Skip to main content
SpringerLink
Log in

Debate-Based Learning Game for Constructing Mathematical Proofs

  • Conference paper
  • First Online:
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10369))

  • 590 Accesses

Abstract

Debate is a valuable and effective method of learning. It is an interactive process in which learners cooperate by exchanging arguments and counter-arguments to solve a common question. We propose a debate-based learning game for mathematics classroom to teach how to structure and build mathematical proofs. Dung’s argumentation framework and its extensions are used as a means to extract acceptable arguments that form the proof. Moreover this allows instructors to provide continuous feedbacks to learners without information overload.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Called attack in [4].

  2. 2.

    Notice that \(P_1\cup P_2\) may be inconsistent but remind that the validity of arguments is decided by learners.

  3. 3.

    \(A_{11}\) and \(A_{12}\) need not to be considered separately. In fact \(A_{11}\wedge A_{12}\) is needed and sufficient.

References

  1. Amir, Y., Sharan, S., Ben-Ari, R., Desegregation, S.: Cross-Cultural Perspectives. Psychology Press, New York (1984)

    Google Scholar 

  2. Cayrol, C., Lagasquie-Schiex, M.C.: Bipolarity in argumentation graphs: Towards a better understanding. IJAR 54(7), 876–899 (2013)

    MathSciNet  MATH  Google Scholar 

  3. Davidson, N.: Enhancing Thinking through Cooperative Learning. Teachers College Press, New York (1992)

    Google Scholar 

  4. Dung, P.M.: On the acceptability of arguments and its fundamental role in non-monotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 321–357 (1995)

    Article  MATH  Google Scholar 

  5. Durand-Guerrier, V., Boero, P., Douek, N., Epp, S., Tanguay, D.: Argumentation and proof in the mathematics classroom. In: Hanna, G., de Villiers, M. (eds.) Proof and Proving in Mathematics Education, pp. 349–367. Springer, Dordrecht (2012)

    Google Scholar 

  6. Johnson, D.W., Johnson, R.T.: Learning Together and Alone: Cooperative, Competitive, and Individualistic Learning. Allyn and Bacon, Boston (1999)

    Google Scholar 

  7. Kaci, S., van der Torre, L.: Preference-based argumentation: arguments supporting multiple values. IJAR 48, 730–751 (2008)

    MathSciNet  MATH  Google Scholar 

  8. Kennedy, R.R.: The power of in-class debates. Act. Learn. High Educ. 10(3), 225–236 (2009)

    Article  Google Scholar 

  9. Maudet, N., Moore, D.: Dialogue games as dialogue models for interacting with, and via, computers. Informal Logic 21(3), 219–243 (2001)

    Article  Google Scholar 

  10. Modgil, S.: Hierarchical argumentation. In: Fisher, M., Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 319–332. Springer, Heidelberg (2006). doi:10.1007/11853886_27

    Chapter  Google Scholar 

  11. Nouioua, F., Risch, V.: Bipolar argumentation frameworks with specialized supports. In: ICTAI 2010, pp. 215–218 (2010)

    Google Scholar 

  12. Oren, N., Norman, T.J.: Semantics for evidence-based argumentation. In: COMMA 2008, pp. 276–284 (2008)

    Google Scholar 

  13. Oros, A.L.: Let’s debate: active learning encourages student participation and critical thinking. J. Polit. Sci. Educ. 3(3), 293–311 (2007)

    Article  MathSciNet  Google Scholar 

  14. Park, C., Kier, C., Jugdev, K.: Debate as a teaching strategy in online education: a case study. Can. J. Learn. Technol. 37(3), 17–20 (2011)

    Google Scholar 

  15. Pease, A., Budzynska, K., Lawrence, J., Reed, C.: Lakatos games for mathematical argument. In: COMMA 2014, pp. 59–66 (2014)

    Google Scholar 

  16. Rahwan, I., Larson, K.: Argumentation and game theory. In: Simari, G., Rahwan, I. (eds.) Argumentation in Artificial Intelligence, pp. 321–339. Springer, New York (2009)

    Chapter  Google Scholar 

  17. Thimm, M., García, A.J.: Classification and strategical issues of argumentation games on structured argumentation frameworks. In: AAMAS 2010, pp. 1247–1254 (2010)

    Google Scholar 

  18. Weigand, E.: Argumentation: the mixed game. Argumentation 20(1), 59–87 (2006)

    Article  Google Scholar 

  19. Yuan, T., Svansson, V., Moore, D., Grierson, A.: A computer game for abstract argumentation. In: CMNA (IJCAI 2007 Workshop), pp. 62–68 (2007)

    Google Scholar 

  20. Zemplén, G.: History of Science and Argumentation in Science Education, pp. 129–140. SensePublishers, Rotterdam (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIRMM, Montpellier, France

    Nadira Boudjani, Abdelkader Gouaich & Souhila Kaci

Authors
  1. Nadira Boudjani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdelkader Gouaich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Souhila Kaci
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Souhila Kaci .

Editor information

Editors and Affiliations

  1. IDSIA, Lugano, Switzerland

    Alessandro Antonucci

  2. ONERA, Toulouse, France

    Laurence Cholvy

  3. Aix-Marseille University, Marseille, France

    Odile Papini

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Boudjani, N., Gouaich, A., Kaci, S. (2017). Debate-Based Learning Game for Constructing Mathematical Proofs. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-61581-3_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61580-6

  • Online ISBN: 978-3-319-61581-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation