logo logo European Journal of Educational Research

EU-JER is is a, peer reviewed, online academic research journal.

Subscribe to

Receive Email Alerts

for special events, calls for papers, and professional development opportunities.


Publisher (HQ)

Eurasian Society of Educational Research
Eurasian Society of Educational Research
Christiaan Huygensstraat 44, Zipcode:7533XB, Enschede, THE NETHERLANDS
Eurasian Society of Educational Research
Christiaan Huygensstraat 44, Zipcode:7533XB, Enschede, THE NETHERLANDS
open ended problems open approach mathematics education teaching methods teaching practice

The Open-Ended Approach Framework

Lloyd Munroe

This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining h.


This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical Knowledge and Applying Mathematical Knowledge. The sections were cross-analyzed with students’ responses to provide a comprehensive analysis of how teachers use various techniques to support students. It is proposed that teachers can use this framework to create an environment that promotes learning with open-ended as well as other open problems in their mathematics classroom. The OPA framework can contribute to teacher education, the design of mathematics curricula and to educational research.

Keywords: Open-ended problems, open approach, mathematics education, teaching methods, teaching practice

cloud_download PDF
Article Metrics


Becker, J. P., & Shimada, S. (1997). The open-ended approach: A new proposal for teaching mathematics: Reston, Virgina. Mathematics National Council of Teachers of Mathematics, INC.

Bogdan, R. C., & Biklen, S. K. (1992). Qualitative research in education: An introduction to theory and methods. Boston: Allyn and Bacon.

Carroll, W.M. (1999). Using short questions to develop and assess reasoning. In L.V. Stiff & F.R. Curcio (Eds.). Developing mathematical reasoning in grades K-12 (pp. 247-255). Reston, VA: National Council of Teachers of Mathematics.

Cooper, B., & Dunne, M. (1998). Anyone for tennis? Social class differences in children's responses to national curriculum mathematics testing. The Sociological Review, 41(1), 115-148.

Floriano, V. (2012) Open-ended tasks in the promotion of classroom communication in mathematics. International Electronic Journal of Elementary Education, 4(2), 287-300.

Kilpatrick, J., Swafford, J., & Findell, B. (2001).  Adding it Up: Helping children learn mathematics. Washington, DC: National Academy Press.

Kabiri, M., Smith, L. N. (2003). Turning traditional problems into open-ended problems. Mathematics Teaching in the Middle School, 9(3), 186- 192.

Lewis, C. C. (1995). Educating hearts and minds: Reflections on Japanese preschool and elementary education.  Cambridge: Cambridge University Press.

Limjap, A. A. (2001). Issues on Problem Solving: Drawing Implications for a Techno-Mathematics Curriculum at the Collegiate Level.

Maitree, I. (2006). Open-ended approach and teachers education, center for research in mathematics education faculty of education. Tsukuba Journal of Educational Study in Mathematics, 25, 169-177.

Munroe L. (2015). Observations of Classroom Practice. Using the Open Approach to Teach Mathematics in a Grade Six Class in Japan. Paper presented at EARCOME 7, Philippines.

National Council of Teachers of Mathematics NCTM (1997). Multiple solutions to problems in mathematics teaching: Do teachers really value them? Principles and standards for school mathematics.

Nohda, N. (2000). A Study of "Open-Approach" method in School Mathematics Teaching. Paper presented at the 10th ICME, Makuhari, Japan.

Ontario Ministry of Education (2011). Capacity building series provoking student thinking/deepening conceptual understanding in the mathematics classroom. Eight tips for asking effective questions.

Ontario Ministry of Education. (2006). A guide to effective instruction in mathematics, Kindergarten to Grade 6. 2: Problem solving and communication. Toronto: Queen's Printer.

Phonapichat, P., Wongwanich, S., & Sujiva, S. (2014). An analysis of elementary school students’ difficulties in mathematical problem solving. Procedia-Social and Behavioral Sciences, 116, 3169-3174.

Radley, K. M. (2007). Open-ended approach to teaching and learning of high school mathematics. Vaal University of Technology, South Africa.

Sekiguchi, Y. (2006). Development of mathematical norms in an eight-grade Japanese classroom. The learners’ perspective study. In: D. Clarke, C. Keitel & Y.Shimizu (Eds.), Mathematics classroom in twelve countries: The Insiders’ perspective (pp. 289-306). Dordrecht: Sense Publishers

Sekiguchi, Y. (2002). Mathematical proof, argumentation, and classroom communication: from a cultural perspective. Tsukuba Journal of Educational Study in Mathematics, 21, 11-20.

Shimada, S. (ed.) 1977. Open-end approach in arithmetic and mathematics - A new Proposal toward teaching improvement. Tokyo: Mizuumishobo. [in Japanese]

Stevenson, H., & Stigler, J. W. (1994). Learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. New York: Simon & Schuster Inc.