Landy Elena Sosa-Moguel, Eddie Aparicio-Landa


Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers’ perceptions of inductive reasoning and interprets this mathematical reasoning type in teaching the quadratic equation. The data were collected from a questionnaire administered to 22 teachers and an interview conducted to expand their answers. Through the thematic analysis method, it was found that more than half the teachers perceived inductive reasoning as a process for moving from the particular to the general and as a way to acquire mathematical knowledge through questioning. Because teachers have little clarity about inductive phases and processes, they expressed confusion about teaching the quadratic equation inductively. Results indicate that secondary school teachers need professional learning experiences geared towards using inductive reasoning processes and tasks to form concepts and generalizations in mathematics.


Perception; Inductive Reasoning; In-service Mathematics Teachers; Secondary School

Full Text:



AMTE [Association of Mathematics Teacher Educators]. (2017). Standards for preparing teachers of mathematics. Available online at

Ashton, R., & Roberts, E. (2006). What is valuable and unique about the educational psychologist? Educational Psychology in Practice: Theory, research and practice in educational psychology, 22(2), 111–123.

Bills, L., & Rowland, T. (1999). Examples, generalisation and proof. Advances in Mathematics Education, 1(1), 103–116.

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.

Braun, V., & Clarke, V. (2012). Thematic analysis. In H. Cooper (Ed.), APA handbook of research methods in psychology: Research designs: Quantitative, qualitative, neuropsychological, and biological (Vol. 2, pp. 57–71). Washington, DC: American Psychological Association.

Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309–333.

Cañadas, M. C., & Castro, E. (2007). A proposal of categorisation for analysing inductive reasoning. PNA, 1(2), 67–78.

Cañadas, M. C., Castro E., & Castro, E. (2008). Patterns, generalization and inductive strategies of secondary students working on the tiles problem. PNA, 2(3), 137–151.

Cañadas, M. C., Castro, E., & Castro, E. (2009). Using a model to describe students’ inductive reasoning in problem solving. Electronic Journal of Research in Educational Psychology, 7(1), 261–278.

Cañadas, M. C., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, O. (2007). The conjecturing process: Perspectives in theory and implications in practice. Journal of Teaching and Learning, 5(1), 55–72.

Christou, C., & Papageorgiou, E. (2007). A framework of mathematics inductive reasoning. Learning and Instruction, 17(1), 55–66.

Conner, A., Singletary, L., Smith, R., Wagner, P., & Francisco, R. (2014). Identifying kinds of reasoning in collective argumentation. Mathematical Thinking and Learning, 16, 181–200.

Csapó, B. (1997). The development of inductive reasoning: Cross-sectional assessments in an educational context. International Journal of Behavioral Development, 20(4), 609–626.

Davydov, V. (1990). Type of generalization in instruction: Logical and psychological problems in the structuring of school curricula. In J. Kilpatrick (Ed.), Soviet studies in mathematics education (Vol. 2). Reston, VA: National Council of Teachers of Mathematics.

De Koning, E., & Hamers, J. H. M. (1999). Teaching inductive reasoning: Theoretical back- ground and educational implications. In J. Hamers, J. van Luit, & B. Csapó (Eds.), Teaching and learning thinking skills (pp. 156–188). Lisse: Swets & Zeitlinger.

De Koning, E., Hamers, J. H., Sijtsma, K., & Vermeer, A. (2002). Teaching inductive reasoning in primary education. Developmental Review, 22(2), 211–241.

El Mouhayar, R. (2018). Exploring teachers’ attention to students’ responses in pattern generalization tasks. Journal of Mathematics Teacher Education, 22(1).

Fernández-León, A., Gavilán-Izquierdo, J. M., & Toscano, R. (2021). A case study on how primary- school in-service teachers conjecture and prove: An approach from the mathematical community. Journal on Mathematics Education, 12(1), 49–72.

Freitas, E., Lerman, S., & Parks, L. (2017). Qualitative methods. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 159–182). Reston, VA: National Council of Teachers of Mathematics.

Haverty, L., Koedinger, K., Klahr, D., & Alibali, M. (2000). Solving inductive reasoning problems in mathematics: Not-so-trivial pursuit. Cognitive Science, 24(2), 249–298.

Hayes, B. K., Heit, E., & Swendsen, H. (2010). Inductive reasoning. Cognitive Science, 1(2), 278–292.

Herbert, S., Vale, C., Bragg, L. A., Loong, E., & Widjaja, W. (2015). A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26–37.

Hodnik, T., & Manfreda, V. (2015). Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem. Educational Studies in Mathematics, 89(2), 283-306.

Honomichl, R. D., & Chen, Z. (2012). The role of guidance in children’s discovery learning. Wiley Interdisciplinary Reviews: Cognitive Science, 3(6), 615–622.

Klauer, K. J. (1990). A process theory of inductive reasoning tested by the teaching of domain-specific thinking strategies. European Journal of Psychology of Education, 5(2), 191–206.

Klauer, K. J. (1996). Teaching inductive reasoning: Some theory and three experimental studies. Learning and Instruction, 6(1), 37–57.

Klauer, K. J., & Phye, G. D. (2008). Inductive reasoning: A training approach. Review of Educational Research, 78(1), 85–123.

Lee, K. (2016). Students’ proof schemes for mathematical proving and disproving of propositions. The Journal of Mathematical Behavior, 41, 26-44.

Manfreda, V., Slapar, M., & Hodnik, T. (2012). Comparison of competences in inductive reasoning between primary teachers’ students and mathematics teachers’ students. In B. Maj-Tatsis & K. Tatsis (Eds.), Generalization in mathematics at all educational levels (pp. 299–311). Rzeszów: Wydawnictwo Uniwersytetu Rzeszowskiego.

