CalGeo: Teaching Calculus using dynamic geometric tools
Outcome 1.4.2 “Bibliography about student understanding of topics in Calculus’’.
BIBLIOGRAPHY
Adams, R. (2003). Calculus: A complete course. (5th ed.). Addison-Wesley.
Agwu, N. M. A. (1995). Using a computer laboratory setting (CLS) to teach college calculus.
(Syracuse University, 1995). Dissertation Abstracts International, 57/02, 611.
Alcock, L.J. (2001). Categories, definitions and mathematics: Student reasoning about objects in
analysis. Unpublished Ph.D. Thesis, Mathematics Education Research Centre, University
of Warwick, UK.
Alcock, L.J. and Simpson, A.P. (2002). Definitions: Dealing with categories mathematically. For
the Learning of Mathematics, 22(2), 28–34.
Alcock, L.J. and Simpson, A.P. (In press). Convergence of sequences and series: Interactions
between visual reasoning and the learners beliefs about their own role. Educational Studies
in Mathematics.
Alcock, L.J., & Simpson, A.P. (2001). The Warwick analysis project: Practice and theory. In D.
Holton (Ed.), The teaching and learning of mathematics at university level (pp. 99–111).
Dordrecht: Kluwer.
Aldis, G. K., Sidhu, H. S., & Joiner, K. F. (1999). Trial of calculus and maple with heterogeneous
student groups at the Australian defense force academy. The International Journal of
Computer Algebra in Mathematics Education, 6(3), 167-189.
Almeqdadi, F., (1997). Graphics calculators in calculus: An analysis of students’ and teachers’
attitudes. (Ohio University, 1997). Dissertation Abstracts International , 58/05, 1627.
Alves Dias, M., & Artigue, M. (1995). Articulation problems between different systems of
symbolic representations in linear algebra. In L. Meira (Ed.), Proceedings of the 19th
international conference on the psychology of mathematics education (Vol. I, pp. 34–41).
Recife, Brazil.
Andersen, K. (1985). Cavalieri's method of indivisibles, Archive for History of the Exact
Sciences, 31, 291–367.
Anderson, J., Austin, K., Barnard, T., & Jagger, J. (1998). Do third-year mathematics
undergraduates know what they are supposed to know. International Journal of
Mathematical Education in Science and Technology, 29(3), 401-420.
Arcavi A. (2003). The role of visual representations in the learning of mathematics. Educational
Studies in Mathematics 52(3), 215–241.
1
Armstrong, G. M. & Hendrix, L. J., (1999). Does traditional or reformed calculus prepart
students better for subsequent courses? A preliminary study. Journal of Computers in
Mathematics and Science teaching, 18(2), 95–103.
Artigue, M. (1986). The notion of differential for undergraduate students in the sciences. P.M.E.
10,London, 235-240.
Artigue, M. (1991). Analysis. In D.O. Tall (Ed.), Advanced Mathematical Thinking (pp. 166–
198). Dordrecht: Kluwer.
Artigue, M. (2000). Teaching and learning calculus: What can be learned from education
research and curricular changes in France? In E. Dubinsky, A. H. Schoenfeld & J. Kaput
(Eds.). Research in collegiate mathematics education IV, American Mathematical Society
(pp. 1–15). Providence, Rhode Island.
Artigue, M. (2003).Learning and teaching analysis: What can we learn from the past in order to
think about the future? In D. Coray, F. Furinghetti, H. Gispert, B.R. Hodgson & G.
Schubring (Eds.). One Hundred Years of L’Enseignement Mathématique. Moments of
Mathematics Education in the Twentieth Century. L’Enseignement Mathématique, Genève,
213–223.
Artigue, M., Chartier, G., & Dorier, J.L. (2000). Presentation of other research works. In J.L.
Dorier (Ed.), On the Teaching of Linear Algebra (pp. 247–271). Dordrecht: Kluwer
Academic Publishers.
Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A
framework for research and curriculum development in undergraduate mathematics
education. In: E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in collegiate
mathematics education (Vol. 2, pp. 1–32). Providence, RI: American Mathematical
Society.
Asiala, M., Cottrill, J., Dubinsky, E., & Schwingendorf, K. (1997). The development of students’
graphical understanding of the derivative. Journal of Mathematical Behavior, 16(3),
(pages?).
Ayers, T., Davis G., Dubinsky E. & Lewin P. (1988). Computer experiences in learning
composition of functions. Journal for Research in Mathematical Education, 19(3), 248-59.
Baker, B., Hemenway, C., & Trigueros, M. (2000). On transformations of basic functions. In: H.
Chick, K. Stacey, & J. Vincent (Eds.), Proceedings of the 12th ICMI Study Conference on
the Future of the Teaching and Learning of Algebra (Vol. 1, pp. 41–47). University of
Melbourne.
Barnes, M. (1988). Understanding the Function Concept: Some Results of Interviews with
Secondary and Tertiary Students. Research on Mathematics Education in Australia, 24-33.
Baron, M.E. (1987). The Origins of the Infinitesimal Calculus. New York: Dover.
Barton, S. D. (1996). Graphing calculators in college calculus: An examination of teachers’
conceptions and instructional practice. (Oregon State University, 1995). Dissertation
Abstracts International, 56/10, 3868.
Bell, J.L. (1988).Infinitesimals. Synthese, 75, 285–315.
2
Berry, J., & Nyman, M. (2003). Promoting students’ graphical understanding of the calculus.
Journal of Mathematical Behaviour, 22. 481-497
Biehler, R. (in press) Reconstruction of meaning as a didactical task: The concept of function as
an example. In J. Kilpatrick, C. Hoyles & O. Skovsmose (Eds.), Meaning in Mathematics
Education. Dordrecht: Kluwer.
Bishop, E. (1967). Foundations of constructive analysis. McGraw-Hill.
Bishop, E. (1977). Review of elementary calculus. In H.J. Keisler (Ed.), Bulletin of the American
Mathematical Society 83(2), (pp. 205–208).
Bloch, I. (1999). L’articulation du travail mathématique du professeur et de l’élève dans
l’enseignement de l’analyse en première scientifique. Recherches en Didactique des
Mathématiques, 19(2), 135–194.
Boero, P. , Dreyfus, T., Gravemeijer K., Gray, E., Hershkowitz, R., & Schwarz, B. (2002).
Abstraction: theories about the emergence of knowledge structures. In: A.D. Cockburn &
E. Nardi, (Eds.), Proceedings of the 26th international conference for the psychology of
mathematics education (Vol. 1, pp. 113–138). UEA, Norwich, UK.
Bolzano, B. (1950). Paradoxes of the infinite (translated from the German of the posthumous
edition by Fr. Prihonsky and furnished with a historical introduction by Donald A.
Steele).London: Routledge & Paul.
Bookman, J., & Charles F. (1999). The evaluation of project CALC at Duke University 19891994. In B. Gold, S. Keith, & W. Marion (Eds.), Assessment practices in undergraduate
mathematics, MAA Notes, 49, (pp.253-256). Washington DC: Mathematical Association of
America.
Borasi, R. (1985). Errors in the enumeration of infinite sets. Focus on Learning Problems in
Mathematics, 7, 77–89.
Borasi, R. (1985). Intuition and rigor in the evaluation of infinite expressions. Focus on
LearningProblems in Mathematics, 7(3-4), 65-75.
Borba, M. C. (1993). Students' understanding of transformations of functions using
multirepresentational software. Doctoral Dissertation, Cornell University, U.S.A..
Published in 1994-Lisbon, Portugal: Associação de Professores de Matemática.
Borba, M. C. (1995a) Overcoming Limits of software tools: A student's solution for a problem
involving transformation of functions. In L.Meira et al. (Eds.), Proceedings of the XVIII
Psychology of Mathematics Education (Vol. II, pp. 248–255). Recife, Brazil: UFPE.
Borba, M. C., & Confrey, J. (1992). Transformations of functions using multirepresentational
software. Proceedings of the XVI Psychology of Mathematics Education (Vol. III, pp. 149)
Durham: University of New Hampshire.
Borba, M.C., & Confrey, J. (1996). A students’ construction of transformations of functions in a
multirepresentational environment. Educational Studies in Mathematics, 31(3), 319–337.
Borgen, K.L., & Manu, S.S. (2002). What do students really understand? Journal of
Mathematical Behavior, 21(2), 151-165.
3
Bos, H.J.M. (1974). Differentials, higher-order differentials and the derivative in the Leibnizian
calculus. Archive for History of the Exact Sciences, 14, 1–90.
Bottazzini, U. (1986). The higher calculus: A history of real and complex analysis from Euler to
Weierstrass. New York: Springer-Verlag.
Bowden, J., & Ference M. (1998). University of learning: Beyond quality and competence in
higher education. London: Kogan Page; Sterling, VA: Stylus Publishing.
Boyer, C. B. (1985). A History of Mathematics. Princeton, NJ: Princeton University Press.
Boyer, C.B. (1941). Cavalieri, limits and discarded infinitesimals. Scripta Mathematica, 8, 79–
91.
Boyer, C.B. (1959). The History of the Calculus and its Conceptual Development. New York:
Dover.
Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992).Development of the process
conception of function. Educational Studies in Mathematics, 23, 247–285.
Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (in preparation). Development of the
Process Concept of Function.
Bremigan, E.G. (2005). An Analysis of Diagram Modification and Construction in Students'
Solutions to Applied Calculus Problems, JRME, 36(3), 248-277.
Bressoud, D. (1994). A Radical Approach to Real Analysis. Washington, DC: Mathematical
Association of America.
Briggs, A. W. (1998). Defining uniform continuity first does not help. Letters to the editor,
Notices of the AMS, 45 5, 462.
Burn, R.P. (1992). Numbers and functions: Steps into Analysis. Cambridge: Cambridge
University Press.
