Recursive and explicit rules: How can we build student algebraic understanding?

Journal of Mathematical Behavior

Volumn 25, Issue 4, 2006, Pages 299-317

  Lannin, John K ^a   Barker, David D ^b   Townsend, Brian E ^c  

^a UNIVERSITY OF MISSOURI   (United States)

^b ILLINOIS STATE UNIVERSITY   (United States)

^c UNIVERSITY OF NORTHERN IOWA   (United States)

Author keywords

Algebra; Explicit rules; Recursive rules; Student understanding

Indexed keywords

EID: 33846165073     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2006.11.004     Document Type: Article

References (32)

1. Abramovich S. Cognitive heterogeneity in computer-mediated mathematical action as a vehicle for concept development. Journal of Computers in Mathematics and Science Teaching 22 1 (2003) 19-41
2. Ainley J., Wilson K., and Bills L. Generalising the context and generalising the calculation. In: Pateman N.A., Dougherty B.J., and Zilliox J. (Eds). Proceedings of the twenty-seventh conference of the International Group for the Psychology of Mathematics Education held jointly with the twenty-fifth conference of PME-NA, Vol. 2. Hawai'i (2003) 9-16
3. Australian Education Council. Mathematics: A curriculum profile for Australian schools (1994), Curriculum Corporation, Carlton, VIC.
4. Bishop, J. W. (1997, April). Middle school students' understanding of mathematical patterns and their symbolic representations. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
5. 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
6. Cobb P. Conducting teaching experiments in collaboration with teachers. In: Kelly A., and Lesh R. (Eds). Handbook of research design in mathematics and science education (2000), Lawrence Erlbaum Associates, Mahwah, NJ 307-334
7. Courant R. Reminiscences from Hilbert's Gottingen. Mathematical Intelligencer 3 (1981) 154-164
8. Davydov, V. V. (1990). Types of generalization in instruction (Soviet studies in mathematics education, Vol. 2, J. Kilpatrick, Ed., J. Teller, Trans.). Reston, VA: National Council of Teachers of Mathematics.
9. Department for Education and Skills. Frameworks for teaching mathematics: Years 7, 8 and 9 (2001), DfES Publications, London
10. Drier H.S. Teaching and learning mathematics with interactive spread-sheets. School Science and Mathematics 101 4 (2001) 170-179
11. Healy L., and Hoyles C. Visual and symbolic reasoning in mathematics: Making connections with computers. Mathematical Thinking and Learning 1 (1999) 59-84
12. Hewitt D. Train spotters' paradise. Mathematics Teaching 140 (1992) 6-8
13. Jones G.A., Langrall C.W., Thornton C.A., and Mogill A.T. Students' probabilistic thinking in instruction. Journal for Research in Mathematics Education 30 5 (1999) 487-519
14. Kaput J.J. Teaching and learning a new algebra. In: Fennema E., and Romberg T. (Eds). Mathematics classrooms that promote understanding (1999), Lawrence Erlbaum Associates, Mahwah, NJ 133-155
15. Lamon S.J. Teaching fractions and ratios for understanding (1999), Lawrence Erlbaum Associates, Mahwah, NJ
16. Lannin J.K. Generalization and justification: The challenge of introducing algebraic reasoning through patterning. Mathematical Thinking and Learning 7 3 (2005) 231-258
17. Lee L. Initiation into algebraic culture: Generalization. In: Bednarz N., Kieran C., and Lee L. (Eds). Approaches to algebra: Perspectives for research and teaching (1996), Kluwer Academic Publishers, Dordrecht, The Netherlands 87-106
18. MacGregor M., and Stacey K. The effect of different approaches to algebra on students' perceptions of functional relationships. Mathematics Education Research Journal 7 1 (1995) 69-85
19. Mack N.K. Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education 26 5 (1995) 422-441
20. Mason J. Expressing generality and roots of algebra. In: Bednarz N., Kieran C., and Lee L. (Eds). Approaches to algebra: Perspectives for research and teaching (1996), Kluwer Academic Publishers, Dordrecht, The Netherlands 65-86
21. Miles M.B., and Huberman A.M. Qualitative data analysis: An expanded sourcebook. 3rd ed. (1994), Sage Publications, Newbury Park, CA
22. National Council of Teachers of Mathematics. Principles and standards for school mathematics (2000), NCTM, Reston, VA
23. Orton J., Orton A., and Roper T. Pictorial and practical contexts and the perception of pattern. In: Orton A. (Ed). Pattern in the teaching and learning of mathematics (1999), Cassel Wellington House, London 121-136
24. Radford L. Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization. Mathematical Thinking and Learning 5 1 (2003) 37-70
25. Sandefur J.T. Discrete dynamical modeling (1993), Oxford University Press, New York
26. Sowder J., Armstrong B., Lamon S., Simon M., Sowder L., and Thompson A. Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education 1 2 (1998) 127-155
27. Stacey K. Finding and using patterns in linear generalizing problems. Educational Studies in Mathematics 20 (1989) 147-164
28. Stacey K., and MacGregor M. Curriculum reform and approaches to algebra. In: Lins R. (Ed). Perspectives on school algebra (2001), Kluwer Academic Publishers, Dordrecht, The Netherlands 141-153
29. Strauss A.L., and Corbin J. Basics of qualitative research: Grounded theory procedures and techniques. 2nd ed. (1998), Sage, Thousand Oaks
30. Sutherland R., and Rojano T. A spreadsheet approach to solving algebra problems. Journal of Mathematical Behavior 12 4 (1993) 353-383
31. Swafford J.O., and Langrall C.W. Grade 6 students' preinstructional use of equations to describe and represent problem situations. Journal for Research in Mathematics Education 31 (2000) 89-112
32. Wilson K., Ainley J., and Bills L. Spreadsheet generalising and paper and pencil generalising. In: Johnsen Hoines M., and Berit Fuglestad A. (Eds). Proceedings of the twenty-eighth conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway, Vol. 4 (2004) 441-448