RUMEC Published Papers and Preprints

PapersRUMEC paper abstracts are available below. We regret that the full texts are not available online to non-members, due to copyright restrictions. However, if you email the authors, they may be able to send you a copy.

 

Terms used in RUMEC papers have very specific, negotiated meanings. While these meanings have and will continue to change over time, you can see how we currently define them in the RUMEC Glossary.

2005

Dubinsky, E., Weller, K., McDonald, M., & Brown, A. (in press). Some historical issues and paradoxes regarding the concept of infinity: An APOS based analysis: Part 2. Educational Studies in Mathematics.

 

Dubinsky, E., Weller, K., McDonald, M., & Brown, A. (in press). Some historical issues and paradoxes regarding the concept of infinity: An APOS based analysis: Part 1. Educational Studies in Mathematics.

 

Trigueros, M. and Oktac, A. (in press) "La Theorie APOS et l'Enseignement de l'Algebre Lineaire". Annales de Didactique et de Sciences Cognitives.

 

Cooley, L., Trigueros, M., Baker, B. (in review). Schema thematization: a framework and an example. Journal for Research in Mathematics Education.

 

Trigueros, M., Baker, B., & Hemenway, C. (in review). Does teaching transformation of basic functions work? Journal for Mathematical Behavior.

2004

Vidakovic, D. and Martin, W. O. (2004). Small-group searches for mathematical proofs and individual reconstructions of mathematical concepts. Journal of Mathematical Behavior 23(4), 465-492.

 

Weller, K., Brown, B., Dubinsky, E., McDonald, M., & Stenger, C. (2004). Intimations of Infinity, Notices of the AMS, 51(7), 741-750.

 

DeVries, D. &  Arnon, I. (2004). Solution-what does it mean? Helping linear algebra students develop the concept while improving research tools. Proceedings of the 28th Conference for the International Group for the Psychology of Mathematics Education (Vol 2 pp. 55-62). Bergen, Norway.

2003

Arnon, A. and DeVries, D. (2003). What Does the Term “A solution of a system of equations?” mean to students? The 10th annual conference of the organization for the advancement of mathematics education in Israel (p. 25). Tel-Aviv, Israel.

 

Cooley, L., Trigueros, M. Baker, B. (2003). Thematization of the calculus graphing schema, In Pateman, N.A., Dougherty, B.J., Zilliox, J.T., (Eds.) Proceedings of the 2003 joint meeting of the International Group for the Psychology of Mathematics Education and the Psychology of Mathematics Education-North American Chapter, (Vol. 2, pp. 57-64.). Honolulu, Hawaii: University of Hawaii.

 

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). Providence: American Mathematical Society.

2002

Cooley, L. (2002). Reflective abstraction and writing in calculus. Journal of Mathematical Behavior, 21(3), 255-282.

 

Baker, B., Trigueros, M., Cooley, L. (2002). On the integration of knowledge: geometrical interpretation of the properties of functions. Proceedings of the 2nd International Conference on the Teaching of Mathematics (at the undergraduate level), (p. 73). Hersonissos, Crete, Greece: John Wiley & Sons, Inc.

 

Trigueros, M. and Oktac, A. (in press) "La Theorie APOS et l'Enseignement de l'Algebre Lineaire". Annales de Didactique et de Sciences Cognitives.

2001

Brown, A., Thomas, K., & Tolias, G. (2001).  Conceptions of divisibility: Success and understanding.  In S. R. Campbell & R. Zazkis (eds.) Learning and Teaching Number Theory:  Research in Cognition and Instruction.  In C. Maher & R. Speiser (series eds.) Learning and Cognitions:  Monograph Series of the Journal of Mathematical Behavior, Ablex Publishing.

 

Czarnocha, B., Dubinsky, E., Loch, S., Prabhu, V., and Vidakovic, D. (2001). Conceptions of area: In students and in history. Collegiate Mathematics Journal, 32(2), 99-109.

 

Czarnocha, B., Loch, S., Prabhu, V., & Vidakovic, D. (2001). The concept of the definite integral: Coordination of two schemas. Proceedings of the 25th Annual Meeting of the International Group for the Psychology of Mathematics Education (PME25), V. 2, pp. 297-304, Utrecht: Freudental Institute, July 12-17.