Martinez, M. V., & Pedemonte, B. (2014). Relationship between inductive arithmetic argumentation and deductive algebraic proof. Educational Studies in Mathematics, 86, 125–149.

Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186.

Melhuish, K., Thanheiser, E., & Guyot, L. (2018). Elementary school teachers’ noticing of essential mathematical reasoning forms: Justification and generalization. Journal of Mathematics Teacher Education, 23, 35–67.

Ministry of Public Education (2017). Key learnings for comprehensive education. Plan and study programs for basic education. Mexico City: Author.

Molnár, G. (2011). Playful fostering of 6- to 8-year-old students’ inductive reasoning. Thinking Skills and Creativity, 6(2), 91–99.

Molnár, G., Greiff, S., & Csapó, B. (2013). Inductive reasoning, domain specific and complex problem solving: Relations and development. Thinking Skills and Creativity, 9, 35–45.

Mousa, M. (2017). The influence of inductive reasoning thinking skill on enhancing performance. International Humanities Studies, 4(3), 37–48. Retrieved from

NCTM [National Council of Teachers of Mathematics]. (2014). Principles to actions. Ensuring mathematical success for all. Reston, VA: Author.

NCTM [National Council of Teachers of Mathematics]. (2020). Standards for the preparation of middle level mathematics teachers. Reston, VA: Author.

Papageorgiou, E. (2009). Towards a teaching approach for improving mathematics inductive reasoning problem solving. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 313–320). Thessaloniki, Greece: Aristotle University of Thessaloniki.

Peterson, R. (2000). Constructing Effective Questionnaires. Thousand Oaks, CA: SAGE Publications, Inc.

Polya, G. (1957). How to solve it. A new aspect of mathematical method. New York, NY: Doubleday.

Polya, G. (1967). Le découverte des mathématiques. Paris, France: DUNOD.

Reid, D., & Knipping, C. (2010). Types of reasoning. In D. Reid & C. Knipping (Eds.), Proof in mathematics education: Research, learning and teaching (pp. 83–127). Rotterdam: Sense.

Rivera, F. D., & Becker, J. R. (2003). The effects of numerical and figural cues on the induction processes of preservice elementary teachers. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th PME-NA Conference (pp. 63–70). Honolulu: University of Hawai‘i. Retrieved from

Rivera, F. D., & Becker, J. R. (2007). Abduction–induction (generalization) processes of elementary majors on figural patterns in algebra. Journal of Mathematical Behavior, 26(2), 140–155.

Rivera, F. D., & Becker, J. R. (2016). Middle school students’ patterning performance on semi-free generalization tasks. Journal of Mathematical Behavior, 43, 53–69.

Rosli, R., Goldsby, D., Onwuegbuzie, A. J., Capraro, M. M., Capraro, R. M., & Gonzalez, E. G. Y. (2020). Elementary preservice teachers’ knowledge, perceptions and attitudes towards fractions: A mixed-analysis. Journal on Mathematics Education, 11(1), 59–76.

Rott, B., & Leuders, T. (2016). Inductive and deductive justification of knowledge: Flexible judgments underneath stable beliefs in teacher education. Mathematical Thinking and Learning, 18(4), 271–286.

Rott, B. (2021). Inductive and deductive justification of knowledge: epistemological beliefs and critical thinking at the beginning of studying mathematics. Educational Studies in Mathematics, 106(1), 117–132.

Siswono, T. Y. E., Hartono, S., & Kohar, A. W. (2020). Deductive or inductive? Prospective teachers’ preference of proof method on an intermediate proof task. Journal on Mathematics Education, 11(3), 417–438.

Soler-Álvarez, M. N., & Manrique, V. H. (2014). Discovery process in mathematics class: Abductive, inductive and deductive reasoning. ENSENANZA DE LAS CIENCIAS, 32(2), 191-219.

Sosa, L., & Aparicio, E. (2020). Difficulties in inductive reasoning of middle schoolteachers when generalizing a quadratic pattern. In A. Silva & A. Vieira (Orgs.), Prospecção de Problemas e Soluções nas Ciências Matemáticas 3 (pp. 103–115). Parana, Brasil: Atena Editora.

Sosa, L., Aparicio, E., & Cabañas, G. (2019). Characterization of inductive reasoning in middle school mathematics teachers in a generalization task. International Electronic Journal of Mathematics Education, 14(3), 563–581.

Sosa, L., Aparicio, E., & Cabañas, G. (2020). Inductive reasoning stages presented by mathematics teachers when solving a generalization problem. PNA, 14(2), 118–140.

Sosa, L., Cabañas, G., & Aparicio, E. (2019). Induction generalization tasks to form the power concept. In F. Machado (Org.), Educaçao Matemática e suas Tecnologias 2 (pp. 181–191). Paraná, Brazil: Atena Editora.

Sriraman, B., & Adrian, H. (2004). The pedagogical value and the interdisciplinary nature of inductive processes in forming generalizations: Reflections from the classroom. Interchange, 35(4), 407–422.

Tomic, W. (1995). Training in inductive reasoning and problem solving. Contemporary Educational Psychology, 20(4), 483–490.

Yurniwati, & Hanum, L. (2017). Improving mathematics achievement of Indonesian 5th grade students through guided discovery learning. Journal on Mathematics Education, 8(1), 77–84.

Zohrabi, M. (2013). Mixed method research: Instruments, validity, reliability and reporting findings. Theory & Practice in Language Studies, 3(2), 254–262.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Creative Commons License
Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.

View My Stats