De Clercq, A. (2003). Can offline metacognition enhance mathematical problem solving? Journal of Educational Psychology, 95, 188-200.
19. Elia, I., Gagatsis, A., & Demetriou, A. (2007). The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction, 17, 658-672.
20. Forsstrom, J. J., & Dalton, K. J. (1995). Artificial neural networks for decision support in clinical medicine. Annals of Medicine, 27, 509-517.
21. Fuchs, L. S., Fuchs, D., Prentice, K.,Hamlett, C. L., Finelli, R.,&Courey, S. J. (2004). Enhancing mathematical problem solving among third-grade students with schema-based instruction. Journal of Educational Psychology, 96, 635-647.
22. Fuson, K. C, Wearne, D., Hiebert, J. C., Murray, H. G., Human, P. G., Olivier,A. I., et al. (1997). Children's conceptual structures formulitdigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28, 130-162.
23. Gagne, R. M. (1962). The acquisition of knowledge. Psychological Review, 69, 355-365.
24. Gagnon, J. C., & Maccini, P. (2001). Preparing students with disabilities for algebra. Teaching for Exceptional Children, 34, 8-15.
25. Greenwood, C. R. (1991). Longitudinal analysis of time, engagement, and achievement in at-risk versus non-risk students. Exceptional Children, 56, 521-535.
26. Hecht, S. A., Torgeson, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills. A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79, 192-227.
27. Heirdsfield, A. M., & Cooper, T. J. (2002). Flexibility and inflexibility in accurate mental addition and subtraction: Two case studies. The Journal of Mathematical Behavior, 21, 57-74.
28. Helmke, A. (1988). Leistungssteigerung und Ausgleich von Leistungsunterschieden in Schulklassen: unvereinbare Ziele? [Overall performance improvements and reduction of performance difference among students in the classroom: Irreconcilable goals?]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 20, 45-76.
29. Hiebert, J., & Wearne, D. (1996). Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction, 14, 251-283.
30. Hilgard, E. R., Irvine, R. P., & Whipple, J. E. (1953). Rote memorization, understanding, and transfer: An extension of Katona's card-trick experiments. Journal of Experimental Psychology, 46, 288-292.
31. Jamison, D., Suppes, P., & Wells, S. (1974). The effectiveness of alternative instructional media: A survey. Review of Educational Research, 44, 1-67.
32. Jitendra,A. K., Griffin, C. C., Haria, P., Leh, J.,Adams, A.,&Kaduvettoor, A. (2007). A comparison of single and multiple strategy instruction on third-grade students' mathematical problem solving. Journal of Educational Psychology, 99, 115-127.
33. Kail, R., & Hall, L. K. (1999). Sources of developmental change in children's word-problem performance. Journal of Educational Psychology, 91, 660-668.
34. Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational psychologist, 41, 75-86.
35. Koedinger, K. R., Anderson, J. R., Hadley, W. H., & Mark, M. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in Education, 8, 30-43.
36. 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.
37. Ku, H.-Y., Harter, C. A., Liu, P.-L., Thompson, L.,&Cheng, Y.-C. (2007). The effects of individually personalized computer-based instructional program on solving mathematics problems. Computers inHuman Behavior, 23, 1195-1210.
38. Kulik, J. A. (1994). Meta-analytic studies of findings on computer-based instruction. In E. L. Baker & H. F. O'Neil (Eds.), Technology assessment in education and training (pp. 9-33). Hillsdale, NJ: Erlbaum.
39. Laue, C.,&Putz-Osterloh,W. (2002).Computergestütztes Lernen inMathematik bei Grundschülern [Computer assisted learning in elementary mathematics]. In B. Spinath & E. Heise (Hg.) Pädagogische Psychologie unter gewandelten gesellschaftlichen Bedingungen (pp. 68-83). Hamburg: Verlag Dr. Kovac.
