In pursuit of knowledge: Comparing self-explanations, concepts, and procedures as pedagogical tools

Journal of Experimental Child Psychology

Volumn 104, Issue 1, 2009, Pages 1-21

  Matthews, Percival ^a   Rittle Johnson, Bethany ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Conceptual knowledge; Problem solving; Procedural knowledge; Self explanation; Transfer

Indexed keywords

ARTICLE; CHILD; CONCEPT FORMATION; FEMALE; HUMAN; KNOWLEDGE; LEARNING; MALE; MATHEMATICS; NEUROPSYCHOLOGICAL TEST; PROBLEM SOLVING; PSYCHOLOGICAL ASPECT; SCHOOL; STUDENT;

CHILD; CONCEPT FORMATION; FEMALE; HUMANS; KNOWLEDGE; LEARNING; MALE; MATHEMATICS; NEUROPSYCHOLOGICAL TESTS; PROBLEM SOLVING; SCHOOLS; STUDENTS; TRANSFER (PSYCHOLOGY);

EID: 67349276617     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jecp.2008.08.004     Document Type: Article

References (63)

1. Aleven V.A.W.M.M., and Koedinger K.R. An effective metacognitive strategy: Learning by doing and explaining with a computer-based cognitive tutor. Cognitive Science 26 (2002) 147-179
2. Alibali M.W. How children change their minds: Strategy change can be gradual or abrupt. Developmental Psychology 35 (1999) 127-145
3. Anderson J.R. The architecture of cognition (1983), Harvard University Press, Cambridge, MA
4. Atkinson R.K., Renkl A., and Merrill M.M. Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked out steps. Journal of Educational Psychology 95 (2003) 774-783
5. Baroody A.J., and Dowker A. The development of arithmetic concepts and skills: Constructing adaptive expertise (2003), Lawrence Erlbaum, Mahwah, NJ
6. Baroody A.J., Feil Y., and Johnson A.R. An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education 38 (2007) 115-131
7. Baroody A.J., Ginsburg H.P., and Waxman B. Children's use of mathematical structure. Journal for Research in Mathematics Education 14 (1983) 156-168
8. Bednarz N., and Janvier B. A constructivist approach to numeration in primary school: Results of a three year intervention with the same group of children. Educational Studies in Mathematics 19 (1988) 299-331
9. Blöt A.W., Van der Burg E., and Klein A.S. Students' flexibility in solving two-digit addition and subtraction problems: Instruction effects. Journal of Educational Psychology 93 (2001) 627-638
10. Byrnes J.P. The conceptual basis of procedural learning. Cognitive Development 7 (1992) 235-257
11. Calin-Jageman R.J., and Ratner H.H. The role of encoding in the self-explanation effect. Cognition and Instruction 23 (2005) 523-543
12. Chi M.T.H. Self-explaining: The dual processes of generating inference and repairing mental models. In: Glaser R. (Ed). Advances in instructional psychology, Vol. 5: Educational design and cognitive science (2000), Lawrence Erlbaum, Mahwah, NJ 161-238
13. Chi M.T.H., Bassok M., Lewis M.W., Reimann P., and Glaser R. Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science 13 (1989) 145-182
14. Chi M.T.H., DeLeeuw N., Chiu M.H., and LaVancher C. Eliciting self-explanations improves understanding. Cognitive Science 18 (1994) 439-477
15. Cobb P., Wood T., Yackel E., Nicholls J., Wheatley G., Trigatti B., et al. Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education 22 (1991) 3-29
16. Conati C., and VanLehn K.A. Toward computer based support of meta-cognitive skills: A computational framework to coach self-explanation. International Journal of Artificial Intelligence in Education 11 (2000) 398-415
17. Crowley K., Shrager J., and Siegler R.S. Strategy discovery as a competitive negotiation between metacognitive and associative mechanisms. Developmental Review 17 (1997) 462-489
18. de Bruin A.B.H., Rikers R.M.J.P., and Schmidt H.G. The effect of self-explanation and prediction on the development of principled understanding of chess in novices. Contemporary Educational Psychology 32 (2007) 188-205
19. Didierjean A., and Cauzinille Marmeche E. Eliciting self-explanations improves problem solving: What processes are involved?. Current Psychology of Cognition 16 (1997) 325-351
20. Fuson K.C., and Briars D.J. Using a base-ten blocks learning/teaching approach for first- and second-grade place value and multidigit addition and subtraction. Journal for Research in Mathematics Education 21 (1990) 180-206
21. Goldin-Meadow S., Alibali M.W., and Church R.B. Transitions in concept acquisition: Using the hand to read the mind. Psychological Review 100 (1993) 279-297
22. Graham J.W., Hofer S.M., and MacKinnon D.P. Maximizing the usefulness of data obtained with planned missing value patterns: An application of maximum likelihood procedures. Multivariate Behavioral Research 31 (1996) 197-218
23. Greeno J.G., Riley M.S., and Gelman R. Conceptual competence and children's counting. Cognitive Psychology 16 (1984) 94-143
24. Grobe C.S., and Renkl A. Example-based learning with multiple solution methods facilitates understanding. In: Schmalhofer F., Young R.M., and Katz G. (Eds). Proceedings of the European Cognitive Science Conference 2003 (2003), Lawrence Erlbaum, Mahwah, NJ 163-168
25. Hiebert J., and Grouws D.A. Effective teaching for the development of skill and conceptual understanding of number: What is most effective? Reston (2007), National Council of Teachers of Mathematics, VA
26. Hiebert J., and Wearne D. Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction 14 (1996) 251-283
27. Kamii C., and Dominick A. To teach or not to teach algorithms. Journal of Mathematical Behavior 16 (1997) 51-61