Burn, R.P. (2003). Some comments on The Role of Proof in Comprehending and Teaching
Elementary Linear Algebra by F. Uhlig. Educational Studies in Mathematics, 51, 183–184.
Cajori, F. (1923). Grafting of the theory of limits on the calculus of Leibniz. American
Mathematical Monthly, 30, 223–234.
Cajori, F. (1925). Indivisibles and ghosts of departed quantities in the history of mathematics.
Scientia, 37, 301–306.
Carlson, M., Jacobs, S., Coe, T., Larsen, S.,& Hsu, E. (2002) Applying Covariational Reasoning
While Modeling Dynamic Events: A Framework and a Study. Journal for Research in
Mathematics Education,33 (5), 352-378.
Carraher, D., Schliemann, A., & Nevirovsky, R., (1995). Graphing from everyday experience.
Hands on. 10(2) (http://www.terc.edu/handson/f95/graphing.html). Terc, Mass.
Castillo, T. (1998). Visualization, attitude and performance in multivariable calculus: relationship
between use and nonuse of graphing calculator (college students). (The University of Texas
at Austin, 1997). Dissertation Abstracts International, 59/02, 438.
4
Chevallard, Y. (2002a). ‘Organiser L’étude 1. Structures et fonctions’, in J.-L. Dorier et al. (eds.),
Actes de la 11 e école d’été de didactique des mathématiques – Corps 21–30 Août 2001,
La Pensée Sauvage, Grenoble, pp. 3–22.
Christou, C., Zachariades, Th., & Papageorgiou, E. (2002). The difficulties and reasoning of
undergraduate mathematics students in the identification of functions. Proceedings in the
10th ICME Conference. Crete: Wiley.
Christou, C., Pitta-Pantazi, D., Souyoul, A., & Zachariades, T. (2005). The embodied, proceptual
and formal worlds in the context of functions. Canadian Journal of Science, Mathematics
and Technology Education, 5(2), 241-252.
Cipra, B.A. (1988). Calculus: Crisis Looms in Mathematics’ Future. Science, 239, 1491-1492.
Confrey, J. (1991a). Function Probe [computer program]. Santa Barbara: Intellimation Library
for the Macintosh.
Confrey, J. (1992). Function Probe. [MacIntosh sofware] Santa Barbara, CA: Intellimation
Library for the MacIntosh.
Confrey, J. (1992). Using computers to promote students' inventions of the function concept. In
S.Malcom, L.Roberts, & K.Sheingold (Eds.), This Year In School Science 1991 (pp. 141–
174).Washington D.C: American Association for the Advancement of Science.
Confrey, J. (1993a). The role of technology in reconceptualizing functions and algebra. In J.
R.Becker & B. J.Pence (Eds.), Proceedings of the XV Psychology of Mathematics
Education-NA (Vol. I, pp. 47–74). San Jose, U.S.A.: Center for Mathematics and Computer
Science Education at San Jose State University.
Confrey, J. (1993b). Diversity, tools, and new approaches to teaching functions. Paper presented
at the China-Japan-U.S. Meeting on Mathematics Education, Shanghai: East-China Normal
University.
Confrey, J. (1994a). Six approaches to transformation of functions using multirepresentational
software. Proceedings of the XVIII Psychology of Mathematics Education (Vol. I, pp. 47–
74), Lisbon: Lisbon University.
Confrey, J., Rizutti, J., Scher, D., & Piliero, S. (1991). Documentation of Function Probe,
unpublished manuscript. Ithaca, NY: Cornell University.
Connors, M. A. (1995). Achievement and gender in computer-integrated calculus. Journal of
Women and Minorities in Science and Engineering, 2, 113-121.
Cooley, L. A. (1996). Evaluating the effects on conceptual understanding and achievement of
enhancing an introductory calculus course with a computer algebra system (New York
University, 1995). Dissertation Abstracts International, 56/10, 3869.
Cooley, L. A. (1997). Evaluating student understanding in a calculus course enhanced by a
computer algebra system. Primus, 7(4), 308-316.
Cooney, T.J., & Wilson, M.R. (1993). Teachers' thinking about function: Historical and research
perspectives. In T.A. Romberg, E. Fennema & T. Carpenter (Eds.), Integrating Research
about the Graphical Representations of Function (pp. 131–158). Hillsdale, NJ: Erlbaum.
5
Cornu, B. (1981). Apprentissage de la notion de limite: modèles spontanés et modèles propres.
Actes du Cinquième Colloque du Groupe Internationale PME, Grenoble, 322-326.
Cornu, B. (1983). Apprentissage de la notion de limite: Conceptions et obstacles. Doctoral
Dissertation, Université Scientifique et Médicale, Grenoble.
Cornu, B. (1983). Apprentissage de la notion de limite: Conceptions et Obstacles. Thèse de
Doctorat, Grenoble.
Cornu, B. (1983). L'apprentissage de la Notion de Limites: Conceptions et Obstacles.
Unpublished PhD thesis, L'Universite Scientifique et Medicale de Grenoble.
Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 153–166).
Dordrecht: Kluwer Academic Publishers.
Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996).
Understanding the Limit Concept: Beginning with a Coordinated Process Scheme. Journal
of Mathematical Behavior,15(2), 167-192.
Courant, R., & John, F. (1965). Introduction to Calculus and Analysis 1. Wiley International.
Cowell, R. H., & Prosser, R.T. (1991). Computers with calculus at Dartmouth. Primus, 1(2), 149158.
Crocker, D. A. (1993). Development of the concept of derivative in a calculus class using the
computer algebra system Mathematica. In L. Lum (Ed.), Proceedings of the Fourth Annual
International Conference on Technology in Collegiate Mathematics (pp. 251-255).
Reading, MA: Addison Wesley.
Dauben, J.W. (1988). Abraham Robinson and nonstandard analysis: history, philosophy, and
foundations of mathematics. In W. Aspray & P. Kitcher (Eds.), History and Philosophy of
Modern Mathematics (pp. 177–200). Minneapolis: University of Minnesota Press.
Davis, B., Porta, H., & Uhl, J. (1994). Calculus & Mathematica®: Addressing fundamental
questions about technology. In L. Lum (Ed.) Proceedings of the Fifth Annual International
Conference on Technology in Collegiate Mathematics (pp. 305-314). Reading MA:
Addison Wesley.
Davis, M., & Hersh, R. (1972). Nonstandard analysis. Scientific American, 226, 78–86.
Davis, R. B., & Vinner, S. (1986). The notion of limit: Some seemingly unavoidable
misconception stages. Journal of Mathematical Behavior,5(3), 281-303.
Davis, R.B., & Vinner, S. (1986). The Notion of Limit: Some Seemingly Unavoidable
Misconception Stages. Journal of Mathematical Behaviour, 5(3), 281-303.
de La Vallée Poussin, 1954 C. de La Vallée Poussin, d’Analyse Infinitésimale (8th ed.),
Gauthiers-Villars, Paris.
Demana & Waits 1988. Pitfalls in graphical computation, or why a single graph isn’t enough.
College Mathematics Journal,19 (2) 177-183.
Dennis, D., & Confrey, J. (1995). Functions of a curve: Leibniz's original notion of functions and
its meaning for the parabola. The College Mathematics Journal, 26(3).
6
Dorier, J.-L. (2000). On the Teaching of Linear Algebra. Dordrecht: Kluwer Academic
Publishers.
Dorier, J.-L. (2002). Teaching linear algebra at university. In Li Tatsien (Ed.), Proc. Int. Congr.
Mathematician, Beijing 2002, August 20-28, Vol III (Invited Lectures), pp. 875–884.
Dorier, J.-L., & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra.
In D. Holton et al. (Eds.), The Teaching and Learning at University Level - An ICMI Study
(pp. 253–271).Dordrecht: Kluwer Academic Publishers.
Dorier, J.-L., Robert, A., Robinet, J. and Rogalski, M. (1994). The teaching of linear algebra in
first year of French science university, in Proc. 18th Conf. Int. Group for the Psychology of
Mathematics Education, Lisbon, 4(4), pp. 137–144.
Dorier, J.-L., Robert, A., Robinet, J. and Rogalski, M. (2000). On a research program about the
teaching and learning of linear algebra in first year of French science university.
International Journal of Mathematical Education in Sciences and Technology, 31(1), 27–
35.
Dorofeev, G. V. (1978). The concept of function in mathematics and in school. Mathematics in
School, 2, 10 -27.
Douglas, R. G. (Ed.) Towards a lean and lively calculus, MAA Notes 6. Washington, DC: MAA.
Dreyfus, T. & Vinner, S. (1989). Images and Definitions for the Concept of Function. Journal
forResearch in Mathematics Education, 20(4), 356-366.
Dreyfus, T., & Eisenberg, T. (1982). Intuitive functional concepts: a Baseline Study on
Intuitions. Journal for Research in Mathematical Education, 6(2), 18-24.
Dreyfus, T., & Eisenberg, T. (1983). The Function Concept in College Students: Linearity,
Smoothness, and Periodicity. Unpublished manuscript.
Dreyfus, T., & Eisenberg, T. (1996). On different facets of mathematical thinking. In: R.
Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 253–284).
Mahwah, NJ: Lawrence Erlbaum Associates.
Dreyfus, T., & Halevi, T. (1990/91). QuadFun-A case Study of Pupil Computer Interaction,
Journal of Computers in Math and Science Teaching, 10 (2) 43-48.
Dreyfus, T., & Tsamir, P. (2002). Ben’s consolidation of knowledge structures about infinite sets.
Tel Aviv University, Israel: Technical Report, available from the authors.
Dreyfus, T., & Tsamir, P. (2004). Ben’s consolidation of knowledge structures about infinite sets.
The Journal of Mathematical Behavior, 23(3), 271-300.
