Abstract
Details are presented of a study in which problem posing was an integral component of a mathematical modelling class for preservice and practicing middle-school teachers. One of the activities involved a project in which students individually planned and drafted mathematical modelling problems. Students then shared their draft problems with their peers before developing and presenting final versions of their problems to the class. Their personal reflections on the project formed an important part of the activity. Results are discussed in terms of an Active Learning Framework, and characteristics of a pedagogy for problem posing are proposed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ball, D. L., Bass, H., Lewis, J., Sleep, L., Suzuka, K., Babson, A., …, Zopf, D. (2008, April). Designing and using problems to teach mathematical knowledge for teaching. Paper presented at the National Council of Teachers of Mathematics Research Pre-session, Salt Lake City, UT.
Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Philadelphia, PA: Franklin Institute Press.
Brown, S. I., & Walter, M. I. (1993). Problem posing: Reflections and applications. Hillsdale, NJ: Lawrence Erlbaum.
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garbern, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57–69.
Clements, M. A., & Ellerton, N. F. (2006). Historical perspectives on mathematics elegance: To what extent is mathematical beauty in the eye of the beholder? In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures, and learning spaces (pp. 147–154). Adelaide, Australia: Mathematics Education Research Group of Australasia.
Del Campo, G., & Clements, M. A. (1987). A manual for the professional development of teachers of beginning mathematicians. Melbourne, Australia: Association of Independent Schools of Victoria, and the Catholic Education Office of Victoria.
Ellerton, N. F. (1986). Children’s made-up mathematics problems: A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261–271.
Ellerton, N. F. (2013). Engaging preservice middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87–101.
English, L. (1997). Promoting a problem-posing classroom. Teaching Children Mathematics, 4(3), 172–179.
Freire, P. (1970). Pedagogy of the oppressed. New York, NY: Continuum Press.
Lin, P.-J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning. In M. J. Hoines (Ed.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 257–264). Bergen, Norway: PME.
Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(5), 584–635.
National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Silver, E. A., & Burkett, M. L. (1994, April). The posing of division problems by preservice elementary school teachers: Conceptual knowledge and contextual connections. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA.
Staebler-Wiseman, H. A. (2011). Problem posing as a pedagogical strategy: A teacher’s perspective (PhD dissertation). Illinois State University, Normal, IL.
Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Melbourne, Australia: Mathematics Education Research Group of Australasia.
Tarr, J. E., Grouws, D. A., Chávez, Ó., & Soria, M. (2013). The effects of content organization and curriculum implementation on students’ mathematics learning in second-year high school courses. Journal for Research in Mathematics Education, 44(4), 683–729.
Victorian Curriculum and Assessment Authority. (2008). Victorian essential learning standards. Melbourne, Australia: Author.
Westbury, I. (1980). Change and stability in the curriculum: An overview of the questions. In H. G. Steiner (Ed.), Comparative studies of mathematics curricula: Change and stability 1960–1980 (pp. 12–36). Bielefeld, Germany: Institut für Didaktik der Mathematik-Universität Bielefeld.
Wilhelm, A. G. (2014). Mathematics teachers’ enactment of cognitively demanding tasks: Investigating links to teachers’ knowledge and conceptions. Journal for Research in Mathematics Education, 45(5), 636–674.
Acknowledgment
The author gratefully acknowledges the willing participation of all students in this study.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendices
Appendix AProject Problems Created by Undergraduate Students
Six project problems created by undergraduate students have been presented in Figures 25.A1 through 25.A6. As part of each figure, quotations from the reflections of the student who created the problem have been given. These quotations are listed under five headings: Inspiration for Problem, Challenges in Creating Problem, Group Feedback, Relevance of Creating Problem to Own Learning, and Additional Comments by Student.
Appendix BProject Problems Created by Practicing Teachers
Three project problems created by practicing teachers have been presented in Figures 25.B1 through 25.B3. As part of each figure, quotations from the reflections of the student who created the problem have been given. These quotations are listed under five headings: Inspiration for Problem, Challenges in Creating Problem, Group Feedback, Relevance of Creating Problem to Own Learning, and Additional Comments by Student.
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ellerton, N.F. (2015). Problem Posing as an Integral Component of the Mathematics Curriculum: A Study with Prospective and Practicing Middle-School Teachers. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_25
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6258-3_25
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6257-6
Online ISBN: 978-1-4614-6258-3
eBook Packages: Humanities, Social Sciences and LawEducation (R0)