# A Novice Teacher Researcher’s Action Research Project: Posing Problems to Promote Concepts of Graphs in Calculus

**Abstract views:**732 /

**PDF downloads:**30

## DOI:

https://doi.org/10.51724/arise.42## Keywords:

action research, problem posing, novice teacher, calculus, graphical representation, graphing competence## Abstract

A novice mathematics teacher researcher (TR) conducted an “interactive action research” (AR) to determine what problems would be most beneficial to teach her students about creating graphs based on a function’s attributes. After a number of trials that included adjusting her goals, the TR successfully designed problems appropriate for her goals. This paper describes the problem-posing process the TR used to derive the problems, and which include the four steps described in the literature: i) plan the problem, ii) pose it, iii) solve it, and iv) organize and complete it (see Güveli, 2015) plus an additional overall step added by this author, v) develop awareness of common perceptions (and misconceptions) that students have with respect to graphing. The contribution of this study is twofold. The first is the theoretical model of a five-step AR process, which can be used to guide TRs when conducting a mathematics posing problem AR: mathematical objective, source of inspiration, concerns related to formulation, mathematical uncertainties, and decisions taken. The second is that it demonstrates how TR’s formative assessment of the student’s solutions can improve her problem-posing heuristics and guide her to adjust her didactic goal(s). In addition, this paper documents her professional development on two aspects: developments and transitions in her thinking, and her development in skills required for reaching a didactic or mathematical goal.

### Downloads

## References

Abramovich, S. (2015). Mathematical problem posing as a link between algorithmic thinking and conceptual knowledge. Teaching of Mathematics, 18(2), 45-60.

Briscoe, C., & Wells, E. (2002). Reforming primary science assessment practices: a case study of one teacher’s professional development through action research. Science Education 86, 417–435.

Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Philadelphia, PA: Franklin Institute Press.

Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., et al. (2019). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ problem posing and lesson design. International Journal of Educational Research. doi: 10.1016/j.ijer.2019.02.004

Cai, J., & Hwang, S. (2019). Learning to teach mathematics through problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research. doi: 10.1016/j.ijer.2019.01.001

Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA, 6(4), 135–146.

Chen, T., & Cai, J. (2019). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. International Journal of Educational Research. doi: 10.1016/j.ijer.2019.03.004

Chang, B. L., Cromley, J. G., & Tran, N. (2016). Coordinating multiple representations in a reform calculus textbook. International Journal of Science and Mathematics Education, 14(8), 1475-1497.

Cochran-Smith, M., & Lytle, S. L. (2009). Inquiry as stance: Practitioner research for the next generation. New York, NY: Teachers College Press.

Corbin, J., & Strauss, A. (2014). Basics of qualitative research: Techniques and procedures for developing grounded theory. Newbury Park, CA: Sage Publications.

David, E. J., Roh, K. H., & Sellers, M. E. (2019). Value-thinking and location-thinking: Two ways students visualize points and think about graphs. The Journal of Mathematical Behavior, 54, 100675.

Davis, J., Clayton, C., & Broome, J. (2018). Thinking like researchers: Action research and its impact on novice teachers’ thinking. Educational Action Research, 26(1), 59-74.

De Bock, D., Van Dooren, W., & Verschaffel, L. (2015). Students’ understanding of proportional, inverse proportional, and affine functions: Two studies on the role of external representations. International Journal of Science and Mathematics Education, 13(1), 47-69.

Dreyfus, T., & Eisenberg, T. (1986). On the aesthetics of mathematical thought. For the Learning of Mathematics, 6(1), 2-10.

Eisenberg, T., & Dreyfus, T. (1991). On the reluctance to visualize in mathematics. In W. Zimmermann, & S. Cunningham (Eds.) Visualization in teaching and learning mathematics (pp. 25-37). Washington, DC: Mathematical Association of America.

English, L. D. (2019). Teaching and learning through mathematical problem posing: Commentary. International Journal of Educational Research. doi:10.1016/j.ijer.2019.06.014

Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83, 87–101.

Ellerton, N. (2015). Problem posing as an integral part of the mathematics curriculum: A study with prospective and practicing middle-school teachers. In F. Singer, N. Ellerton, & J. Cai (Eds.), Problem posing in mathematics: From research to effective practice (pp. 513-546). New York, NY: Springer.