40. Lehmann, R., & Seeber, S. (2005). "Accelerated Mathematics" in grades 4 through 6. Retrieved March 12, 2010, from http://zope.ebf.huberlin. de/document/accelerated/view?searchterm=Accele
41. Lovett, M. C., & Anderson, J. R. (1996). History of success and current context in problem solving: Combined influences on operator selection. Cognitive Psychology, 31, 168-217.
42. Luchins, A. S. (1942). Mechanization in problem solving: The effect of einstellung. Psychological Monographs, 54, 95-111.
43. Mevarech, Z. R., & Rich, Y. (1985). Effects of computer-assisted mathematics instruction on disadvantaged pupil's cognitive and affective development. Journal of Educational Research, 79, 5-11.
44. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics: Standards 2000. Reston, VA: Author.
45. Ohlsson, S., & Rees, E. (1991). The function of conceptual understanding in the learning of arithmetic procedures. Cognition and Instruction, 8, 103-179.
46. Paas, F. G. W. C., & Merriënboer, J. J. G. (1994). Variability of worked examples and transfer of geometrical problem-solving skills:Acognitiveload approach. Journal of Educational Psychology, 86, 122-133.
47. Pearl, J. (2001). Probabilistic reasoning in intelligent systems. San Francisco: Morgan Kaufmann.
48. Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skills: Studies in developmental psychology (pp. 75-110) Hove, UK: Psychology Press/Taylor & Francis.
49. Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35, 481-498.
50. Roick, T., Gölitz, D., & Hasselhorn, M. (2004). DEMAT 3+. Deutscher Mathematiktest für dritte Klassen [German mathematics test for grade 3]. Göttingen, Germany: Beltz Test.
51. Rost, J. (2004). Lehrbuch Testtheorie-Testkonstruktion [Theory and construction of mental tests]. Bern, Switzerland: Huber.
52. Schoppek, W. (2008). A hierarchy of elementary arithmetic skills as a basis for individualised instruction. Unpublished manuscript. Retrieved March 12, 2010, from http://www.uni-bayreuth.de/departments/ psychologie/schoppek/ arithskill.pdf
53. Sherin, B., & Fuson, K. C. (2005). Multiplication strategies and the appropriation of computational resources. Journal for Research in Mathematics Education, 36, 347-395.
54. Star, J. R. & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18, 565-579.
55. Stark, R.,Mandl, H., Gruber, H., & Renkl, A. (1999). Instructional means to overcome transfer problems in the domain of economics: Empirical studies. International Journal of Educational Research, 31, 591-609.
56. Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12, 257-285.
57. Treiber, B., Weinert, F. E., & Groeben, N. (1982). Unterrichtsqualität, Leistungsniveau von Schulklassen und individueller Lernfortschritt [Quality of instruction, class performance, and individual learning progress]. Zeitschrift für Pädagogik, 27, 65-75.
58. Tronsky, L. N. (2005). Strategy use, the development of automaticity, and working memory involvement in complex multiplication. Memory & Cognition, 33, 927-940.
59. Tronsky, L. N., & Royer, J. M. (2002). Relationships among basic computational automaticity, working memory, and complex mathemati cal problem solving: What we know and what we need to know. In J. M. Royer (Ed.), Mathematical cognition (pp. 117-146) Greenwich, CT: Information Age Publishing.
60. Van Essen, G., & Hamaker, C. (1990). Using self-generated drawings to solve arithmetic word problems. The Journal of Educational Research, 83, 301-312.
61. Verschaffel, L., DeCorte, E., & Vierstraete, H. (1999). Upper elementary school pupils' difficulties in modeling and solving nonstandard additive word problems involving ordinal numbers. Journal for Research in Mathematics Education, 30, 265-285.
62. White, R. T. (1976). Effects of guidance, sequence, and attribute-treatment interactions on learning, retention, and transfer of hierarchically ordered skills. Instructional Science, 5, 133-152.
63. Ysseldyke, J., Spicuzza, R., Kosciolek, S., & Boys, C. (2003). Effects of a learning information system onmathematics achievement and classroom structure. The Journal of Educational Research, 96, 163-173.