Educational Studies in Mathematics

, Volume 102, Issue 2, pp 257–274 | Cite as

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

  • Nadia AzrouEmail author
  • Abdelkader Khelladi


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.


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



  1. 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
  2. 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
  3. Brousseau, G. (1988). Le contrat didactique: le milieu. Recherche en Didactique des Mathématiques, 9(3), 309–336.Google Scholar
  4. Cummins, J. (1984). Bilingualism and special education. Clevedon, UK: Multilingual Matters.Google Scholar
  5. Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38(1), 85–109.CrossRefGoogle Scholar
  6. 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
  7. Halliday, M. A. K. (1985). An introduction to functional grammar. London, UK: Arnold.Google Scholar
  8. 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
  9. Lew, K. (2016). Conventions of the language of mathematical proof writing at the undergraduate level. PhD thesis. New Brunswick, NJ: Rutgers University.Google Scholar
  10. 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
  11. Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266.CrossRefGoogle Scholar
  12. Morselli, F. (2007). Sui fattori culturali nei processi di congettura e dimostrazione. PhD Thesis. Torino, Italy: Università degli Studi.Google Scholar
  13. Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics, 66, 23–41.CrossRefGoogle Scholar
  14. 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
  15. Sarrazy, B. (1995). Le contrat didactique. Revue Française de Pédagogie, 112, 85–118.CrossRefGoogle Scholar
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. Selden, A. & Selden, J. (2013). The genre of proof. Tech report no. 2013–1. Cookeville, TN: Tennessee Tech University.Google Scholar
  22. Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, 10(23), 133–170.Google Scholar
  23. Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119.CrossRefGoogle Scholar
  24. 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
  25. Weber, K. (2015). Mathematics professors and mathematics majors’ expectations of lectures in advanced mathematics. [Blog post.] from Accessed 10 Jan 2017.
  26. Zill, D. G., & Shanahan, P. D. (2003). A first course in complex analysis with applications. Sudbury (MA): Jones and Bartlett Publishers. from Accessed 20 Dec 2017

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.University Yahia FaresMedeaAlgeria
  2. 2.USTHBAlgiersAlgeria

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