Skip to main content
SpringerLink
Log in

Sources of students’ frustration in pre-university level, prerequisite mathematics courses

  • Published:
Instructional Science Aims and scope Submit manuscript

Abstract

This paper looks at sources of frustration in students of “prerequisite” mathematics courses (PMC), that is, courses required for admission into undergraduate programs in a large, urban, North American university. The research was based on responses to a questionnaire addressed to students and interviews with students and instructors. In the design of the questionnaire and the analysis of responses, an “institutional” theoretical perspective was taken, where frustration was conceived not only as a psychological process but also as a situation experienced by participants in a concrete educational institution. Several sources of frustration were identified as important in the group of respondents: the fast pace of the courses, inefficient learning strategies, the need to change previously acquired ways of thinking, difficult rapport with truth and reasoning in mathematics, being forced to take PMC, insufficient academic and moral support on the part of teachers, and poor achievement. These sources of frustration are discussed from the point of view of their impact on the quality of the mathematical knowledge that students develop in the PMC. Consideration is also given to the possibilities of improving the quality of this knowledge, given the institutional constraints implicated in the sources of students’ frustration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. We use terms such as “affect”, “attitudes”, “beliefs”, “emotions” in the sense of McLeod (1992)

  2. The questionnaire, together with raw statistical data about responses, can be viewed at http://www.asjdomain.ca/frequencies_table.html

  3. More details about these courses and reasons for choosing them can be found in (Sierpinska et al. 2007)

  4. Links to documentation are available from http://www.asjdomain.ca

  5. We distinguish between “expression of emotion” and “rationalization of emotions.” In this paper we focus on the latter.

  6. An overview of mathematics education research conducted from an institutional perspective can be found in the document by Sierpinska, “Looking at mathematics education from an institutional perspective”, posted at http://www.asjdomain.ca/institutional_perspective.html

  7. The following document succinctly summarizes the assumptions of Chevallard’s Anthropological Theory of Didactics: http://www-leibniz.imag.fr/EEDDM11/Theme3/AteMarseille.html

  8. Outcomes can be described in terms of tasks necessary to obtain them, and tasks can be described in terms of outcomes they are supposed to achieve.

  9. Refusal to listen as a source of power has already been stressed by Plato in The Republic, where, in Book I, he says, ‘But can you persuade us, if we refuse to listen to you?’(for a commentary on this aspect in The Republic, see Sesonske 1966).

  10. http://www.asjdomain.ca/sources_of_frustration.html

  11. “Mathematics is so pervasive that most university courses require, often implicitly, at least basic algebra and often more. Many students are literally shocked to find that the degree such as nursing or human resource management not only assumes pre-requisite mathematics but makes actual explicit demands in the course…. Students who may have avoided mathematics in choosing their area of study are now forced to confront it.” (FitzSimons and Godden 2000: 28).

  12. The frequencies were: 53% (51), 56% (35), 49% (16). Our estimation was based on responses to Item 62. Math is hard, explanations of reasons for not liking mathematics (Item 66), reasons of poor achievement (Item 68), and responses to Item 76. Complete the sentence, “Math is…”.

  13. The exact frequencies were: 18% (17), 16% (10), 21% (7).

  14. In response to Item 13. I’d rather NOT take this course if I had the choice, 59% (57), 54% (34), 70% (23) students agreed with the statement. In response to Item 64. I’ll never use most of the material we covered in this course, 42% (40), 37% (23), 52% (17) agreed with the statement. The number of students who agreed with both statements was 34% (33), 29% (18), 46% (15).

  15. The expression is borrowed from Crozier and Friedberg (1980) and was quoted earlier in this paper.

  16. The letters in “FOIL” stands for “first”, “outer”, “inner” and “last” terms in multiplying (a + b) by (c + d). In PMC the identity (a + b)(c + d) = ac + bc + ad + bd is derived from the axiom of distributivity of multiplication relative to addition in real numbers. FOIL suggests writing the right hand side in a different order, namely ac + ad + bc + bd; it also suggests, wrongly, that the order matters, contrary to the axiom of commutativity of addition. Besides, it leaves students without a clue when it comes to multiplying polynomials in general.

  17. We speak here from our own experience of teaching the prerequisite courses.

  18. Disposition” in Smith III and Star (2007) includes affective variables such as attitudes, beliefs, emotions, career objectives and preferences for learning activities.

  19. We took the union of respondents who agreed with the statements, “the teacher wanted me to completely change my thinking” (item 43), “I wasn’t allowed to use whatever method I liked” (item 44), “I had the impression that my thinking was different from the teacher’s” (item (60), “the math in this course was very different from what I’ve seen so far” (item 63).