 

Arnon, I.,  Nesher, P., & Nirenburg, R. (2001). Where do fractions encounter their equivalents?  Can this encounter take place in elementary school? International Journal of Computers for Mathematical Learning, V, 6(2), 167-214.

 

Dubinsky, E. and McDonald, M.A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research, in Derek Holton et al. (eds.), The teaching and learning of mathematics at University level: An ICMI study, Kluwer, Netherlands, pp. 273-280.

 

Baker, B., Hemenway, C., & Trigueros, M. (2001). On transformations of basic functions.  In Chick, H., Stacey, K., Vincent, J. & Vincent, J. (Eds.), Proceedings of the 12th ICMI Study Conference: The Future of the Teaching and Learning of Algebra (Vol. 1, pp. 41-47). Melbourne, Australia: The University of Melbourne.

 

Baker, B., Hemenway, C. & Trigueros, M. (2001). On transformations of functions. In R. Speiser, C. A. Maher and C. N. Walter (Eds.), Proceedings of the XXIII Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 91-98). Columbus, OH: ERIC Clearinghouse for Science, Mathematics and Environmental Education.

2000

Baker, B., Cooley, L., Trigueros, M., (2000). The schema triad - a calculus example. Journal for Research in Mathematics Education, 31(5), 557 – 578.

 

McDonald, M. A., Mathews, D. M., & Strobel, K. H. (2000). Understanding sequences: A tale of two objects. In E. Dubinsky, A. Schoenfeld, and J. Kaput (eds.), Research in Collegiate Mathematics Education IV (pp. 77-102). Providence: American Mathematical Society.

1999

Arnon, I.,  Nesher, P., & Nirenburg, R. (1999). What can be Learnt About Fractions Only with Computers. In O. Zaslavsky (Ed.), Proceedings of the Twenty-Third International Conference for the Psychology of Mathematics Education (Vol 2, pp. 33-40). Haifa, Israel.

 

Baker, B., Cooley, L., Trigueros, M. (1999). On schema interaction: a calculus example. In Proceedings of the twenty first annual meeting of the International Group for the Psychology of Mathematics Education - North American Chapter. Cuernavaca, Morelos, Mexico: University of Morelos and the Center for Research and Advanced Studies.

 

Clark, J., Hemenway, C., St. John, D., Tolias, G., & Vakil, R. (1999). Student Attitudes towards abstract algebra. Primus, 9(1).

 

Cottrill, J. (1999). Students’ understanding of the concept of chain rule in first year calculus and the relation to their understanding of composition of functions. Unpublished doctoral dissertation, Purdue University, West Lafayette, Indiana.

 

Czarnocha, B., Dubinsky, E., Prabhu, V., & Vidakovic, D. (1999). One theoretical perspective in undergraduate mathematics education research. Proceedings of the XXIII International Group for the Psychology of Mathematics Education. Haifa,  Israel.

 

1998

Asiala, M., Brown, A., Kleiman, J., & Mathews, D. (1998). The Development of Students' Understanding of Permutations and Symmetries. International Journal of Computers for Mathematical Learning, 3, 13-43.

 

Arnon, I. (1998). In the mind's eye: how children develop mathematical concepts -extending Piaget's theory. Unpublished doctoral dissertation, School of Education, Haifa University.

 

Baker, B., Cooley, L., Trigueros, M., (1998). Double triad levels of Piaget and Garcia in schema development. In Berenson, S.B., Dawkins, K.R., Blanton, M., Coulombe, W. N., Kolb, J., Norwood, K., Stiff, L. (Eds.) Proceedings of the twentieth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 267 – 268). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

1997

Arnon, I. & Dubinsky, E. (1997). Teaching fraction-concepts as concrete objects versus teaching them as concrete actions. In M. Hejny & J. Novotna (Eds.), Proceedings of ERCME 97, European Research Conference on Mathematical Education (pp. 46-49).  Prague, Prometheus Publishing House.

 

Asiala, M. Cottrill, J., Dubinsky, E., & Schwingendorf, K. (1997). The development of students’ graphical understanding of the derivative. Journal of Mathematical Behavior, 16(4), 399-431.

 

Asiala, M., Dubinsky, E., Mathews, D., Morics, S., & Oktac, A. (1997). Student understanding of cosets, normality and quotient groups. Journal of Mathematical Behavior, 16(3), 241-309.