28. Kieran C. Concepts associated with the equality symbol. Educational Studies in Mathematics 12 (1981) 317-326
29. Knuth E.J., Stephens A.C., McNeil N.M., and Alibali M.W. Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education 37 (2006) 297-312
30. Koedinger K.R., and Anderson J.R. Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science 14 (1990) 511-550
31. Kotovsky K., Hayes J.R., and Simon H.A. Why are some problems hard? Evidence from Tower of Hanoi. Cognitive Psychology 17 (1985) 248-294
32. Larkin J., McDermott J., Simon D.P., and Simon H.A. Expert and novice performance in solving physics problems. Science 208 (1980) 1335-1342
33. LeFevre J.A., Greenham S.L., and Waheed N. The development of procedural and conceptual knowledge in computational estimation. Cognition and Instruction 11 (1993) 95-132
34. McNeil N.M., and Alibali M.W. Learning mathematics from procedural instruction: Externally imposed goals influence what is learned. Journal of Educational Psychology 92 (2000) 734-744
35. McNeil N.M., and Alibali M.W. You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science 28 (2004) 451-466
36. McNeil N.M., and Alibali M.W. Knowledge change as a function of mathematics experience. All contexts are not created equal. Journal of Cognition and Development 6 (2005) 285-306
37. Mwangi W., and Sweller J. Learning to solve compare word problems: The effect of example format and generating self-explanations. Cognition and Instruction 16 (1998) 173-199
38. National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. Retrieved July 20, 2008, from www.ed.gov/MathPanel.
39. Peled I., and Segalis B. It's not too late to conceptualize: Constructing a generalized subtraction schema by abstracting and connecting procedures. Mathematical Thinking and Learning 7 (2005) 207-230
40. Perry M. Learning and transfer: Instructional conditions and conceptual change. Cognitive Development 6 (1991) 449-468
41. Peskin J. Constructing meaning when reading poetry: An expert-novice study. Cognition and Instruction 16 (1998) 235-263
42. Peugh J.L., and Enders C.K. Missing data in educational research: A review of reporting practices and suggestions for improvement. Review of Educational Research 74 (2004) 525-556
43. Pine K.J., and Messer D.J. The effect of explaining another's actions on children's implicit theories of balance. Cognition and Instruction 18 (2000) 35-52
44. Pirolli P., and Recker M. Learning strategies and transfer in the domain of programming. Cognition and Instruction 12 (1994) 235-275
45. Proctor R.W., and Dutta A. Skill acquisition and human performance (1995), Sage, Thousand Oaks, CA
46. Renkl A. Learning from worked-out examples: A study on individual differences. Cognitive Science 21 (1997) 1-29
47. Renkl A. Worked-out examples: Instructional explanations support learning by self-explanations. Learning and Instruction 12 (2002) 529-556
48. Renkl A., Stark R., Gruber H., and Mandl H. Learning from worked-out examples: The effects of example variability and elicited self-explanations. Contemporary Educational Psychology 23 (1998) 90-108
49. Rittle-Johnson B. Promoting transfer: Effects of self-explanation and direct instruction. Child Development 77 (2006) 1-29
50. Rittle-Johnson B., and Alibali M.W. Conceptual and procedural knowledge of mathematics: Does one lead to the other?. Journal of Educational Psychology 91 (1999) 175-189
51. Rittle-Johnson B., Saylor M., and Swygert K. Learning from explaining: Does it matter if mom is listening?. Journal of Experimental Child Psychology 100 (2007) 215-224
52. Rittle-Johnson B., Siegler R.S., and Alibali M.W. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 93 (2001) 346-362
53. Schafer J.L., and Graham J.W. Missing data: Our view of the state of the art. Psychological Methods 7 (2002) 147-177
54. Schoenfeld A.H., and Herrmann D.J. Problem perception and knowledge structure in expert and novice mathematical problem solvers. Journal of Experimental Psychology:. Learning, Memory, and Cognition 8 (1982) 484-494
55. Schworm S., and Renkl A. Learning argumentation skills through the use of prompts for self-explaining examples. Journal of Educational Psychology 99 (2007) 285-296
56. Siegler R.S. How does change occur? A microgenetic study of number conservation. Cognitive Psychology 28 (1995) 225-273
57. Siegler R.S. Emerging minds: The processes of change in children's thinking (1996), Oxford University Press, New York
58. Siegler R.S. Microgenetic studies of self-explanation. In: Garnott N., and Parziale J. (Eds). Microdevelopment: A process-oriented perspective for studying development and learning (2002), Cambridge University Press, Cambridge, MA 31-58
59. Star J.R. Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education 36 (2005) 404-411
60. Star J.R., and Seifert C. The development of flexibility in equation solving. Contemporary Educational Psychology 31 (2006) 280-300
61. Sweller J. Cognitive load during problem solving: Effects on learning. Cognitive Science 12 (1988) 257-285
62. Sweller J., van Merrienboer J.J.G., and Paas F.G.W.C. Cognitive architecture and instructional design. Educational Psychology Review 10 (1998) 251-296
63. Wong R.M.F., Lawson M.J., and Keeves J. The effects of self-explanation training on students' problem solving in high-school mathematics. Learning and Instruction 12 (2002) 233-262