Dreyfus, T., Hershkowitz, R., & Schwarz, B. B. (2001). Abstraction in context II: the case of peer
interaction. Cognitive Science Quarterly, 1(3/4), 307–368.
Dreyfus,T., & Vinner, S. (1982). Some aspects of the function concept in college students and
junior high school teachers. Proceedings of the Sixth International Conference for the
Psychology of Mathematics Education, Antwerp, 12-17.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.),
Advanced Mathematical Thinking (pp. 95–126). Dordrecht: Kluwer Academic Publishers.
7
Dubinsky, E. (1992). A learning theory approach to calculus. In Z.A. Karian (Ed.), Symbolic
Computation in Undergraduate Mathematics Theory. MAA Notes, 24 (pp. 43–
55).Washington.
Dubinsky, E., & MacDonald, M. (2001). APOS: a constructivist theory of learning in
undergraduate mathematics education research. In: D. Holton (Ed.), The Teaching and
Learning of Mathematics at University Level: An ICMI Study (pp. 273–280). Dordrecht:
Kluwer Academic Publishers.
Dubinsky, E., & Yiparaki, O. (2000). On student understanding of AE and EA quantification. In
E. Dubinsky, A. H. Schoenfeld & J. Kaput (Eds.), Research in Collegiate Mathematics
Education IV (pp. 239–289).American Mathematical Society, Providence, Rhode Island,
Dubinsky, E., Weller, K., Mcdonald, M.A., & Brown, A. (2005). Some historical issues and
paradoxes regarding the concept of infinity: An Apos analysis: Part 2. Educational Studies
in Mathematics, 60(2), 253-266.
Dudley, U. (1993). Readings for Calculus. Washington, DC: Mathematical Association of
America.
Dugdale, S. (1982). Green globs: A microcomputer application for graphing equations.
Mathematics Teacher, 75, 208–214.
Dugdale, S. (1984). Computers: Applications unlimited. In V. Hansen & M. Zweng (Eds.),
Computers in Mathematics Education [NCTM Yearbook] (pp. 82–89). Reston, VA:
NCTM.
Dugdale, S., & Kibbey, D. (1989) Building a qualitative perspective before formalizing
procedures: graphical representations as a foundation of trigonometric identities,
Proceedings of the 11th Meeting of PME-NA. NJ.
Edwards, B. (1997). An undergraduate student's understanding and use of mathematical
definitions in real analysis. In J. Dossey, J.O. Swafford, M. Parmentier & A.E. Dossey
(Eds.), Proceedings of the 19th Annual Meeting of the North American Chapter of the
International Group for the Psychology of Mathematics Education, Columbus, OH,17–22.
Edwards, C.H. (1979). The Historical Development of the Calculus. New York: Springer-Verlag.
Edwards, C.H., & Penney, D. (2002). Calculus. (6th ed.) Prentice Hall International.
Eisenberg, T., & Dreyfus, T. (1991). On visualizing functions transformations, Technical Report.
Rehovot: The Weizmann Institute of Science.
Eisenberg, T., & Dreyfus, T. (1994). On understanding how students learn to visualize function
transformations. In: E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in collegiate
mathematics education (Vol. 1, pp. 45–68). Providence, RI: American Mathematical
Society.
Ellis, R., & Gulik, D. (1991). Calculus, one and several variables, Saunders, Fort Worth.
Ellison, M. (1994). The effect of computer and calculator graphics on students’ ability to
mentally construct calculus concepts. (University of Minnesota, 1993). Dissertation
Abstracts International, 54/11, 4020.
8
English, L.D. (1997). Mathematical Reasoning. Analogies, Metaphors and Images. Mahwah, NJ:
Erlbaum.
Ervynck, G. (1981). Conceptual difficulties for first year students in the acquisition of the notion
of limit of a function, Actes du Cinquième Colloque du Groupe Internationale PME,
Grenoble, 330-333.
Ervynck, G. (1981). Conceptual difficulties for first year university students in the acquisition of
the notion of limit of a function. Proceedings of the Fifth Conference of the International
Group for the Psychology of Mathematics Education, Berkeley, 330-333.
Espinoza, L. (1998). Organizaciones matemáticas y didácticas en torno al objeto ‘límite de
función’. Del ‘pensamiento del profesor’ a la gestión de los momentos del studio. Doctoral
Thesis, Universitat Autónoma de Barcelona, Barcelona.
Estes, K. A. (1990). Graphics technologies as instructional tools in applied calculus: Impact on
instructor, students, and conceptual and procedural achievement. (University of South
Florida, 1990). Dissertation Abstracts International, 51/04, 1147.
Even, R. (1988). Prospective secondary mathematics teachers’ knowledge and understanding
about mathematical function. Unpublished Ph.D. thesis. Michigan State University.
Even, R. (1989). Prospective Secondary Mathematics Teachers Knowledge and Under-standing
about Mathematical Functions. Unpublished doctoral dissertation, Michigan State
University, East Lansing.
Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational
Studies in Mathematics, 21, 521–544.
Even, R. (1998). Factors involved in linking representations of functions. The Journal of
Mathematical Behavior, 17(1), 105–122.
Falk, R. (1994). Infinity: A cognitive challenge. Theory and Psychology, 4(1), 35– 60.
Falk, R., Gassner, D., Ben Zoor, F., & Ben Simon, K. (1986). How do children cope with the
infinity of numbers? Proceedings of the 10th Conference of the International Group for the
Psychology of Mathematics Education, UK, London, 13–18.
Farrell, J.P., & Heyneman, S.P. (1994). Planning for textbook development in developing
countries. In T. Husén and T.N. Postlethwaite (Eds.), International Encyclopedia of
Education (2nd ed., Vol. 2, pp. 6360–6366). BPC Wheatons, Exeter.
Ferrini-Mundi, J., & Graham, K. (1994). Research in calculus learning: Understanding of limits,
derivatives and integrals. In J. Kaput & E. Dubinsky (Eds.), Reserach Issues in
Undergraduate Mathematics Learning. MAA Notes 33, Washington, pp. 31–45.
Ferrini-Mundy, J., & Graham K.G., (1991). An Overview of the Calculus Curriculum Reform
Effort: Issues for Learning, Teaching, and Curriculum Development. American
Mathematical Monthly, 98 (7), 627-635.
Fischbein E., Tirosh D., & Melamed, U. (1981). Is it possible to measure the intuitive acceptance
of a mathematical statement? Educational Studies in Mathematics, 12, 491-512.
Fischbein, E. (1978). Intuition and mathematical education, Osnabrücker Schriften zür
Mathematik, 1, 148–176.
9
Fischbein, E. (1982). Intuition and proof. For the Learning of Mathematics, 3(2), 9–24.
Fischbein, E. (1987). Intuition in Science and Mathematics. Dordrecht, The Netherlands: Reidel.
Fischbein, E. (2001). Tacit models and infinity. Educational Studies in Mathematics, 48(2-3),
309-329.
Fischbein, E., Jehiam, R., & Cohen, D. (1995). The concept of rational numbers in high school
students and prospective teachers. Educational Studies in Mathematics, 29, 29–44.
Fischbein, E., Tirosh, D., & Hess, P. (1979). The intuition of infinity. Educational Studies in
Mathematics, 10, 3–40.
Fischbein, E., Tirosh, D., & Melamed, U. (1981). Is it possible to measure the intuitive
acceptance of a mathematical statement? Educational Studies in Mathematics, 12, 491–
512.
Fischbein, E., Tirosh, D., Hess, P. (1979). The intuition of infinity, Educational Studies in
Mathematics, 12, 491-512.
Fiske, M. (1995). A comparison of the effects on student learning of two strategies for teaching
the concept of derivative. (The Ohio State University, 1994). Dissertation Abstracts
International, 56/01, 125.
Fitzsimmons, R. W. (1995). The relationship between cooperative student pairs’ Van Hiele levels
and success in solving geometric calculus problems following graphing calculator-assisted
spatial training. (Columbia University, 1995). Dissertation Abstracts International, 56/06,
2156.
Fraser, C. (1989). The calculus as algebraic analysis: some observations on mathematical analysis
in the 18th century. Archive for History of the Exact Sciences, 39, 317–335.
Fredenberg, V. (1994). Supplemental visual computer-assisted instruction and student
achievement in Freshman College calculus (Visualization). (Montana State University,
1993). Dissertation Abstracts International, 55/01, 59.
Frid, S. (1994). Three approaches to undergraduate calculus instruction: Their nature and
potential impact on students' language use and sources of conviction. In E. Dubinsky, J.
Kaput & A. Schoenfeld (Eds.), Research in Collegiate Mathematics Education I. AMS,
Providence, RI
Frid, S. (1994). Three approaches to undergraduate calculus instruction: Their nature and
potential impact on students' language use and sources of conviction. CBMS Issues in
Mathematics Education, 4, 69-100.
Galindo, E. (1995). Visualization and students' performance in technology-based calculus. In D.
T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual
Meeting of the North America Chapter of the International Group for the Psychology of
Mathematics Education (pp. 321). Columbus, OH: ERIC Clearinghouse.
Galindo-Morales, E. (1994). Visualization in the calculus class: Relationship between cognitive
style, gender, and use of technology (The Ohio State University, 1994). Dissertation
Abstracts International, 55/10, 3125.
10
Goldenberg, E. P. (1988). Mathematics, metaphors, and human factors: mathematical, technical,
and pedagogical challenges in the educational use of graphical representation of functions.
Journal of Mathematical Behavior,7(2), 135-173.
Goldenberg, E. P. , Harvey, W., Lewis, P.G., Umiker, R.J., West, J., & Zodhiates, P. (1988).
Mathematical, technical and pedagogical challenges in the graphical representation of
functions (Tech. Rep. No.88-4), Educational Technology Center, Harvard Graduate School
of Education.