Gilbert, J. K., & Newberry, M. (2004). The Cams Hill Science Consortium: An inter-institutional collaborative action research project in science education. In: B. Ralle and I. Eilks (Eds.) Quality in practice-oriented research in science education (pp. 53-62). Aachen: Shaker.

Glazer, N. (2011). Challenges with graph interpretation: A review of the literature. Studies in science education, 47(2), 183-210.

‘Goldin, G. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Penkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59-72). Dordrecht: Kluwer.

Goodnough, K. (2010). The role of action research in transforming teacher identity: Modes of belonging and ecological perspectives. Educational Action Research, 18(2), 167-182.

Gray, C. (2013). Bridging the teacher/researcher divide: Master’s-level work in initial teacher education. European Journal of Teacher Education, 36(1), 24-38.

Güveli, E. (2015). Prospective elementary mathematics teachers’ problem posing skills about absolute value. Turkish Journal of Teacher Education, 4(1), 1-17.

Koichu, B. (2008). Theoretical framework for characterizing responses to multiple problem posing tasks. In R. Leikin, Levav-Waynberg & Appelbaum, M. (Eds.), Proceedings of the International Workshop on Multiple Solution Connecting Tasks, 45-52, Haifa, Israel.

Laudonia, I., Mamlok-Naaman, R., Abels, S., & Eilks, I. (2018). Action research in science education–An analytical review of the literature. Educational Action Research, 26(3), 480-495.

Lee, Y., Capraro, R. M., & Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. IEJME-Mathematics Education, 13(2), 75-90.

Lysaker, J., & Thompson, B. (2013). Teacher research as a practical tool for learning to teach. Language Arts, 90(3), 181-191.

Mamlok-Naaman, R., Rauch, F., Markic, S. & Fernandez, C. (2013). How to keep myself being a professional chemistry teacher. In: I. Eilks and A. Hofstein (Eds.) Teaching Chemistry – A studybook (pp. 269–297). Rotterdam: Sense.

Moore, K. C. (2016). Graphing as figurative and operative thought. In: C. Csíkos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th conference of the international groups for the psychology of mathematics education, Vol. 3, (pp. 323-330). Szeged, Hungary: PME.

Moore, K. C., & Thompson, P. W. (2015). Shape thinking and students’ graphing activity. In: T. Fukawa-Connelly, N. E. Infante, K. Keene, & M. Zandieh (Eds.), Proceedings of the 18th meeting of the MAA special interest group on research in undergraduate mathematics education, (pp. 782-789). Pittsburgh, PA: RUME.

Neidorf, T., Arora, A., Erberber, E., Tsokodayi, Y., & Mai T. (2020). Student misconceptions and errors in physics and mathematics: Exploring data from TIMSS and TIMSS Advanced. IEA Research for Education, vol. 9. Cham, Switzerland: Springer,

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Park, J. (2015). Is the derivative a function? If so, how do we teach it? Educational Studies in Mathematics, 89(2), 233-250.

Rosli, R., Capraro, M., Goldsby, D., Gonzalez y Gonzalez, E., Onwuegbuzie, A., & Capraro, R. (2015). Middle grade preservice teachers’ mathematical problem solving and problem posing. In F. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 333- 354). New York, NY: Springer.

Schoenfeld, A. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In Grows, D. A. (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York: Macmillan.

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19 – 28.

Snow-Gerono, J. L. (2005). Naming inquiry: PDS teachers’ perceptions of teacher research and living an inquiry stance toward teaching. Teacher Education Quarterly, 32(4), 79-95.

Souto-Manning, M. (2012) Teacher action research in teacher education. Childhood Education, 88(1), 54-56. http://dx.doi.org/10.1080/00094056.2012.643726.

Stern, T. 2014. “What is Good Action Research?” In: T. Stern, A. Townsend, F. Rauch, & A. Schuster (Eds.) Action research, innovation and change, (pp. 202–220). London: Routledge.

Tall, D. (2010). A sensible approach to the calculus. In: Plenary at the national and international meeting on the teaching of calculus. Puebla, Mexico.

Tichá, M., & Hošpesová, A. (2012). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143.

## Downloads

## Published

## How to Cite

*Action Research and Innovation in Science Education*,

*4*(1), 13–23. https://doi.org/10.51724/arise.42

## Issue

## Section

## License

Copyright (c) 2021 Tikva Ovadiya

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

Copyright © Authors