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The processes of learning mathematics are immensely complex and we largely lack insights into these processes. This is especially problematic when it comes to tertiary mathematics education, which has been much less researched than primary and secondary mathematics education. It is thus far from possible to clarify all relevant issues related to university mathematics learning difficulties. This paper will discuss the notion of learning difficulties and some related insights.Keywords: university mathematics, learning difficulties(Published: 1 June 2011)Citation: Education Inquiry Vol. 2, No. 2, May 2011, pp.289–303
Adams, R. (2006). Calculus: A Complete Course. Addison-Wesley, sixth edition.
Artigue, M. (1996). Teaching and learning elementary analysis. In Alsina, C., Alvarez, J., Hodgson, B., Laborde, C., and Perez, A., (eds.s, 8th International Congress on Mathematical Education. Seville (Spain). Selewcted lectures, pages 15-29.
Artigue, M. (1998). What can we learn from Didactic Research carried out at University Level? In Pre-proceedings, ICMI Study Conference On the Teaching and Learning of Mathematics at University Level, Singapore.
Artigue, M., Batanero, C., and Kent, P. (2007). Mathematics thinking and learning at post-secondary level. In Lester, F., editor, Second Handbook of Research on Mathematics Teaching and Learning, pps 1011-1050. Information Age Publishing, Charlotte, NC.
Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., and Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. In Schoenfeld, A., Kaput, J., and Dubinsky, E., (eds.s, Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education, pps 1-32. American Mathematical Society.
Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. In Pimm, D., (ed.r, Mathematics, teachers and children, pps 216-235. London: Hodder and Stoughton.
Bergqvist, E. (2007). Types of reasoning required in university exams in mathematics. Journal of mathematical behavior, 26:348-370.
Bergqvist, E., Bergqvist, T., Boesen, J., Helenius, O., Lithner, J., Palm, T., and Palmberg, B. (2010a). Matematikutbildningens mål och undervisningens ändamålsenlighet grundskolan, våren 2009. National Center for Mathematics Education, University of Gothenburg, in Swedish.
Bergqvist, E., Bergqvist, T., Boesen, J., Helenius, O., Lithner, J., Palm, T., and Palmberg, B. (2010b). Matematikutbildningens mål och undervisningens ändamålsenlighet gymnasieskolan, hösten 2009. National Centrr for Mathematics Education, University of Gothenburg, in Swedish.
Brousseau, G. (1997). Theory of Didactical Situations In Mathematics. Dordrecht: Kluwer.
Chazan, D. (1993). High school geometry students' justification for their views of empirical evi - dence and mathematical proof. Educational Studies in Mathematics, 24:359-387.
Courant, R. and John, F. (1965). Introduction to Calculus and Analysis, vole 1. Wiley International.
de La Vall ́ee Poussin, C. (1954). d'Analyse Infinit ́esimale. Paris: Gauthiers-Villars, eighth edition.
Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist, 23:167-180.
Dubinsky, E., Mathews, D., and Reynolds, B. (1997). Readings in Cooperative Learning for Undergraduate Mathematics. MAA notes 44. The Mathematical Association of America.
Edwards, C. and Penney, D. (2002). Calculus. Prentice Hall International, sixth edition.
Gueudet, G. (2008). Investigating the secondary-tertiary transition. Educational Studies In Mathematics, 67:237-254.
Guzman, M., Hodgson, B., Robert, A., and Villani, V. (1998). Difficulties in the passage from sec - ondary to tertiary education. In Fischer, G. and Rehmann, U., (ers.), Proceedings of the International Congress of Mathematicians, Berlin 1998. Invited lectures. Vol. 3, pps 747-762.
Hanna, G. and Jahnke, N. (1996). Proof and proving. In Bishop, A., Clements, K., Keitel, C., Kilpatrick, J., and Laborde, C., (eds.s, International Handbook of Mathematics Education, pps 877-908. Dordrecht: Kluwer.
Harel, G. and Dubinsky, E., (eds.s (1992). The Concept of Function: Aspects of Epistemology and Pedagogy. Washington, DC: Mathematical Association of America.
Harel, G. and Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In Lester, F., (ed.r, Second Handbook of Research on Mathematics Teaching and Learning, pps 805-842. Information Age Publishing, Charlotte, NC.
Hiebert, J. (2003). What research says about the NCTM standards. In Kilpatrick, J., Martin, G., and Schifter, D., (eds.s, A Research Companion to Principles and Standards for School Mathematics, pps 5-26. Reston, Va.: National Council of Teachers of Mathematics.