  20. For details, see supporting documentation at http://www.asjdomain.ca/sources_of_frustration.html

References

  • Arsac, G., Balacheff, N., & Mante, M. (1992). Teacher’s role and reproducibility of didactic situations. Educational Studies in Mathematics, 23(1), 5–29.

    Article  Google Scholar 

  • Artigue, M. (1999). The teaching and learning of mathematics at the university level. Crucial questions for contemporary research in education. Notices of the American Mathematical Society, 46(11), 1377–1385.

    Google Scholar 

  • Balacheff, N. (1991). Benefits and limits of social interaction: The case of teaching mathematical proof. In A. Bishop, S. Mellin-Olsen, & J. van Dormolen (Eds.), Mathematical knowledge: Its growth through teaching (pp. 175–192). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Bandura, A. (1963). Social learning and personality development. New York: Holt, Rinehart & Winston.

    Google Scholar 

  • Bandura, A. (1989). Human agency in social cognitive theory. American Psychologist, 44(9), 1175–1184.

    Article  Google Scholar 

  • Boaler, J., & Greeno, J. G. (2000). Identity, agency and knowing in the mathematical worlds. In J. Boaler (Ed.), Multiple perspectives in mathematics teaching and learning (pp. 171–200). Westport: Ablex Publishing.

    Google Scholar 

  • Bobos, G. (2004). The effect of weekly quizzes on the development of students’ theoretical thinking. (Master’s thesis). Concordia University, Montreal.

  • Borba M. C. & Villareal M. E. (Eds.) (2006). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, visualization and experimentation. New York: Springer.

    Google Scholar 

  • Brenner M. E., Moschkovich J. N. (Eds.) (2002). Everyday and academic mathematics in the classroom. Monograph of the Journal for Research in Mathematics Education. Reston: NCTM.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dortrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–266.

    Google Scholar 

  • Chevallard, Y. (2002). Organiser l’étude 1. Structures et fonctions. In J.-L. Dorier, M. Artaud, M. Artigue, R. Berthelot, & R. Floris (Eds.), Actes de la 11e Ecole d’Eté de Didactique des Mathématiques—Corps, 21–30 Août 2001 (pp. 3–22). Grenoble: La Pensée Sauvage éditions.

    Google Scholar 

  • Chiarugi, O., Fracassina, G., & Furinghetti, F. (1990). Learning difficulties behind the notion of absolute value. In G. Booker, P. Cobb, & T. N. De Mendicutti (Eds.), Proceedings of the 14th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 231–238). Oaxtepec, Mexico: PME.

    Google Scholar 

  • Crozier, M., & Friedberg, E. (1980). Actors and systems. The politics of collective action. Chicago and London: The University of Chicago Press.

    Google Scholar 

  • Diez-Palomar, J., Simic, K., & Varley, M. (2007). “Math is everywhere”: Connecting mathematics to students’ lives. Journal of Mathematics and Culture, 1(2), 20–36.

    Google Scholar 

  • Drouhard, J.-P., Sackur, C., Maurel, M., Paquelier, Y., & Assude, T. (1999, March). Necessary mathematical statements and aspects of knowledge in the classroom. Philosophy of Mathematics Education Journal 11. Retrieved November 21, 2006, from http://www.people.ex.ac.uk/PErnest/pome11/art8.htm.

  • Engelbrecht, J., & Harding, A. (2003). Online assessment in mathematics: Multiple assessment formats. New Zealand Journal of Mathematics, 32(Suppl.), 57–65.

    Google Scholar 

  • Engelbrecht, J., & Harding, A. (2005a). Teaching undergraduate mathematics on the internet. Part 1. Educational Studies in Mathematics, 58(2), 235–252.

    Article  Google Scholar 

  • Engelbrecht, J., & Harding, A. (2005b). Teaching undergraduate mathematics on the internet. Part 2. Educational Studies in Mathematics, 58(2), 253–276.

    Article  Google Scholar 

  • Evans, J. (2000). Adults’ mathematical thinking and emotions, a study of numerate practices. London and New York: Routledge/Falmer.

    Google Scholar 

  • FitzSimons, G. E. (1994a). TAFE students: The affective domain and mathematics. In G. Bell, B. Wright, N. Leeson, & J. Geake (Eds.), Challenges in mathematics education: Constraints on construction (pp. 233–241). Lismore: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • FitzSimons, G. E. (1994b). Teaching mathematics to adults returning to study. Geelong, Victoria: Deakin University Press.

    Google Scholar 

  • FitzSimons, G. E. (2007). Book review: Marcelo C. Borba and Mónica E. Villarreal/Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, visualization and experimentation. Educational Studies in Mathematics, 65(3), 385–392.

    Article  Google Scholar 

  • FitzSimons, G. E., & Godden, G. L. (2000). Review of research on adults’ mathematics learning. In D. Coben, J. O’Donoghue, & G. E. FitzSimons (Eds.), Perspectives on adults learning mathematics (pp. 13–46). Dortrecht: Kluwer Academic Publishers.

    Google Scholar 

  • FitzSimons, G. E., Jungwirth, H., Maaß, J., & Schlöglmann, W. (1996). Adults and mathematics. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 755–784). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Gadanidis, G., Graham, L., McDougall, D., & Roulet, G. (2002). On-line mathematics: Visions and opportunities, issues and challenges, and recommendations. White Paper based on the Fields Institute for Research in Mathematical Sciences Mathematics On-Line Working Meeting. November 15–17, 2001. Retrieved May 15, 2007, from the link to “Online Report” at the Mathematics Education Forum of The Fields Institute web page: http://www.fields.utoronto.ca/programs/mathed/meforum/index.html.

  • Gagatsis, A., & Thomaidis, I. (1994). Une étude multidimensionnelle du concept de valeur absolue. In M. Artigue, R. Gras, C. Laborde, P. Tavignot, & N. Balacheff (Eds.), Vingt Ans de Didactique de Mathématiques en France (pp. 343–348). Grenoble: La Pensée Sauvage.

    Google Scholar 

  • Gutstein, E. (2006). Reading and writing the world with mathematics: Towards a pedagogy for social justice. New York: Routledge.

    Google Scholar 

  • Haladyna, T., Shaughnessy, J., & Shaugnessy, J. M. (1983). A causal analysis of attitude towards mathematics. Journal for Research in Mathematics Education, 14(1), 19–29.

    Article  Google Scholar 

  • Handa, Y. (2003). A phenomenological exploration of mathematical engagement: Approaching an old metaphor anew. For the Learning of Mathematics, 23(1), 22–29.

    Google Scholar 

  • Illeris, K. (2004). The three dimensions of learning. Malabar: Krieger Publishing Co.

    Google Scholar 

  • Kantowski, M. G. (1977). Processes involved in mathematical problem solving. Journal for Research in Mathematics Education, 8, 163–180.

    Article  Google Scholar 

  • Knox, A. B. (1978). Adult development and learning. San Francisco: Jossey-Bass Publishers.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge, New York: Cambridge University Press.

    Google Scholar 

  • Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior. In D. B. McLeod, & V. M. Adams (Eds.), Affect and mathematical problem solving. A new perspective (pp. 75–88). New York: Springer.

    Google Scholar 

  • Lubienski, S. T. (2000). A clash of social cultures? Students’ experiences in a discussion-intensive seventh-grade mathematics classroom. Elementary School Journal, 100, 377–403.

    Article  Google Scholar 

  • Major, J. (2006). Rola zadań i problemów w kształtowaniu pojęć matematycznych na przykładzie wartości bezwzględnej liczby rzeczywistej. Dydaktyka Matematyki—Rocznik Polskiego Towarzystwa Matematycznego, Seria V, 29, 297–310 (In Polish. English title: The role of tasks and problems in the formation of mathematical concepts on the example of the absolute value of the real number).

  • Malmivuori, M.-L. (2001). The dynamics of affect, cognition, and social environment in the regulation of personal learning processes. The case of mathematics. Dissertation. Research Report 172. University of Helsinki, Helsinki.

  • Margolinas, C. (1992). De l’importance du vrai et du faux dans la classe des mathématiques. Grenoble: La Pensée Sauvage.

    Google Scholar 

  • McLeod, D. (1992). Research on affect in mathematics education: A reconceptualisation. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan.

    Google Scholar 

  • McLeod, D. B., & Adams, V. M. (1989). Affect and mathematical problem solving: A new perspective. New York: Springer.

    Google Scholar 

  • Mioduser, D., Nachmias, R., Lahav, O., & Oren, A. (2000). Web-based learning environments: Current pedagogical and technological state. Journal of Research on Computing in Education, 33(1), 55–76.

    Google Scholar 

  • Ostrom, E. (2005). Understanding institutional diversity. Princeton, New Jersey: Princeton University Press.

    Google Scholar 

  • Ostrom, E., & Hess, C. (2007). A framework for analyzing the knowledge commons. In C. Hess, & E. Ostrom (Eds.), Understanding knowledge as a commons. From theory to practice. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Paquelier, Y. (1988). Se tromper avec ou sans raisons? Vers une poétique de l’erreur. Actes de la 39e rencontre internationale de la CIEAEM tenue à Sherbrooke, Québec, du 27 juillet au 1er août 1987 (pp. 187–193). Sherbrooke, QC: Université de Sherbrooke.

