# Why do students write poor proof texts? A case study on undergraduates’ proof writing

Article

First Online:

- 107 Downloads

## Abstract

This paper deals with writing a proof text as the final step of the proving process at university level, particularly when it results in a disorganized, unclear draft. The reported study concerns third year university students when dealing with proof tasks for which the proving process has to be built up, as opposed to tasks that students may tackle by known proving procedures. By comparing the analysis of students’ proof texts with their interview responses, a strong influence of the didactic contract, lack of meta-knowledge about proof, and a weak mastery of concepts were identified as possible reasons for the poor quality of the proof texts. Some educational implications and hints for further research are provided.

## Keywords

Proof writing Proving-problems Undergraduate students Meta-knowledge about proof Didactic contract## Notes

## References

- Baker, D., & Campbell, C. (2004). Fostering the development of mathematics thinking: Observations from a proofs course.
*Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 14*(4), 345–353.CrossRefGoogle Scholar - Boero, P., Douek, N., & Ferrari, P. L. (2008). Developing mastery of natural language. Approaches to some theoretical aspects of mathematics. In L. English (Ed.),
*International handbook of research in mathematics education*(pp. 262–295). New York, NY: Routledge.Google Scholar - Brousseau, G. (1988). Le contrat didactique: le milieu.
*Recherche en Didactique des Mathématiques, 9*(3), 309–336.Google Scholar - Cummins, J. (1984).
*Bilingualism and special education*. Clevedon, UK: Multilingual Matters.Google Scholar - Dreyfus, T. (1999). Why Johnny can’t prove.
*Educational Studies in Mathematics, 38*(1), 85–109.CrossRefGoogle Scholar - Guala, E., & Boero, P. (2017). Cultural analysis of mathematical content in teacher education: The case of elementary arithmetic theorems.
*Educational Studies in Mathematics, 96*(2), 207–227.CrossRefGoogle Scholar - Halliday, M. A. K. (1985).
*An introduction to functional grammar*. London, UK: Arnold.Google Scholar - Harel, G., & Sowder, L. (1998). Students’ proof schemes. Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.),
*Research on collegiate mathematics education, III*(pp. 234–283). Providence RI: AMS.Google Scholar - Lew, K. (2016).
*Conventions of the language of mathematical proof writing at the undergraduate level.*PhD thesis. New Brunswick, NJ: Rutgers University.Google Scholar - Mamona-Downs, J., & Downs, M. (2009). Necessary realignments from mental argumentation to proof presentation. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.),
*Proceedings of the 6th congress of the European Society for Research in Mathematics Education*(pp. 2336–2345)*.*Lyon, France: INRP.Google Scholar - Moore, R. C. (1994). Making the transition to formal proof.
*Educational Studies in Mathematics, 27*(3), 249–266.CrossRefGoogle Scholar - Morselli, F. (2007).
*Sui fattori culturali nei processi di congettura e dimostrazione.*PhD Thesis. Torino, Italy: Università degli Studi.Google Scholar - Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed?
*Educational Studies in Mathematics, 66*, 23–41.CrossRefGoogle Scholar - Raman, M., Sandefur, J., Birky, G., Campbell, C., & Somers, K. (2009). “Is that a proof?”: An emerging explanation for why students don't know they (just about) have one. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.),
*Proceedings of the 6th congress of the European Society for Research in Mathematics Education*(pp. 301–310). Lyon, France: INRP.Google Scholar - Sarrazy, B. (1995). Le contrat didactique.
*Revue Française de Pédagogie, 112*, 85–118.CrossRefGoogle Scholar - Schoenfeld, A. H. (1988). Problem solving. In P. J. Campbell & L. S. Grinstein (Eds.),
*Mathematics education in secondary schools and two-year colleges: A source book*(pp. 81–96). New York, NY: Garland Publishing Inc.Google Scholar - Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. Grows (Ed.),
*Handbook for research on mathematics teaching and learning*(pp. 334–370). New York, NY: Macmillan.Google Scholar - Selden, A., & Selden, J. (2003a). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?
*Journal of Research in Mathematics Education, 34*(1), 4–36.CrossRefGoogle Scholar - Selden, A. & Selden, J. (2003b).
*Errors and misconceptions in college level theorem proving.*Tech report no. 2003–3. Cookeville, TN: Tennessee Tech University*.*Google Scholar - Selden, A. & Selden, J. (2007).
*Overcoming students’ difficulties in learning to understand and construct proofs.*Tech report no. 2007–1. Cookeville, TN: Tennessee Tech University.Google Scholar - Selden, A. & Selden, J. (2013).
*The genre of proof.*Tech report no. 2013–1. Cookeville, TN: Tennessee Tech University.Google Scholar - Vergnaud, G. (1990). La théorie des champs conceptuels.
*Recherches en Didactique des Mathématiques, 10*(23), 133–170.Google Scholar - Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge.
*Educational Studies in Mathematics, 48*(1), 101–119.CrossRefGoogle Scholar - Weber, K. (2004). A framework for describing the processes that undergraduates use to construct proofs. In M. Johnsen Høines & A. B. Fuglestad (Eds.),
*Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education*(Vol. 4, pp. 425–432)*.*Bergen, Norway: PME.Google Scholar - Weber, K. (2015).
*Mathematics professors and mathematics majors’ expectations of lectures in advanced mathematics.*[Blog post.] from http://blogs.ams.org/matheducation/2015/02/10/mathematics-professors-and-mathematics-majors-expectations-of-lectures-inadvancedmathematics/. Accessed 10 Jan 2017. - Zill, D. G., & Shanahan, P. D. (2003).
*A first course in complex analysis with applications*. Sudbury (MA): Jones and Bartlett Publishers. from https://mariosuazo.files.wordpress.com/2013/08/dennis_zill_a_first_course_in_complex_analysis_wbookfi-org.pdf. Accessed 20 Dec 2017

## Copyright information

© Springer Nature B.V. 2019