Holton, D., (ed.) (2001). The Teaching and Learning of Mathematics at University Level, an ICMI Study. Kluwer Academic.
Hoyles, C. (1997). The curricular shaping of students approaches to proof. For the Learning of Mathematics, 17:7-16.
Leron, U. and Hazzan, O. (1997). The world according to Johnny: a coping perspective in mathematics education. Educational Studies In Mathematics, 32:265-292.
Lester, F. (1994). Musings about mathematical problem-solving research. Journal for Research in Mathematics Education, 25:660-675.
Lithner, J. (2000). Mathematical reasoning in task solving. Educational Studies In Mathematics, 41:165-190.
Lithner, J. (2002a). Lusten att lära, Luleå (The motivation to learn, Luleå). Skolverkets nationella kvalitetsgranskningar (Quality inspections of the Swedish national agency for education), in Swedish.
Lithner, J. (2002b). Lusten att lära, Osby (The motivation to learn, Osby). Skolverkets nationella kvalitetsgranskningar (Quality inspections of the Swedish National Agency for Education), in Swedish.
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. Journal of Mathematical Behavior, 23:405-427.
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies In Mathematics, 67:255-276.
McGinty, R., VanBeynen, J., and Zalewski, D. (1986). Do our mathematics textbooks reflect what we preach? School Science and Mathematics, 86:591-596.
NCTM (2000). Principles and Standards for School Mathematics. The Council, Reston, VA.
Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies In Mathematics, 40:1-24.
Niss, M. (2007). Reflections on the state and trends in research on mathematics teaching and learning: From here to utopia. In Lester, F., (ed.r, Second Handbook of Research on Mathematics Teaching and Learning, pps 1293-1312. Information Age Publishing, Charlotte, NC.
Palm, T., Boesen, J., and Lithner, J (2011). The mathematical reasoning requirements in upper secondary level assessments. Accepted for publication in International Journal for Mathematics Teaching and learning.
Plomp, T. (2009). Educational design research: an introduction. In Plomp, T. and Nieveen, N., (eds.s, An Introduction to Educational Design Research, pps 9-36. SLO Netherlands institute for curriculum development.
Schoenfeld, A. (1985). Mathematical Problem Solving. Orlando, FL: Academic Press.
Schoenfeld, A. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In Voss, J., Perkins, D., and Segal, J., (eds.s, Informal Reasoning and Education, pps 311-344. Hillsdale, NJ: Lawrence Erlbaum Associates.
Selden, A. (2005). New developments and trends in tertiary mathematics education: Or, more of the same? International Journal of Mathematical Education in Science and Technology, 36:131-147.
Selden, J. and Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29:123-151.
Selden, J., Selden, A., and Mason, A. (1994). Even good students can't solve nonroutine problem. In Kaput, J. and Dubinsky, E., (eds.s, Research issues in Undergraduate Mathematics Learning, pps 19-26. Washington DC: Mathematical Association of America.
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.
Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt fuer Didaktik der Mathematik, 29(3):75-80.
Sjöberg, G. (2006). If it is not dyscalculia - what is it? (in Swedish). PhD thesis, Dept. of Mathematics and Science, Umeå University.
Tall, D., (ed.) (1991). Advanced mathematical thinking. Kluwer.
Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In Grouws, D., (ed.r, Handbook for Research on Mathematics Teaching and Learning, pps 495-511. New York: Macmillan.
Tall, D. (1996). Functions and calculus. In Bishop, A., Clements, K., Keitel, C., Kilpatrick, J., and Laborde, C., (eds.s, International Handbook of Mathematics Education, pps 289-325. Dordrecht: Kluwer.
Tall, D. (1999). The chasm between thought experiment and formal proof. In Kadunz, G., Ossimitz, G., Peschek, W., Schneider, E., and Winkelmann, B., (eds.s, Mathematical literacy and new technologies, pps 319-343. Conference: 8. internationales Symposium zur Didaktik der Mathematik, Klagenfurt (Austria).
Tall, D. (2004). Three Worlds of Mathematics. For the Learning of Mathematics, 23(3):29-33.
Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational Studies in Mathematics, 34:97-129.
Yackel, E. and Hanna, G. (2003). Reasoning and proof. In Kilpatrick, J., G. Martin, and Schifter, D., (eds.s, A Research Companion to Principles and Standards for School Mathematics, pps 227-236. Reston, Va.: National Council of Teachers of Mathematics.