Flexibility in problem solving: The case of equation solving

Learning and Instruction

Volumn 18, Issue 6, 2008, Pages 565-579

  Star, Jon R ^a   Rittle Johnson, Bethany ^b  

^a HARVARD GRADUATE SCHOOL OF EDUCATION   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Direct instruction; Discovery learning; Equation solving; Flexibility in problem solving; Strategy use

Indexed keywords

EID: 53049092693     PISSN: 09594752     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.learninstruc.2007.09.018     Document Type: Article

References (43)

1. Alibali M.W. How children change their minds: strategy change can be gradual or abrupt. Developmental Psychology 35 1 (1999) 127-145
2. In: Baroody A.J., and Dowker A. (Eds). The development of arithmetic concepts and skills: Constructing adaptive expertise (2003), Lawrence Erlbaum, Mahwah, NJ
3. Beishuizen M., van Putten C.M., and van Mulken F. Mental arithmetic and strategy use with indirect number problems up to one hundred. Learning and Instruction 7 1 (1997) 87-106
4. Blöte A.W., Klein A.S., and Beishuizen M. Mental computation and conceptual understanding. Learning and Instruction 10 (2000) 221-247
5. Blöte 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
6. Bryk A.S., and Raudenbush S.W. Toward a more appropriate conceptualization of research on school effects: a three-level hierarchical linear model. American Journal of Education 97 1 (1988) 65-108
7. Carpenter T.P., Franke M.L., Jacobs V.R., Fennema E., and Empson S.B. A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education 29 1 (1998) 3-20
8. Chen Z., and Klahr D. All other things being equal: acquisition and transfer of the control of variables strategy. Child Development 70 5 (1999) 1098-1120
9. Dowker A. Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education 23 1 (1992) 45-55
10. Dowker A. Young children's addition estimates. Mathematical Cognition 3 (1997) 141-154
11. Dowker A., Flood A., Griffiths H., Harriss L., and Hook L. Estimation strategies of four groups. Mathematical Cognition 2 2 (1996) 113-135
12. Fuson K.C., Wearne D., Hiebert J.C., Murray H.G., Human P.G., Olivier A.I., et al. Children's conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education 28 2 (1997) 130-162
13. von Glasersfeld E. Radical constructivism: A way of knowing and learning (1995), Falmer Press, Taylor & Francis, Bristol, PA
14. Hedges L.V. Correcting a significance test for clustering. Journal of Educational and Behavioral Statistics 32 2 (2007) 151-179
15. Hiebert J., and Carpenter T. Learning and teaching with understanding. In: Grouws D. (Ed). Handbook of research on mathematics teaching and learning (1992), Simon & Schuster Macmillan, New York 65-97
16. Hiebert J., Carpenter T.P., Fennema E., Fuson K., Human P., Murray H., et al. Problem solving as a basis for reform in curriculum and instruction: the case for mathematics. Educational Researcher 25 (1996) 12-21
17. Hiebert J., and Wearne D. Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction 14 3 (1996) 251-283
18. Kamii C., and Dominick A. The harmful effects of algorithms in grades 1-4. In: Morrow L.J., and Kenney M.J. (Eds). The teaching and learning of algorithms in school mathematics. 1998 Yearbook (1998), National Council of Teachers of Mathematics, Reston, VA 130-140
19. Kieran C. The learning and teaching of school algebra. In: Grouws D. (Ed). Handbook of research on mathematics teaching and learning (1992), Simon & Schuster, New York 390-419
20. Kirschner P.A., Sweller J., and Clark R.E. Why minimal guidance does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist 41 2 (2006) 75-86
21. Klahr D., and Nigam M. The equivalence of learning paths in early science instruction: effects of direct instruction and discovery learning. Psychological Science 15 10 (2004) 661-667
22. Miller P.H., and Seier W.L. Strategy utilization deficiencies in children: when, where, and why. In: Reese H.W. (Ed). Advances in child development and behavior Vol. 25 (1994), Academic, New York 107-156
23. National Research Council. How people learn: Brain, mind, experience, and school (2000), National Academy Press, Washington, DC
24. Perry M. Learning and transfer: instructional conditions and conceptual change. Cognitive Development 6 (1991) 449-468
25. Piaget J. To understand is to invent (1973), Grossman, New York
26. Resnick L.B. The role of invention in the development of mathematical competence. In: Kluwe R.H., and Spada H. (Eds). Developmental models of thinking (1980), Academic, New York 213-244
27. Resnick L.B., and Ford W.W. The psychology of mathematics for instruction (1981), Lawrence Erlbaum, Hillsdale, NJ
28. Rittle-Johnson B. Promoting transfer: the effects of direct instruction and self-explanation. Child Development 77 1 (2006) 1-15
29. Rittle-Johnson B., and Star J.R. Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology 99 3 (2007) 561-574
30. Rosenshine B., and Stevens R. Teaching functions. In: Wittrock M.C. (Ed). Handbook of research on teaching (1986), McMillan, New York 376-391
31. Schwartz D.L., and Bransford J.D. A time for telling. Cognition and Instruction 16 4 (1998) 475-522
32. Siegler R.S. How does change occur: a microgenetic study of number conservation. Cognitive Psychology 28 3 (1995) 225-273
33. Siegler R.S. Emerging minds: The process of change in children's thinking (1996), Oxford University Press, New York
34. Siegler R.S., and Jenkins E. How children discover new strategies (1989), Lawrence Erlbaum, Hillsdale, NJ
35. Star, J. R. (2001). Re-conceptualizing procedural knowledge: Innovation and flexibility in equation solving. Unpublished doctoral dissertation, University of Michigan, Ann Arbor.
36. Star J.R., and Seifert C. The development of flexibility in equation solving. Contemporary Educational Psychology 31 (2006) 280-300
37. Sweller J. Cognitive load during problem solving: effects on learning. Cognitive Science 12 (1988) 257-285
38. Sweller J. Evolution of human cognitive architecture. In: Ross B.H. (Ed). The psychology of learning and motivation Vol. 43 (2003), Academic, San Diego, CA 215-266
39. Sweller J., and Cooper G.A. The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction 2 1 (1985) 59-89
40. Timmermans R.E., Van Lieshout E.C.D.M., and Verhoeven L. Gender-related effects of contemporary math instruction for low performers on problem-solving behavior. Learning and Instruction 17 1 (2007) 42-54
41. Torbeyns J., Verschaffel L., and Ghesquiere P. The development of children's adaptive expertise in the number domain 20 to 100. Cognition and Instruction 24 4 (2006) 439-465
42. Veenman M., Kok R., and Blöte A.W. The relation between intellectual and meta-cognitive skills in early adolescence. Instructional Science 33 3 (2005) 193-211
43. Zhu X., and Simon H.A. Learning mathematics from examples and by doing. Cognition and Instruction 4 3 (1987) 137-166