Skip to main content
SpringerLink
Log in

Exploration of the Truth Values of Conditionals Set Up in Everyday Context and in Open Sentences

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

This study aimed to design a task in an everyday context to support high school students’ exploration of the truth values of propositional conditionals and to understand their difficulties. The results showed that students could identify that the truth value of a propositional conditional is determined by two variables (the truth values of the antecedent and the consequent) while organizing the propositional conditionals generated from the open sentence and that a social contract situation can help students understand why the truth value of a conditional with a false antecedent is true. The study also revealed that students’ difficulties in determining the truth values of conditionals are closely related to the time variable in an everyday context and the confusion between conditionals and causality. The findings from this study on the strategy and difficulties exhibited by students when determining the truth value of everyday conditional sentences can inform future efforts to teach formal mathematics in real-world contexts.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Antonini, S., & Mariotti, M. A. (2008). Indirect proof: What is specific to this way of proving? ZDM—The International Journal on Mathematics Education, 40, 401–412.

  • Beller, S., & Kuhnmünch, G. (2007). What causal conditional reasoning tells us about people’s understanding of causality. Thinking & Reasoning, 13(4), 426–460.

    Article  Google Scholar 

  • Bennett, J. (2003). A philosophical guide to conditionals. Oxford University Press.

    Book  Google Scholar 

  • Blanchette, I. (2006). The effect of emotion on interpretation and logic in a conditional reasoning task. Memory & Cognition, 34(5), 1112–1125.

    Article  Google Scholar 

  • Bronkhorst, H., Roorda, G., Suhre, C., & Goedhart, M. (2020). Logical reasoning in formal and everyday reasoning tasks. International Journal of Science and Mathematics Education, 18(8), 1673–1694.

    Article  ADS  Google Scholar 

  • Cobb, P., & Whitenack, J. W. (1996). A method for conducting longitudinal analyses of classroom videorecordings and transcripts. Educational Studies in Mathematics, 30(3), 213–228.

    Article  Google Scholar 

  • Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches. Sage.

    Google Scholar 

  • Cummins, D. D., Lubart, T., Alksnis, O., & Rist, R. (1991). Conditional reasoning and causation. Memory & Cognition, 19(3), 274–282.

    Article  CAS  Google Scholar 

  • Damarin, S. K. (1977). The interpretation of statements in standard logical form by preservice elementary teachers. Journal for Research in Mathematics Education, 8(2), 123–131.

    Article  Google Scholar 

  • Dawkins, P. C., & Cook, J. P. (2017). Guiding reinvention of conventional tools of mathematical logic: Students’ reasoning about mathematical disjunctions. Educational Studies in Mathematics, 94, 241–256.

    Article  Google Scholar 

  • Dawkins, P. C., Inglis, M., & Wasserman, N. (2019). The use(s) of is in mathematics. Educational Studies in Mathematics, 100, 117–137.

    Article  Google Scholar 

  • Dawkins, P.C. & Norton, A. (2022) Identifying mental actions for abstracting the logic of conditional statements. The Journal of Mathematical Behavior, 66. https://doi.org/10.1016/j.jmathb.2022.100954

  • De Vega, M., Urrutia, M., & Riffo, B. (2007). Cancelling updating in the comprehension of counterfactuals embedded in narratives. Memory & Cognition, 35(6), 1410–1421.

    Article  Google Scholar 

  • Dreyfus, T., & Tsamir, P. (2004). Ben’s consolidation of knowledge structures about infinite sets. Journal of Mathematical Behavior, 23, 271–300.

    Article  Google Scholar 

  • Durand-Guerrier, V. (2003). Which notion of implication is the right one? From logical considerations to a didactic perspective. Educational Studies in Mathematics, 53, 5–34.

    Article  Google Scholar 

  • Durand-Guerrier, V. (2008). Truth versus validity in mathematical proof. ZDM the International Journal on Mathematics Education, 40(3), 373–384.

    Article  Google Scholar 

  • Durand-Guerrier, V. (2014). Logic in mathematics education. In M. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 361–364). Springer.

    Chapter  Google Scholar 

  • Durand-Guerrier, V., Boero, P., Douek, N., Epp, S., & Tanguay, D. (2012). Examining the role of logic in teaching proof. In G. Hanna & M. De Villiers (Eds.), ICMI study 19 book: Proof and proving in mathematics education (pp. 369–389). Springer.

    Chapter  Google Scholar 

  • Duval, R. (2007). Cognitive functioning and the understanding of mathematical processes of proof. In P. Boero (Ed.), Theorems in school (pp. 137–161). Sense Publishers.

  • Edgington, D. (1995). On conditionals. Mind, 104(414), 235–329.

    Article  MathSciNet  Google Scholar 

  • Epp, S. S. (2003). The role of logic in teaching proof. The American Mathematical Monthly, 110(10), 886–899.

  • Fillenbaum, S. (1974). Information amplified: Memory for counterfactual conditionals. Journal of Experimental Psychology, 102(1), 44–49.

    Article  Google Scholar 

  • Freudenthal, H. (1966). The Language of Logic. Elsevier Publishing Company.

    Google Scholar 

  • Freudenthal, H. (1969). A teachers course colloquium on sets and logic. Educational Studies in Mathematics, 2(1), 32–58.

    Article  Google Scholar 

  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. D. Reidel Publishing Company.

    Google Scholar 

  • Goel, V., & Vartanian, O. (2011). Negative emotions can attenuate the influence of beliefs on logical reasoning. Cognition and Emotion, 25(1), 121–131.