Goldenberg, E. P., & Kliman, M. (1990). What you see is what you see, Technical Report.
Newton: Educational Technology Center.
Goldenberg, E. P., Harvey, W., Lewis, P., Umiker, R., West, J., & Zodhiates, P. (1988).
Mathematical, technical, and pedagogical challenges in the graphical representation of
functions, Technical Report. Cambridge: Educational Technology Center.
Grabiner, J.W. (1981). The Origins of Cauchy's Rigorous Calculus. Cambridge, Mass: MIT
Press.
Grabiner, J.W. (1983). Who gave you the epsilon? Cauchy and the origins of rigorous calculus.
American Mathematical Monthly, 90, 185–194.
Grabiner, J.W. (1983). The changing concept of change: the derivative from Fermat to
Weierstrass. Mathematics Magazine, 56, 195–206.
Graham, K. G., & Ferrini-Mundy, J. (1989). An Exploration of Student Understanding of Central
Concepts in Calculus. Paper presented at the Annual Meeting of the American Educational
Research Association.
Grattan-Guinness, I. (1970) The Development of the Foundations of Mathematical Analysis from
Euler to Riemann. Cambridge, Mass: MIT Press.
Grattan-Guinness, I. (1980). From the Calculus to Set Theory, 1630- 1910. London: Duckworth.
Gray, E.M. Pinto, M., Pitta, D., & Tall, D.O. (1999). Knowledge Construction and diverging
thinking in elementary and advanced mathematics. Educational Studies in Mathematics,
38(1-3), 111–133.
Gueudet-Chartier, G. (in press). Using geometry to teach and learn linear algebra, Research in
Collegiate Mathematical Education. AMS, Providence, Rhode Island.
Hahn, H. (1930/1988). Infinity. In J. R. Newman (Ed.), The World of Mathematics (Vol. 3, pp.
1576–1583). Washington, DC: Tempus Books.
Hahn, H.K.M. (1956). The crisis in intuition. In J.R. Newman (Ed.), The World of Mathematics
(pp. 1957–1976). New York: Simon & Schuster.
Hairer, E., & Wanner, G. (1996). Analysis by its History. New York: Springer-Verlag.
Harding, R. D., & Johnson, D. C. (1979). University level computing and mathematical problem
solving ability. Journal of Research in Mathematics Education 10(1), 37–55.
Hare, A. C. (1997). An investigation of the behavior of calculus students working collaboratively
in an interactive software environment (Mathwright, computers). (The American
University, 1996). Dissertation Abstracts International, 57/09, 3862.
11
Harel, G., & Dubinsky, E. (1992). The concept of function: Aspects of epistemology and
pedagogy. Washington, DC: Mathematical Association of America.
Harel, G., & Kaput, J. (1991). The role of conceptual entities and their symbols in building
mathematical concepts.In D.O. Tall (Ed.), Advanced Mathematical Thinking (pp. 82–94).
Dordrecht: Kluwer.
Harel, G., & Trgalová, J. (1996). Higher mathematics education. In: A. Bishop, K. Clements, C.
Keitel, J. Kilpatrick & C. Laborde (Eds.), International handbook of mathematics
education (pp. 675–700). Dordrecht: Kluwer.
Harnik, V. (1986). Infinitesimals from Leibniz to Robinson: time to bring them back to school.
Mathematical Intelligencer, 8(2), 41–47.
Hauger, G. (1999). High school and college students’ knowledge of rate of change. (Michigan
State University, 1998). Dissertation Abstracts International, 59/10, 3734.
Heid, K. M. (1988). Resequencing Skills and Concepts in Applied Calculus Using the Computer
as a Tool, Journal for Research in Mathematics Education, 19(1), 3-25.
Henle, J. and Kleinberg, M. (1979). Infinitesimal Calculus, MIT Press, Cambridge, Mass.
Hilbert, D. (1925/1989). On the infinite. In: P. Benacerraf, & H. Putnam (Eds.), Philosophy of
Mathematics (pp. 183–201). New York: Cambridge University Press.
Hillel, J., & Sierpinska, A. (1994). On one persistent mistake in linear algebra. Proc. 18th Int.
Conf. on the Psychology of Mathematics Education, Lisbon, Vol. III, 65–72.
Hitt, F. (1998). Difficulties in the articulation of different representations linked to the concept of
function. The Journal of Mathematical Behavior, 17(1), 123–134.
Hitt, F. (1998). Difficulties in the articulation of different representations linked to the concept of
function. Journal of Mathematical Behavior, 17(1), 123-134.
Hsaio, F. S., (1984/85). A New CAI Approach to Teaching Calculus. Computers in Mathematics
and Science Teaching, 4(2), 29-36.
Hughes H. D., Gleason, A. M., et al. (1994). Calculus. New York: John Wiley and Sons (Second
Edition 1998).
Jahnke, H.N. (2001). Cantor’s cardinal and ordinal infinities: an epistemological and didactical
view. Educational Studies in Mathematics, 48(2-3), 175-197.
Janvier, C. (1987). Representations and understanding: The notion of function as an example. In
Janvier, C. (Ed.), Tasks of representation in the teaching and learning of mathematics (pp.
67–71). London: Erlbaum.
Janvier, C. (1998). The notion of chronicle as an epistemological obstacle to the concept of
function. The Journal of Mathematical Behavior, 17(1), 79–103.
Judson, P. T. (1988). Effects of modified sequencing of skills and applications in introductory
calculus (The University of Texas at Austin, 1988). Dissertation Abstracts International,
49/06, 1397.
Judson, P. T. (1990). Elementary business calculus with computer algebra. Journal of
Mathematical Behavior, 9, 153-157.
12
Judson, & Nishimori, (2005)
Kalman, K. (1993). Six ways to sum a series. College Mathematics Journal, 24, 402–421.
Kaput, J. J. (1994). Democratizing access to calculus: new routes to old roots. In: A. Schoenfeld
(Ed.), Mathematical thinking and problem solving (pp. 77–156). Hillsdale, NJ: Erlbaum.
Kaput, J. J., & Roschelle, J. (1997). Deepening the impact of technology. Beyond assistance with
traditional formalisms in order to democratize access to ideas underlying calculus. In: E.
Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the
Psychology of Mathematics Education, Lahti, Finland, July 14–19 (Vol. 1, pp. 105–112).
Lahti, Finland: University of Helsinki.
Kaput, J. J., & Thompson, P. W., (1994). Technology in Mathematics Education Research: The
First 25 Years in the JRME. Journal for Research in Mathematics Education, 25(6), 676684.
Karsenty, R. (2002). What do adults remember from their high school mathematics? The case of
linear functions. Educational Studies in Mathematics,51(1), 117-144.
Karsenty, R., & Vinner, S. (2000). What do we remember when it's over? Adults recollections of
their mathematical experience Proceedings of the 24th international Conference,
Psychology of Mathematics Education (Vol. 3, pp. 119–126) Hiroshima University,
Hiroshima.
Keisler, H.J. (1976). Elementary Calculus, Prindle. Boston: Weber and Schmidt.
Keisler, J. (1986). Elementary Calculus: An Infinitesimal Approach (2nd ed.). Boston:
Prindle,Weber & Schmidt.
Keller, B. A., & Russell, C. A. (1997). Effects of the TI-92 on calculus students solving symbolic
problems. The International Journal of Computer Algebra in Mathematics Education, 4(1),
77-97.
Keller, B. A., Russell, C. A., & Thompson, H. (1999). A large-scale study clarifying the roles of
the TI-92 and instructional format on student success in calculus. The International
Journal of Computer Algebra in Mathematics Education, 6(3), 191- 207.
Kendal, M. & Stacey, K. (1999). Varieties of teacher privileging for teaching calculus with
computer algebra systems. The International Journal of Computer Algebra in Mathematics
Education,6(4), 233-247.
Kenelly, J.W., & Harvey, J. G. (1994). New developments in advanced placement calculus. In A.
Solow (ed.), Preparing for a New Calculus (pp. 46-52), MAA Notes No. 36. Washington,
DC: Mathematical Association of America.
Kerslake, D. (1977). The understanding of graphs, Mathematics in School, 6(2), 22-25.
Kidron, I., & Dreyfus, T. (2004). Constructing knowledge about the bifurcation diagram:
epistemic actions and parallel constructions. In: M. J. Høines, & A. B. Fuglestad (Eds.),
Proceedings of the 28th international conference for the psychology of mathematics
education (Vol. 3, pp. 153–160). Bergen, Norway: Bergen University College.
Kitcher, P. (1973). Fluxions, limits, and infinite littlenesse: a study of Newton's presentation of
the calculus. Isis, 64, 33–49.
13
Kleiner, I. (1989). Evolution of the function concept: A brief survey. The College Mathematics
Journal, 20(4), 282–300.
Kleiner, I. (2001). History of the infinitely small and the infinitely large in calculus. Educational
Studies in Mathematics, 48(2-3), 137-174.
Kline, M. (1983). Euler and infinite series. Mathematics Magazine, 56, 307–314.
Knuth, D. E. (1998). Teach calculus with big O, letters to the editor. Notices of the AMS, 45(6),
687–688.
Lakatos, I. (1978). Cauchy and the continuum: The significance of non-standard analysis for the
history and philosophy of mathematics. Mathematical Intelligencer 1(3), 151–161.
Lakoff, G., & Nunez, R. (2000). Where Mathematics Comes From. New York: Basic Books.
Lang, S. (1986). Cálculo, Addison-Wesley Iberoamericana, New York.
Laugwitz, D. (1997). On the historical development of infinitesimal mathematics, I, II. American
Mathematical Monthly, 104, 447–455, 660- 669.
Lauten, A. D, Graham, K., & Ferrini-Mundy, J. (1994). Student understanding of basic calculus
concepts: Interaction with the graphics calculator. Journal of Mathematical Behavior, 13,
225-237.
