Mathematical reasoning in calculus textbook exercises

Journal of Mathematical Behavior

Volumn 23, Issue 4, 2004, Pages 405-427

  Lithner, Johan ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

Exercises; Mathematical reasoning; Textbooks

Indexed keywords

EID: 10144243321     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2004.09.003     Document Type: Article

References (30)

1. R. Adams Calculus: A complete course 5th ed. 2003 Addison-Wesley
2. Bergqvist T. Lithner J. & Sumpter L. 2003 Reasoning characteristics in upper secondary school students' task solving (Research Reports in Mathematics Education 1). Department of Mathematics, Umea University
3. R. Courant F. John Introduction to Calculus and Analysis: 1 1965 Wiley International
4. C. de La Vallée Poussin d'Analyse Infinitésimale 8th ed. 1954 Gauthiers-Villars Paris
5. W. Doyle Classroom organization and management In M.C. Wittrock Handbook of research on teaching 3rd ed. 1986 Macmillan New York 392-431
6. W. Doyle Work in mathematics classes: The context of students' thinking during instruction Educational Psychologist 23 1988 167-180
7. T. Dreyfus Why Johnny can't prove Educational Studies in Mathematics 38 1999 85-109
8. C.H. Edwards D. Penney Calculus 6th ed. 2002 Prentice Hall International
9. Harel G. & Dubinsky E. (Eds.) 1992 The concept of function: Aspects of epistemology and pedagogy Washington, DC: Mathematical Association of America
10. G. Harel J. Trgalová Higher mathematics education In A. Bishop K. Clements C. Keitel J. Kilpatrick C. Laborde (Eds.) International handbook of mathematics education 1996 Kluwer Dordrecht 675-700
11. M. Hegarty R. Mayer C. Monk. Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers Journal of Educational Psychology 87 1 1995 18-32
12. M. Henningsen M.K. Stein Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning Journal for Research in Mathematics Education 28 5 1997 524-549
13. C. Hoyles The curricular shaping of students approaches to proof For the Learning of Mathematics 17 1997 7-16
14. J. Lithner Mathematical reasoning in task solving Educational studies in mathematics 41 2000 165-190
15. Lithner J. 2003a A framework for analysing qualities of mathematical reasoning: Version 2 (Research Reports in Mathematics Education 3) Department of Mathematics, Umea University
16. Lithner J. 2003b Students' mathematical reasoning in university textbook exercises Educational Studies in Mathematics 52 29-55
17. E. Love D. Pimm "This is so": A text on texts In A. Bishop K. Clements C. Keitel J. Kilpatrick C. Laborde (Eds.) International handbook of mathematics education 1996 Kluwer Dordrecht 371-409
18. R. McGinty J. VanBeynen D. Zalewski Do our mathematics textbooks reflect what we preach? School Science and Mathematics 86 1986 591-596
19. G. Pólya How to solve it 1945 Princeton University Press Princeton, NJ
20. Pólya G. 1954 Mathematics and plausible reasoning (Vols. I and II) Princeton, NJ: Princeton University Press
21. S. Salas E. Hille G. Etgen Calculus: One and several variables 8th ed. 1999 Wiley
22. A. Schoenfeld Mathematical problem solving 1985 Academic Press Orlando, FL
23. A. Schoenfeld On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics In J. Voss D. Perkins J. Segal (Eds.) Informal reasoning and education 1991 Lawrence Erlbaum Associates Hillsdale, NJ 311-344
24. A. Schoenfeld Learning to think mathematically: Problem solving, metacognition and sense-making in mathematics In D. Grouws (Ed.) Handbook for research on mathematics teaching and learning 1992 Macmillan New York 334-370
25. J. Selden A. Selden A. Mason Even good calculus students can't solve non-routine problems In J. Kaput E. Dubinsky (Eds.) Research issues in undergraduate mathematics learning 1994 Mathematical Association of America Washington, DC 19-26
26. Shield M. 1998 Mathematics textbooks: Messages to students and teachers In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching Mathematics in New Times (pp. 516-522) 21st Annual Conference of the Mathematics Education Research Group of Australasia
27. D. Tall Functions and calculus In A. Bishop K. Clements C. Keitel J. Kilpatrick C. Laborde (Eds.) International handbook of mathematics education 1996 Kluwer Dordrecht 289-325
28. P. Thompson Students, functions, and the undergraduate curriculum In E. Dubinsky A. Schoenfeld J. Kaput (Eds.) Research in collegiate mathematics education I, CBMS issues in mathematics education 1994 American Mathematical Society 21-44
29. S. Vinner The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning Educational Studies in Mathematics 34 1997 97-129
30. E. Yackel C. Rasmussen K. King Social and sociomathematical norms in an advanced undergraduate mathematics course The Journal of Mathematical Behavior 19 2000 275-287