  • Peters, B. G. (1999). Institutional theory in political science. London, New York: Continuum.

    Google Scholar 

  • Pickering, A. (1995). The mangle of practice: Time, agency, and science. Chicago: Chicago University Press.

    Google Scholar 

  • Reyes, L. H. (1984). Affective variables and mathematics education. Elementary School Journal, 84, 558–581.

    Article  Google Scholar 

  • Roddick, C. (2003). Calculus reform and traditional students’ use of calculus in an engineering mathematics course. In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (Eds.), Research in collegiate mathematics education V (pp. 56–78). Providence, RI: American Mathematical Society.

    Google Scholar 

  • Sackur, C., Assude, T., Maurel, M., Drouhard, J.-P., & Paquelier, Y. (2005). L’expérience de la nécessité épistémique. Recherches en Didactique des Mathématiques, 25(1), 57–90.

    Google Scholar 

  • Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338–335.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Eds.), Handbook for research on mathematics teaching and learning. (pp. 334–370). New York: MacMillan.

    Google Scholar 

  • Sesonske, A. (1966). Plato’s apology: Republic I. In A. Sesonske (Eds.), Plato’s ‘Republic’: Interpretation and criticism. (pp. 40–47). Belmont, CA: Wadsworth Publishing Company.

    Google Scholar 

  • Sierpinska, A. (1994). Understanding in mathematics. London: Falmer Press.

    Google Scholar 

  • Sierpinska, A. (2005). “Papa veut que je raisonne...”—Quelques refléxions sur la valeur du raisonnement mathématique dans la formation de futurs citoyens et professionnels. In D. Tanguay (Ed.), Actes du colloque du Groupe de didacticiens et didacticiennes du Québec, GDM 2005, Raisonnement mathématique et formation citoyenne, tenu à l’Université du Québec à Montréal, le 3 et 4 mai, 2005 (pp. 197–216). Available online at http://alcor.concordia.ca/∼sierp/).

  • Sierpinska, A. (2006). Sources of students’ frustration in bridging mathematics courses. In J. Novotna (Eds.), Proceedings of 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 121–129). Prague, Czech Republic: PME.

  • Sierpinska, A., Bobos, G., & Knipping, C. (2007). Presentation and partial results of a study of university students’ frustration in pre-university level, prerequisite mathematics courses: Emotions, positions and achievement. Manuscript posted at http://www.asjdomain.ca/emotions.html.

  • Smith, J. P. III, & Star, J. R. (2007). Expanding the notion of impact of K-12 standards-based mathematics and reform calculus programs. Journal for Research in Mathematics Education, 38(1), 3–34.

    Google Scholar 

  • Stodolsky, S. S., Salk, S., & Glaessner, B. (1991). Student views about learning math and social studies. American Educational Research Journal, 28(1), 89–116.

    Google Scholar 

  • Stroup, W. M. (2005). A dialectic analysis of generativity: Issues of network-supported design in mathematics and science. Mathematical Thinking and Learning, 7(3), 181–206.

    Article  Google Scholar 

  • Surman, P. (1993). Empowering students—empowering teachers: Lessons for mainstream tertiary teachers of mathematics from bridging mathematics. In 3rd Australian bridging mathematics network conference proceedings (pp. 31–41). Brisbane: Queensland University of Technology.

  • Taylor, J. A. (1998). Self test: A flexible self assessment package for distance and other learners. Computers and Education, 31, 319–328.

    Article  Google Scholar 

  • Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematics Learning, 9(3), 281–307.

    Article  Google Scholar 

  • Wagner, D. (2007). Students’ critical awareness of voice and agency in mathematics classroom discourse. Mathematical Thinking and Learning, 9(1), 31–50.

    Article  Google Scholar 

  • Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, 63(2), 113–121.

    Article  Google Scholar 

Download references

Acknowledgments

This research has been funded by The Social Sciences and Humanities Research Council of Canada. We thank instructors and students who graciously accepted to participate in our study. Many thanks to the anonymous reviewers, whose constructive remarks and suggestions helped improve the first draft of this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve boulevard West, Montreal, QC, Canada, H3G 1M8

    Anna Sierpinska & Georgeana Bobos

  2. Acadia University, Wolfville, NS, Canada

    Christine Knipping

Authors
  1. Anna Sierpinska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Georgeana Bobos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christine Knipping
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anna Sierpinska.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sierpinska, A., Bobos, G. & Knipping, C. Sources of students’ frustration in pre-university level, prerequisite mathematics courses. Instr Sci 36, 289–320 (2008). https://doi.org/10.1007/s11251-007-9033-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11251-007-9033-6

Keywords

Search

Navigation