Lax, P. D. (1997). Use uniform continuity to teach limits, letters to the editor. Notices of the
AMS, 44(11), 1429.
Lefton, L. E., & Steinbart, E. M. (1995). Calculus and Mathematica: An end-user’s point of view,
Primus, 5(1), 80–96.
Leinhardt, G., Zaslavsky, O., & Stein, M. (1990). Functions, graphs, and graphing: tasks,
learning, and teaching. Review of Educational Research, 60(1), 1–64.
Li, L. & Tall, D. O. (1993). Constructing different concept images of sequences and limits by
programming. Proceedings of the Seventeenth International Conference for the Psychology
of Mathematics Education, Tsukuba, Japan, 2, 41-48.
Lindstrom, T. (1988). An invitation to nonstandard analysis. In N. Cutland (ed.), Nonstandard
Analysis and its Applications (pp. 1–105). Cambridge University Press, Cambridge.
Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises.
Educational Studies in Mathematics, 52, 29–55.
Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. The Journal of
Mathematical Behavior, 23(4), 405-427.
Luzin, N. (1998). The evolution of... function: Part 2. American Mathematical Monthly,105, 263–
270.
MacLane S. (1997). On the Harvard consortium calculus, letters to the editor. Notices of the
AMS, 44, 893.
Maldonado, A. R. (1998). Conversations with Hypatia: The use of computers and graphing
calculators in the formulation of mathematical arguments in college calculus. (The
University of Texas at Austin, 1998). Dissertation Abstracts International, 59/06, 1955.
14
Malik, M.A. (1980). Historical and pedagogical aspects of the definition of a function.
International Journal of Mathematics Education in Science and Technology, 11(4), 489492.
Mamona, J. (1990). Sequences and series –Sequences and functions: Students' confusions.
International Journal of Mathematical Education in Science and Technology, 21, 333–337.
Mamona-Downs, J. (2001). Letting the intuitive bear on the formal; A didactical approach for the
understanding of the limit of a sequence. Educational Studies in Mathematics, 48(2), 259–
288.
Markovits, Z., Eylon, B., & Bruckheimer, M. (1986). Functions today and yesterday, For the
Learning of Mathematics, 6, 18-24.
Markovits, Z., Eylon, B., & Bruckheimer, M. (1988). Difficulties Students have with the
Function Concept. The Ideas of Algebra, K-12, N.C.T.M. 1988 Yearbook, 43-60.
Martin, W. G., & Wheeler, M. M. (1987). Infinity concepts among preservice elementary school
teachers. In: J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th
conference of the international group for the psychology of mathematics education (pp.
362–368). Montreal, Canada.
Mathematical Association (1992). Computers in the Mathematics Curriculum, A report of the
mathematical association (Ed. J F A Mann & D O Tall), The Mathematical Association:
Leicester, UK.
May, K.O., & van Engen, H. (1959). Relations and functions. In National Council of Teachers of
Mathematics (ed.), The 24th Yearbook: The Growth of Mathematical Ideas Grades K-12
(pp. 65–110). National Council of Teachers of Mathematics, Washington, DC.
McDonald, M. A., Mathews, D. M., & Strobel, K. H. (2000). Understanding sequences: A tale of
two objects. In E. Dubinsky, A. H. Schoenfeld, & J. Kaput (eds.), Research in Collegiate
Mathematics Education IV (pp. 77–102). American Mathematical Society, Providence,
Rhode Island.
Meel, D. E. (1996). A comparative study of honor students' understandings of central calculus
conceptsas a result of completing a calculus and Mathematica® or a traditional calculus
curriculum (University of Pittsburgh, 1995). Dissertation Abstracts International, 57/01,
142.
Melin-Conejeros, J. (1992). The effect of using a computer algebra system in a mathematics
laboratory on the achievement and attitude of calculus students (Doctoral dissertation,
University of Iowa, 1992). Dissertation Abstracts International, 53/07, 2283.
Mesa, V. (2000). Conceptions of function promoted by seventh and eighth grade text-books from
eighteen countries. Unpublished Doctoral Dissertation. University of Georgia, Athens,
GA.
Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks:
an empirical approach. Educational Studies in Mathematics, 56(2), 255-286.
Monaghan, J. (1986). Adolescents' understanding of limits and infinity. Unpublished Ph.D.
thesis. Mathematics Education Research Centre, University of Warwick, UK.
15
Monaghan, J. (1991). Problems with the language of limit. For the Learning of Mathematics,
11(3), 20–24.
Monaghan, J. (2001). Young people’s ideas of infinity. Educational Studies in Mathematics,
48(2/3), 239–257.
Monaghan, J. D. (1986). Adolescent’s understanding of limits and infinity. Unpublished Ph.D.
thesis, Warwick University, U.K.
Monaghan, J., & Ozmantar, M. F. (2004). Abstraction and consolidation. In: M. J. Høines, & A.
B. Fuglestad (Eds.), Proceedings of the 28th international conference for the psychology of
mathematics education,3 (pp. 353–360). Bergen, Norway: Bergen University College.
Monaghan, J., Sun S, & Tall, D. O. (1994), Construction of the limit concept with a computer
algebra system. Proceedings of PME 18, Lisbon, III, 279–286.
Monk, G. S., (1987). Students' Understanding of Functions in Calculus Courses. Unpublished
paper.
Monk, S. (1992). Students' understanding of a function given by a physical model. In G. Harel, &
E. Dubinsky (eds.), The Concept of Function: Aspects of Epistemology and Pedagogy,
MAA Notes, 25 (pp. 175–193). Mathematical Association of America, Washington, DC,
Monk, S., & Nemirovsky, R. (1994). The case of Dan: student construction of a functional
situation through visual attributes. Research in Collegiate Mathematics Education, 4, 139–
168.
Moore, A.W. (1995). A brief history of infinity. Scientific American, 272(4), 112–116.
Moore, A.W. (1999). The Infinite. Routledge & Paul, London.
Moore, G. (2002). Hilbert on the infinite: The role of set theory in the evolution of Hilbert's
thought. Historia Mathematica, 29, 40–64.
Moreno, A., & Waldegg, G. (1991). The conceptual evolution of actual mathematical infinity.
Educational Studies in Mathematics, 22, 211–231.
Moschkovich, J., Schoenfeld, A., & Arcavi, A. (1993). Aspects of understanding: On multiple
perspectives and representations of linear relations, and connections among them. In T.A.
Romberg, E. Fennema & T.P. Carpenter (eds.), Integrating Research on the Graphical
Representation of Function (pp. 69–100). Erlbaum, Hillsdale, NJ.
Moschkovich, J.N. (1989).Constructing a Problem Space Through Appropriation: A Case Study
of Guided Computer Exploration of Linear Functions. Paper presented at the annual
meeting of the American Educational Research Association. San Francisco.
Moschkovich, J.N. (2004). Appropriating mathematical practices: A case of learning to use and
explore functions through interaction with a tutor. Educational Studies in Mathematics,
55(1-3), 49-80.
Mumford, D. (1997). Calculus reform—For the millions. Notices of the AMS, 44(5), 559–563.
National Council of Teachers of Mathematics (2000). Principles and standards for school
mathematics. Reston, VA: NCTM.
16
NCTM, 1980. National Council of Teachers of Mathematics. An Agenda for Action:
Recommendations for School Mathematics of the l980s. Reston, VA: National Council of
Teachers of Mathematics.
NCTM, 1989. National Council of Teachers of Mathematics. Curriculum and Evaluation
Standards for School Mathematics. Reston, VA: National Council of Teachers of
Mathematics.
NCTM, 1989. National Council of Teachers of Mathematics. Historical topics for the
mathematics classroom. Reston, VA: National Council of Teachers of Mathematics.
NCTM, 2000. National Council of Teachers of Mathematics. Principles and standards for school
mathematics. Reston, VA: National Council of Teachers of Mathematics.
NCTM, 2002. National Council of Teachers of Mathematics. Principles and standards for school
mathematics. Reston, VA: NCTM.
Nobel, T., Nemirovsky, R., Wright T., & Tierney, C. (2001). Experiencing change: the
mathematics of change in multiple environments. Journal of Research in Mathematics
Education, 32(1), 85–108.
Norman, A. (1992). Teachers' mathematical knowledge of the concept of function. In G. Harel &
E. Dubinsky (eds.), The Concept of Function: Aspects of Epistemology and Pedagogy,
MAA Notes,25 (pp. 215–232). Washington, DC.
Norman, A. (1992). Teachers’ mathematical knowledge of the concept of function. In E.
Dubinsky, & G. Harel (Eds.), The concept of function: Aspects of epistemology and
pedagogy (pp. 215-232). United States: Mathematical Association of America.
Norman, F. A., & Prichard, M. K. (1994). Cognitive obstacles to the learning of calculus: a
Krutetskian perspective. In: J. Kaput, & E. Dubinsky (Eds.), Research issues in
undergraduate mathematics learning: preliminary analyses and results, MAA notes, 33.
Norwood, R. (1997). In praise of Epsilon/Delta. Letters to the Editor. Notices of the AMS, 45(1),
6.
Nunez, R. (1991). A 3-dimensional conceptual space of transformations for the study of the
intuition of infinity in plane geometry. Proceedings of the 15th Conference for the
Psychology of Mathematics Education, Italy, 3, 362–368.
O'Callaghan, B.R. (1998). Computer-intensive algebra and students' conceptual knowledge of
functions. Journal for Research in Mathematics Education, 29(1), 21–40.
Orton, A. (1977). Chords, secants, tangents & elementary calculus. Mathematics Teaching, 78,
48-49.
Orton, A. (1980). A cross-sectional study of the understanding of elementary calculus in
adolescents and young adults. Unpublished Ph.D., Leeds University.