    Article  PubMed  Google Scholar 

  • Grimaldi, R. P. (1998). Discrete and combinatorial mathematics: An applied introduction. Pearson.

    Google Scholar 

  • Hadar, N. (1977). Children’s conditional reasoning, Part I: An intuitive approach to the logic of implication. Educational Studies in Mathematics, 8(4), 413–438.

    Article  Google Scholar 

  • Hadar, N. (1993). Mathematical induction: A focus on conceptual framework. School Science and Mathematics, 8, 408–417.

    Article  ADS  Google Scholar 

  • Hadar, N., & Henkin, L. (1978). Children’s conditional reasoning, Part II: Towards a reliable test of conditional reasoning ability. Educational Studies in Mathematics, 9(1), 97–114.

    Article  Google Scholar 

  • Hoyles, C., & Küchemann., D. (2002). Students’ understanding of logical implication. Educational Studies in Mathematics, 51(3), 193–223.

  • Hub, A., & Dawkins, P. C. (2018). On the construction of set-based meanings for the truth of mathematical conditionals. The Journal of Mathematical Behavior, 50, 90–102.

    Article  Google Scholar 

  • Lefford, A. (1946). The influence of emotional subject matter on logical reasoning. The Journal of General Psychology., 34(2), 127–151.

    Article  CAS  PubMed  Google Scholar 

  • Lewis, D. (1973). Counterfactuals. Blackwell.

    Google Scholar 

  • Lucas, J. F. (1990). Introduction to abstract mathematics. Ardsley House.

    Google Scholar 

  • O’Brien, T. C., Shapiro, B. J., & Reali, N. C. (1971). Logical thinking - Language and context. Educational Studies in Mathematics, 4(2), 201–219.

    Article  Google Scholar 

  • Palha, S., Dekker, R., Gravemeijer, K., & Van Hout-Wolters, B. (2013). Developing shift problems to foster geometrical proof and understanding. The Journal of Mathematical Behavior, 32(2), 142–159.

    Article  Google Scholar 

  • Pfeifer, N. (2013). The new psychology of reasoning: A mental probability logical perspective. Thinking and Reasoning, 19(3), 329–345.

    Article  Google Scholar 

  • Quine, W. V. (1982). Methods of logic. Harvard University Press.

    Google Scholar 

  • Reid, D. A., & Inglis, M. (2005). Talking about logic. For the Learning of Mathematics, 25(2), 24–25.

    Google Scholar 

  • Rogalski, J., & Rogalski, M. (2001). How do graduate mathematics students evaluate assertions with a false premise? In M. van den Heuvel-Panhuizen (Ed.), PME25@NL (Vol. 4, pp. 113–120). Freudenthal Institute, Utrecht University.

    Google Scholar 

  • Santamaria, C., Espino, O., & Byrne, R. M. J. (2005). Counterfactual and semifactual conditionals prime alternative possibilities. Journal of Experimental Psychology: Learning, Memory and Cognition, 31(5), 1149–1154.

    PubMed  Google Scholar 

  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.

    Book  Google Scholar 

  • Shipman, B. A. (2013). Mathematical versus English meaning in implication and disjunction. Teaching Mathematics and Its Applications, 32(1), 38–46.

    Article  Google Scholar 

  • Sriraman, B., & Knott, L. (2006). 1 or 0? Cantorian conundrums in the contemporary classroom, Australian Senior Mathematics Journal, 20(2), 57-61.

  • Stake, R. E. (1995). The art of case study research. Sage.

    Google Scholar 

  • Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. Sage.

    Google Scholar 

  • Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2004). Undergraduate students’ understanding of the contraposition equivalence rule in symbolic and verbal contexts. Educational Studies in Mathematics, 55(1), 133–162.

    Article  Google Scholar 

  • Stylianides, G., Stylianides, A. & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (ed.) Compendium for research in mathematics education. Reston (pp. 237–266). National Council of Teachers of Mathematics.

  • Weber, K., & Alcock, L. (2005). Using warranted implications to understand and validate proofs. For the Learning of Mathematics, 25(1), 34–51.

    Google Scholar 

  • Yopp, D. A. (2017). Eliminating counterexamples: A grade 8 student’s learning trajectory for contrapositive proving. The Journal of Mathematical Behavior, 45, 150–166.

    Article  Google Scholar 

  • Yu, J. Y. W., Chin, E. T., & Lin, C. J. (2004). Taiwanese junior high school students’ understanding about the validity of conditional statements. International Journal of Science and Mathematics Education, 2, 257–285.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics Education, Seoul National University, Seoul, Korea

    Kyung-Jin Lee & Suh-Ryung Kim

  2. Department of Mathematics Education, Gyeongin National University of Education, Incheon, Korea

    JinHyeong Park

Authors
  1. Kyung-Jin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JinHyeong Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Suh-Ryung Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suh-Ryung Kim.

Ethics declarations

Ethical Approval and Consent to Participate

This research was conducted under the approval of the IRB (Institutional Review Board) of Seoul National University (SNUIRB No. E1304/001-047). All necessary ethical considerations were taken into account, including obtaining informed consent, ensuring participant anonymity, and maintaining data confidentiality.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, KJ., Park, J. & Kim, SR. Exploration of the Truth Values of Conditionals Set Up in Everyday Context and in Open Sentences. Int J of Sci and Math Educ 22, 657–678 (2024). https://doi.org/10.1007/s10763-023-10391-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-023-10391-w

Keywords

Search

Navigation