 

Brown, A., DeVries, D., Dubinsky, E., & Thomas, K. (1997).  Learning binary operations, groups, and subgroups.  Journal of Mathematical Behavior, 16(3), 187 - 239.

 

Clark, J., Cordero, F., Cottrill, J., Czarnocha, B., DeVries, D., St. John, D., Tolias, G., & Vidakovic, D. (1997). Constructing a schema: The case of the chain rule. Journal of Mathematical Behavior, 14(4).

 

Dubinsky, E. (1997). Teaching mathematical induction I. Journal of Mathematical Behavior, 6(1), 305-317.

 

Dubinsky, E. (1997). On learning quantification. Journal of Computers in Mathematics and Science Teaching, 16(2/3), 335-362.

 

Trigueros, M. & Ursini, S. (1997). Understanding of different uses of variable: A study with starting college students. Proceedings of the XXI PME International Conference, Finland.

 

Vidakovic, D. (1997). Learning the concept of inverse function in a group versus individual environment. In Dubinsky, E., Mathews, D. & Reynolds, B., (Eds.), Readings in Cooperative Learning, MAA Notes No 44, 173 -195.

1996

Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996).  A framework for research and curriculum development in undergraduate mathematics education.  Research in Collegiate Mathematics Education II.  In J. Kaput, A. H. Schoenfeld, & E. Dubinsky (eds.) CBMS Issues in Mathematics Education, 6, 1 - 32.

 

Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996).  Understanding the limit concept: Beginning with a coordinated process schema.  Journal of Mathematical Behavior, 15, 167-192.

 

Trigueros, M., Ursini, S., & Reyes, A. (1996). College students' conceptions of variable. Proceedings of the XX PME International Conference, Spain.

 

Vidakovic , D. (1996). Learning the concept of inverse function. Journal of Computers in Mathematics and Science Teaching, 15(3), 295-318.

1995

Dubinsky, E. (1995). A programming language for learning mathematics. Communications on Pure and Applied Mathematics, 48, 1-25.

 

Trigueros, M., Ursini, S., Quintero, R., & Reyes, A. (1995). Students' approaches to different uses of variable. Proceedings of the XIX PME International Conference.

1994

Arnon, I., Dubinsky, E. & Nesher, P. (1994). Actions which can be performed in the learner's imagination:  The case of multiplication of a fraction by an integer.  In J. P. da Ponte & J. F. Matos (Eds.),  Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education  II, (pp. 32-39).  Lisbon, Portugal.

 

Dubinsky, E. (1994). A theory and practice of learning college mathematics. In A. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 221-243). Hillsdale: Erlbaum.

 

Dubinsky, E., Dautermann, J., Leron, U., & Zazkis, R. (1994). On learning fundamental concepts of group theory. Educational Studies in Mathematics, 27(3), 267-305.

1993

Vidakovic, D. (1993). Cooperative learning: Differences between group and individual processes of construction of the concept of inverse function. Unpublished doctoral dissertation, Purdue University.

1992

Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247-285.

 

Dubinsky, E. (1992). A learning theory approach to calculus. In Z. Karian (Ed.), Symbolic computation in undergraduate mathematics education, MAA Notes, 24, Mathematical Association of America, 48-55.

 

Dubinsky, E. & Harel, G. (1992).The nature of the process conception of function. In G. Harel & E. Dubinsky, (Eds.) The concept of function: Aspects of epistemology and pedagogy, MAA Notes, 25, Mathematical Association of America, 85-106.

1991

Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall, (Ed.) Advanced Mathematical Thinking, Dordrecht: Kluwer, 95-126.

 

Dubinsky, E. (1991). The constructive aspects of reflective abstraction in advanced mathematics. In L. P. Steffe, (Ed.) Epistemological Foundations of Mathematical Experiences, New York: Springer-Verlag.

1989

Dubinsky, E. (1989). On teaching mathematical induction II. Journal of Mathematical Behavior, 8, 285-304.

1988

Dubinsky, E., Elterman, F., & Gong, C. (1988). The student's construction of quantification. For the Learning of Mathematics, 8(2), 44-51.

 1986

Dubinsky, E. & Lewin, P. (1986). Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness. Journal of Mathematical Behavior, 5, 55-92.

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Last Updated February 2, 2005