Orton, A. (1983). Students' Understanding of Integration. Educational Studies in Mathematics,
14, 1-18.
Orton, A., (1983). Students' Understanding of Differentiation. Educational Studies in
Mathematics, 14, 235-250.
17
Palmiter, J.R. (1986). The impact of a computer algebra system on college calculus (The Ohio
State University, 1986). Dissertation Abstracts International, 47/05, 1640.
Palmiter, J.R. (1991). Effects of computer algebra systems on concept and skill acquisition in
calculus. Journal for Research in Mathematics Education, 22(2), 151-156.
Park, H. & Travers, K. J. (1996). A comparative study of a computer- Based and a standard
college first year calculus course. CBMS Issues in Mathematics Education, 6, 155–176.
Parks, V. W. (1995). Impact of a laboratory approach supported by Mathematica® on the
conceptualization of limit in a first calculus course (Georgia State University, 1995.).
Dissertation Abstracts International, 56/10, 3872.
Pinto, M. (1998). Students’ understanding of real analysis. Unpublished Ph.D. Thesis, Warwick
University.
Pinto, M., & Tall, D.O. (1996). Student teachers conceptions of the rational numbers. In L. Puig
& A. Guitiérrez (Eds.), Proceedings of the 20th International conference on the Psychology
of Mathematics Education,4 (pp. 139–146). Valencia, Spain.
Pinto, M.M.F. (1998). Students' understanding of real analysis. Unpublished PhD Thesis,
Warwick University.
Pinto, M.M.F., & Tall, D.O. (2001). Following students' development in a traditional university
classroom. In M. van den Heuvel-Panhuizen (ed.), Proceedings of the 25 th Conference of
the International Group for the Psychology of Mathematics Education, 4 (pp. 57–64).
Utrecht, The Netherlands.
Pinto, M.M.F., &Tall, D.O. (1999). Student construction of formal theories: Giving and
extracting meaning. In O. Zaslavsky (ed.), Proceedings of the 23rd Meeting of the International Group for the Psychology of Mathematics Education, 1 (pp. 281–288). Haifa,
Israel.
Pontecorvo, C., & Girardet, H. (1993). Arguing and reasoning in understanding historical topics.
Cognition and Instruction, 11, 365–395.
Porzio, D. T. (1995). The effects of differing technological approaches to calculus on students’
use and understanding of multiple representations when solving problems (Doctoral
dissertation, The Ohio State University, 1994). Dissertation Abstracts International, 55/10,
3128.
Przenioslo, M. (2003). Perceiving the concept of limit by secondary school pupils. Disputationes
Scientificae Universitatis Catholicae Ruzomberok, 3, 75–84.
Przenioslo, M. (2004). Images of the limit of function formed in the course of mathematical
studies at the university. Educational Studies in Mathematics, 55, 103–132.
Przenioslo, M. (2004). Images of the limit of function formed in the course of mathematical
studies at the university. Educational Studies in Mathematics,55(1), 103-132.
Rabinovitch, N.L. (1970). Rabbi Hasdai Crescas (1340–1410) on numerical infinities. Isis 61(2),
224–230.
Radford, L. (2001). Signs and meanings in students’ emergent algebraic thinking: a semiotic
analysis. Educational Studies in Mathematics, 42(3), 237–268.
18
Ramey, C. L. (1997). The effect of project-based learning on the achievement and attitudes of
calculus I students: A case study. (University of Missouri –Kansas City, 1997).
Dissertation Abstracts International, 58/03, 786.
Rich, K. (1996). The effect of dynamic linked multiple representations on students’ conceptions
of and communication of functions and derivatives state university of New York at
Buffalo, 1995). Dissertation Abstracts International, 57/01, 142.
Rizzuti, J. (1991). Students' conceptualizations of functions: Effects of a pedagogical approach
involving multiple representations. Doctoral dissertation, Cornell University, Ithaca, NY.
Robert, A. (1988). Nonstandard Analysis. Wiley, New York.
Robert, A., & Speer, N. (2001). Research on the teaching and learning of calculus/elementary
analysis. In D. Holton (ed.), The Teaching and Learning of Mathematics at University
Level (pp. 283–299). Kluwer Academic Publishers, Dordrecht.
Roberts, A.W. (ed.) (1996). Calculus: The Dynamics of Change, MAA Notes No. 39.
Washington, D.C.:Mathematical Association of America.
Robinson, A. (1966). Non-standard Analysis. North Holland, Amsterdam.
Roddick, C. D. (1998). A comparison study of students from two calculus sequences on their
achievement in calculus-dependent courses (Mathematica®), (The Ohio State University,
1997). Dissertation Abstracts International ,58/07, 2577.
Rozier, S., & Viennot, L. (1991). Students' reasoning in thermodynamics. International Journal
of Science Education, 13, 159-170.
Rucker, R. (1982). Infinity and the Mind: The Science and Philosophy of the Infinite. Birkhauser,
Boston.
Sacristán Rock, A. (2001) Students shifting conceptions of the infinite through computer
explorations of fractals and other visual models. In Vol. 4 of the Proceedings of the 25th
Conference of the International Group for the Psychology of Mathematics Education( pp.
129–136). The Freudenthal Institute, Utrecht
Sacristán, R. A. (1997). Windows on the infinite: constructing meanings in a logo-based
microworld. Unpublished PhD thesis. Institute of Education, University of London, UK.
Sajka, M. (2003). A secondary school student’s understanding of the concept of function- A case
study. Educational Studies in Mathematics,53(3), 229-254.
Salas, S., Hille, E., & Etgen G. (1999). Calculus: One and several variables. Wiley.
Schiralli, M., & Sinclair, N. (2003). A constructive response to “Where Mathematics Comes
From”. Educational Studies in Mathematics, 52, 79–91.
Schorr, R. Y., & Lesh, R. (2003). A models and modeling perspective on classroom-based
teacher development. In R. Lesh, & H. Doerr (Eds.), Beyond constructivism: a models and
modeling perspective on teaching, learning, and problem solving in mathematics
education. Hillsdale, NJ: Lawrence Erlbaum.
Schrock, C. S. (1990). Calculus and computing: an exploratory study to examine the
effectiveness of using a computer algebra system to develop increased conceptual
19
understanding in a firstsemester calculus course (Kansas State University, 1989).
Dissertation Abstracts International,50/07, 1926.
Schwarz, B., & Bruckheimer, M. (1988). Representations of functions and analogies. P.M.E.
XII,Hungary, 552-559.
Schwarz, B., Dreyfus, T., & Bruckheimer, M. (1988). The Triple Representation Model
Curriculum for the Function Concept.
Schwarz, B.B,& Hershkowitz, R. (1995). Argumentation and reasoning in a technology-based
class. In J.F. Lehman & J.D. Moore (Eds.), Proceedings of the 17th annual meeting of the
cognitive science societ (pp. 731–735). Mahwah, NJ: Lawrence Erlbaum.
Schwarz, J., & Yerushalmy, M. (1992).Getting students to function in and with algebra. In G.
Harel, & E. Dubinsky (eds.), The Concept of Function: Aspects of Epistemology and
Pedagogy, MAA Notes, 25(pp. 261–289). Mathematical Association of America,
Washington, DC.
Schwarzenberger, R. L., & Tall, D. (1978). Conflict in the learning of real numbers and limits.
Mathematics Teaching, 82, 44–49.
Schwarzenberger, R.L.E., & Tall, D.O. (1978). Conflicts in the learning of real numbers and
limits, Mathematics Teaching, 82, 44-49.
Selden, J., Selden, A., & Mason, A. (1994). Even good calculus students can’t solve non-routine
problems. In: J. Kaput, & E. Dubinsky (Eds.), Research issues in undergraduate
mathematics learning(pp. 19–26). Mathematical Association of America, Washington, DC.
Semb, G.B., & Ellis, J.A. (1992). Knowledge Learned in College: What is Remembered? Paper
presented at the annual meeting of the American Educational Research Association, San
Francisco.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and
objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.
Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reifica-tion:
The case of function. In G. Harel, & E. Dubinsky (eds.), The Concept of Function: Aspects
of Epistemology and Pedagogy, MAANotes, 25(pp. 59–84). Mathematical Association of
America, Washington, DC.
Sherin, B.L. (2000). How students invent representations of motion: a genetic account. Journal of
Mathematical Behavior, 19, 399–443.
Sierksma, G., & Sierksma, W. (1999). The great leap to the infinitely small. Johann Bernoulli:
Mathematician and philosopher. Annals of Science, 56, 433–449.
Sierpinska, A. (1988). Epistemological remarks on functions, P.M.E. XII, Hungary, 568-575.
Sierpinska, A. (1985). Obstacles épistémologiques relatifs á la notion de limite. Recherches en
Didactique des Mathématiques, 6, 5–68.
Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits.
Educational Studies in Mathematics, 18(4), 371–397.
Sierpinska, A. (1990). Some remarks on understanding in mathematics. For the Learning of
Mathematics, 10, 24–36.
20
Sierpinska, A. (1992). On understanding the notion of function. In G. Harel, & E. Dubinsky
(eds.), The Concept of Function: Aspects of Epistemology and Pedagogy, MAA Notes,
25(pp. 25–58). Mathematical Association of America, Washington, DC.
Sierpinska, A. (1994). Understanding in mathematics. London: Falmer Press.
Sierpinska, A. (2000). On some aspects of students' thinking in linear algebra. In J.L. Dorier
(ed.), On the teaching of linear algebra (pp. 209–271), Kluwer Academic Publishers,
Dordrecht.
Sierpinska, A., & Viwegier, M. (1989). How and when attitudes towards mathematics and
infinity become constituted into obstacles in students? In G. Vergnaud, J. Rogalski, & M.
Artigue (Eds.), Proceedings of the 13th annual meeting for the psychology of mathematics
education, 3 (pp. 166–173). Paris, France.
Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits.
Educational Studies in Mathematics, 18, 371-397.
Simmons, G.F. (1972). Differential Equations. McGraw-Hill, New York.
Simmons, G.F. (1992). Calculus Gems: Brief Lives and Memorable Mathematics. McGraw-Hill,
New York.
Smith, D. A., & Moore L. C. (1996), Calculus: Modeling and Application, Boston: Houghton
Mifflin Co.
Smith, E., & Confrey, J. (1992). Using a dynamic software tool to teach transformations of
functions. Proceedings of the fifth Annual Conference on Technology in Collegiate
Mathematics, Reading: Addison-Wesley, 115–242.
Soto-Johnson, H. (1998). Impact of technology on learning infinite series. The International
Journal of Computer Algebra in Mathematics Education, 5(2), 95-109.
Stahl, S. (1999). Real analysis: A historical approach. John Wiley & Sons, New York.
Stavy, R.,& Tirosh, D. (2000). How students (mis-)understand science and mathematics:
Intuitive rules. Teacher College Press, New York.
Steen, L. (1988). Calculus for a New Century. Washington, DC: Mathematical Association of
America.
Stroyan, K. D. (1993). Calculus Using Mathematica. Boston: Academic Press.
Sullivan, K. (1976). The teaching of elementary calculus: an approach using infinitesimals.
American Mathematical Monthly, 83, 370–375.
Sullivan, K. (1976). The teaching of elementary calculus: an approach using infinitesimals.
American Mathematical Monthly,83(5). 370-375.
Sullivan, P. (1996). The Effect of visual, numerical, and algebraic representations on students’
conceptual understanding of differential calculus. (Columbia University Teachers College,
1995). Dissertation Abstracts International , 56/07, 2598.
Szydlik, J.E. (2000). Mathematical beliefs and conceptual understanding of the limit of a
function. Journal for Research in Mathematics Education, 31(3), 258–276.
21
Taback, S. (1975). The child’s concept of limit in Children’s Mathematical Concepts (ed.
Roskopff M.F.) Teachers’ College Press, New York 111-114.
Taback, S. (1975). The child's concept of limit. In M. Rosskopf (ed.), Children's Mathematical
Concepts (pp. 111–144). Teachers College Press, New York.
Tall, D. (1980). The notion of infinite measuring number and its relevance in the intuition of
infinity. Educational Studies in Mathematics, 11, 271–284.
Tall, D. (1990). Inconsistencies in the learning of calculus and analysis. Focus on Learning
Problems in Mathematics,12, 49–64.
Tall, D. (1991). Advanced Mathematical Thinking. Kluwer, Dordrecht, The Netherlands.
Tall, D. (1991). Intuition and rigour: The role of visualization in calculus. In W. Zimmermann &
S. Cunningham (eds.), Visualization in Teaching and Learning Mathematics, MAA Notes,
19( pp. 105–119). Washington.
Tall, D. (1991). The psychology of advanced mathematical thinking. In D. Tall (ed.), Advanced
Mathematical Thinking(pp. 3–23). Kluwer Academic Publishers, Dordrecht.
Tall, D. (1996). Function and calculus. In A.J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C.
Laborde (eds.), International Handbook of Mathematics Education(pp. 289–325). Kluwer
Academic Publishers, Dordrecht.
Tall, D. (1996). Functions and calculus. In: A. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C.
Laborde (Eds), International handbook of mathematics education(pp. 289–325). Kluwer,
Dordrecht.
Tall, D. (2001). Natural and formal infinities. Educational Studies in Mathematics, 48(2-3), 199238.
Tall, D. O. (1985). Using computer graphics as generic organisers for the concept image of
differentiation. Proceedings of the Ninth International Conference of the International
Group for the Psychology of Mathematics Education, Holland, 1, 105–110.
Tall, D. O. (1990). Inconsistencies in the learning of calculus and analysis. Focus on Learning
Problems in Mathematics,12(3 & 4), 49–63.
Tall, D. O. (1992). The transition to advanced mathematical thinking: functions, limits, infinity
and proof. In: D. A. Grouws (Ed.), Handbook of Research in Mathematics Teaching and
Learning (pp. 495–511). New York: Macmillan.
Tall, D. O. (1993). Real Mathematics, Rational Computers and Complex People. Proceedings of
the Fifth Annual International Conference on Technology in College Mathematics
Teaching, 243–258.
Tall, D. O. (2003). Using technology to support an embodied approach to learning concepts in
Ensino da Matema tica (Vol 1, pp.1-28). Rio de Janeiro, Brasil.
Tall, D. O., & Schwarzenberger R. L. (1978). Conflicts in the Learning of Real Numbers and
Limits, Mathematics Teaching, 83, 44-49.
Tall, D. O., Gray, E. M., Bin Ali, M., Crowley, L., DeMarois, P., McGowen, M., Pitta, D., Pinto,
M., Thomas, M., & Yusof, Y. (2000). Symbols and the Bifurcation between Procedural
22
and Conceptual Thinking. The Canadian Journal of Science, Mathematics and Technology
Education, 1, 80–104.
Tall, D., & Pinto, M. (1999). Student constructions of formal theory: giving and extracting
meaning. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the Pschology of
Mathematics Education, Haifa, Israel, 4, 65–73.
Tall, D., & Schwarzenberger, R.L.E. (1978). Conflicts in the learning of real numbers and limits.
Mathematics Teaching, 82, 44–49.
Tall, D., & Tirosh, D. (2001). Infinity – The never-ending struggle. Educational Studies in
Mathematics, 48(2-3), 129-136.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with
particular reference to limit and continuity. Educational Studies in Mathematics, 12, 151–
169.
Tall, D.O, Blokland, P., & Kok, D. (1990). A Graphic Approach to the Calculus, (for I.B.M.
compatible computers). Sunburst.
Tall, D.O. (1977). Conflicts and catastrophes in the learning of mathematics, Mathematical
Education for Teaching, 2(4), 2-18.
Tall, D.O. (1979). Cognitive aspects of proof, with special reference to the irrationality of Ö2.
Proceedings of the Third International Conference for the Psychology of Mathematics
Education, Warwick, 203-205.
Tall, D.O. (1980). The notion of infinite measuring number and its relevance in the intuition of
infinity. Educational Studies in Mathematics, 11, 271–284.
Tall, D.O. (1980b). Looking at graphs through infinitesimal microscopes, windows and
telescopes. Mathematical Gazette, 64, 22–49.
Tall, D.O. (1980b). Mathematical intuition, with special reference to limiting processes,
Proceedings of the Fourth International Conference for the Psychology of Mathematics
Education, Berkeley, 170-176.
Tall, D.O. (1981). Intuitions of infinity, Mathematics in School, 10,(3), 30-33.
Tall, D.O. (1982). Elementary axioms and pictures for infinitesimal calculus. Bulletin of the IMA,
18, 43–48.
Tall, D.O. (1986). Building and Testing a Cognitive Approach to the Calculus using Interactive
Computer Graphics. Ph.D. Thesis in Education, University of Warwick.
Tall, D.O. (1987). Constructing the concept image of a tangent, Proceedings of the Eleventh
International Conference of P.M.E., Montréal, III 69-75.
Tall, D.O. (1990). Inconsistencies in the learning of calculus and analysis. Focus on Learning
Problems in Mathematics, 12, 49–64.
Tall, D.O. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity,
and proof. In D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and
Learning(pp. 495–511). MacMillan, New York.
Tall, D.O. (in press). Introducing three worlds of mathematics. For the Learning of Mathematics.
23
Tall, D.O., & Vinner, S. (1981). Concept image and concept definition in mathematics, with
special reference to limits and continuity. Educational Studies in Mathematics, 12, 151–
169.
Tall, D.O., Gray, E.M., Ali, M.B., Crowley, L.R.F., DeMarois, P., McGowen, M.A., Pitta, D.,
Pinto, M.M.F., Thomas, M.O.J., & Yusof, Y.B.M. (2001). Symbols and the bifurcation
between procedural and conceptual thinking. Canadian Journal of Science, Mathematics
and Technology Education, 1, 81–104.
Thomas, H.L. (1975). The concept of function. In M. Rosskopf (Ed.) Children’s mathematical
concepts. New York: Teachers College, Columbia University.
Thomas, K. (1996). The fundamental theorem of calculus: An investigation into students’
constructions (non-traditional course, Calculus). (Purdue University, 1995). Dissertation
Abstracts International, 57/03, 1068.
Thompson, P. (1994). Students, functions, and the undergraduate curriculum. In: E. Dubinsky, A.
Schoenfeld & J. Kaput (Eds), Research in collegiate mathematics education I (pp. 21–44).
CBMS issues in mathematics education, American Mathematical Society.
Thompson, P. W. (1994). The development of the concept of speed and its relationship to
concepts of rate. In: G. Harel, & J. Confrey (Eds.), The development of multiplicative
reasoning in the learning of mathematics (pp. 181–234). Albany, NY: SUNY Press
Tirosh, D. (1985). The intuition of infinity and its relevance for mathematics education.
Unpublished doctoral dissertation, Tel-Aviv University.
Tirosh, D. (1990). Inconsistencies in students' mathematical constructs. Focus on Learning
Problems in Mathematics, 12, 111–129.
Tirosh, D. (1991). The role of students’ intuitions of infinity in teaching of the cantorial theory.
In: D. Tall (Ed.), Advanced mathematical thinking (pp. 199–214). Kluwer, Dordrecht
(1991).
Tirosh, D. (1999). Finite and infinite sets: Definitions and intuitions. International Journal of
Mathematical Education in Science & Technology, 30(3), 341–349.
Tirosh, D., & Tsamir, P. (1996). The role of representations in students' intuitive thinking about
infinity. International Journal of Mathematics Education in Science and Technology, 27,
33–40.
Toeplitz, O. (1963). The Calculus: A Genetic Approach. The University of Chicago Press,
Chicago.
Travers, K.J., & Westbury, I. (1989). The IEA Study of Mathematics 1: Analysis of Mathematics
Curricula. Pergamon Press, Oxford.
Tsamir, P. (1994). Promoting students consistent responses in respect to their intuitions of actual
infinity, unpublished doctoral thesis, Tel-Aviv University.
Tsamir, P. (1999). The transition from the comparison of finite sets to the comparison of infinite
sets: teaching prospective teachers. Educational Studies in Mathematics, 38, 209–234.
Tsamir, P. (2001). When ‘the same’ is not perceived as such: The case of infinite sets.
Educational Studies in Mathematics, 48(2-3), 289-307.
24
Tsamir, P. (2001). When “the same” is not perceived as such: The case of infinite sets.
Educational Studies in Mathematics, 48, 289–307.
Tsamir, P. (2002). From primary to secondary intuitions: prospective teachers’ transitory
intuitions of infinity. Mediterranean Journal for Research in Mathematics Education, 1,
11–29.
Tsamir, P. (2003). Primary intuitions and instruction: the case of actual infinity. Research in
Collegiate Mathematics Education,12, 79–96.
Tsamir, P., & Dreyfus, T. (2002). Comparing infinite sets-a process of abstraction, The Journal
of Mathematical Behavior, 21(1), 1-23.
Tsamir, P., & Dreyfus, T. (2005). How fragile is consolidated knowledge? Ben’s comparisons of
infinite sets. The Journal of Mathematical Behavior, 24(1), 15-38.
Tsamir, P., & Tirosh, D. (1992). Students' awareness of inconsistent ideas about actual infinity.
Proceedings of the 16th Annual Meeting for the Psychology of Mathematics Education,
3(pp. 90–97). Durham, USA.
Tsamir, P., & Tirosh, D. (1994). Comparing infinite sets: intuitions and representations.
Proceedings of the 18th Annual Meeting for the Psychology of Mathematics Education,
4(pp. 345–352). Lisbon, Portugal.
Tsamir, P., & Tirosh, D. (1999). Consistency and representations: The case of actual infinity.
Journal for Research in Mathematics Education 30(2), 213–219.
Uhlig, F. (2002b). The role of proof in comprehending and teaching elementary linear algebra.
Educational Studies in Mathematics, 50, 335–346.
Vilenkin, N.Y. (1995). In Search of Infinity (translated from the Russian by A. Shenitzer),
Birkhäuser, Boston.
Vinner, S. & Dreyfus, T. (1989) Images and definitions for the concept of function. Journal for
Research in Mathematics Education, 20(4), 356–366.
Vinner, S. (1982). Conflicts between definitions and intuitions - the case of the tangent.
Proceedings of the 6th International Conference of P.M.E., Antwerp, 24-28.
Vinner, S. (1983). Concept definition, concept image, and the notion of function. International
Journal of Mathematics Education in Science and Technology, 14(3), 293–305.
Vinner, S. (1988). Visual considerations in college calculus - students and teachers. Theory of
Mathematics Education, Proceedings of the Third International Conference, Antwerp, 109116.
Vinner, S. (1990). Inconsistencies: their causes and function in learning mathematics, Focus on
Learning Problems in Mathematics, 12(3/4), 85–98.
Vinner, S. (1991). The role of definitions in the teaching and learning mathematics. In D. Tall
(ed.), Advanced Mathematical Thinking(pp. 65–81). Kluwer Academic Publishers,
Dordrecht.
Vinner, S. (1992). The function concept as a prototype for problems in mathematical learning. In
G. Harel & E. Dubinsky (eds.), The Concept of Function: Aspects of Episte-mology and
25
Pedagogy, MAA Notes,25(pp. 195-213). Mathematical Association of America,
Washington, DC.
Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in
mathematics learning. Educational Studies in Mathematics, 34, 97–129.
Vinner, S., & Dreyfus, T. (1989). Images and Definitions for the Concept of a Function, Journal
for Research in Mathematics Education, 20(4), 356-366.
Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in the
development of some simple geometrical concepts, Proceedings of the Fourth
International Conference for the Psychology of Mathematics Education, Berkeley,
California, 177-184.
Vlachos, P. & Kehegias, A. (2000). A computer algebra system and a new approach for teaching
business calculus. The International Journal of Computer Algebra in Mathematics
Education, 72, 87-10.
von Eye, A. (1990). Introduction to configural frequency analysis: The search for types and
antitypes in cross-classifications. Cambridge University Press, Cambridge.
von Eye, A. (2000). Configural frequency analysis: A program for 32-bit windows operating
systems, (Version 2000), unpublished manuscript, East Lansing, Michigan State
University.
Vygotskii, L.S. (1962). Thought and Language. The M.I.T. Press, New York.
Watson A., Spirou P., & Tall D. (2002). The relationship between physical embodiment and
mathematical symbolism: The concept of vector. Mediterranean Journal for Research in
Mathematics Education, 1(2), 73-97.
Watson, A., & Tall, D.O. (2002). Embodied action, effect, and symbol in mathematical growth.
In Anne D. Cockburn & Elena Nardi (Eds.), Proceedings of the 26th Conference of the
International Group for the Psychology of Mathematics Education (Vol. 4, pp.369–376).
Norwich: UK.
Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge.
Educational Studies in Mathematics, 48(1), 101–119.
Weber, K. (2002). Beyond proving and explaining: Proofs that justify the use of definitions and
axiomatic structures and proofs that illustrate technique. For the Learning of Mathematics,
22(3), 14–17.
Weber, K. (2002). The role of instrumental and relational understanding in proofs about group
isomorphism. Proceedings from the 2nd International Conference for the Teaching of
Mathematics, Hersonisoss.
Weber, K. (2003). A procedural route toward understanding of the concept of proof. In N. A.
Pateman & B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the conference of the
International group for the Psychology of Mathematics Education. Honolulu, Hawaii.
Weber, K. (2004). A framework for describing the processes that undergraduates use to construct
proofs. In M. J.Hoines & A. B. Fuglestad (Eds.) Proceedings of the 28th conference of the
International group for the Psychology of Mathematics Education. Bergen, Norway.
26
Weber, K. (2004). Traditional instruction in advanced mathematics courses: a case study of one
professor’s lectures and proofs in an introductory real analysis course. Journal of
Mathematical Behavior 23, (pp.115-133).
Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M., & Merkovsky, R. (2003). Student
performance and attitudes in courses based on APOS Theory and the ACE Teaching Cycle.
In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (eds.), Research in Collegiate Mathematics
Education V(pp. 97–131), American Mathematical Society, Providence.
White, P., & Mitchelmore, M. (1996). Conceptual Knowledge in Introductory Calculus, Journal
for Research in Mathematics Education, 27(1), 79-95.
Wilder, R.L. (1972). History in the mathematics curriculum: its status, quality and function,
American Mathematical Monthly, 79, 479–495.
Williams, C. W. (1996). Relationships between learning style preferences, mathematics attitude,
calculator usage, and achievement in calculus (graphics calculators). (The University of
Tennessee, 1995). Dissertation Abstracts International, 57/02, 616.
Williams, G. (2000). Associations between mathematically insightful collaborative behavior and
positive affect. In A.D. Cockburn & E. Nardi (Eds), Proceedings of the 26th international
conference for the psychology of mathematics education,4(pp. 402-409). UEA, Norwich,
UK.
Williams, G. (2004). The nature of spontaneity in high quality mathematics learning experiences.
In: M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th international
conference for the psychology of mathematics education, 4 (pp. 433–440). Bergen,
Norway: Bergen University College.
Williams, S. (1991). Models of limit held by college calculus students. Journal of Research in
Mathematics Education, 22(3), 219-236.
Williams, S.R. (2001). Predications of the limit concept: An application of repertory grids.
Journal for Research in Mathematics Education, 32(4), 341–367.
Williams, S.R., & Ivey, K.M.C. (2001). Affective assessment and mathematics classroom
engagement: A case study. Educational Studies in Mathematics, 47, 75–100.
Wood, N.G. (1992). Mathematical Analysis: A comparison of student development and historical
development. Unpublished Ph.D. Thesis, Cambridge University, UK.
Wood, T., & McNeal, B. (2003). Complexity in teaching and children's mathematical thinking. In
N.A. Pateman, B.J. Dougherty & J. Zilliox (Eds), Proceedings of the 27th international
conference for the psychology of mathematics education, 4(pp. 435–441). University of
Hawaii, Honolulu, HI.
Wright, T. (2001). Karen in motion: the role of physical enactment in developing an
understanding of distance, time and speed. Journal of Mathematical Behavior,20, 145–162.
Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an
advanced undergraduate mathematics course. The Journal of Mathematical Behavior, 19,
275–287.
27
Yehoshua, D. (1995). Comparing infinite sets: effects of presentations and order of presentation.
An essay presented as a thesis for the Degree of M.A., Tel Aviv University, Tel Aviv,
Israel.
Yerushalmy, M. (1991). Students’ perceptions of aspects of algebraic function using multiple
representation software, Journal of Computer Assisted Learning. Blackwell Scientific
Publications.
Yerushalmy, M. (1997). Designing representations: Reasoning about functions of two variables.
Journal for Research in Mathematics Education, 27(4), 431-466.
Young, R.M. (1992). Excursions in calculus. Mathematical Association of America, Washington,
DC.
Zaslavsky, O. (1997). Conceptual obstacles in the learning of quadratic functions. Focus on
Learning Problems in Mathematics,19(1), 20–44.
Zazkis, R., Liljedahl, P. & Gadowsky, K. (2003). Students' conceptions of function translation:
Obstacles, intuitions and rerouting. Journal of Mathematical Behavior, 22, 437-450.34.
28