Implementation of Problem Solving in School: From Intended to Experienced
In: Implementation and Replication Studies in Mathematics EducationSearch for other papers by Boris Koichu in
Current site
Google Scholar
Search for other papers by Jason Cooper in
Current site
Google Scholar
Search for other papers by Mirela Widder in
Current site
Google Scholar
Abstract
The importance of mathematical problem solving has long been recognized, yet its implementation in classrooms remains a challenge. In this paper we put forth the notion of problem-solving implementation chain as a dynamic sequence of intended, planned, enacted and experienced activity, shaped by researchers, teachers and students, where the nature of the activity and its aims may change at the links of the chain. We propose this notion as an analytical framework for investigating implementation of problem-solving resources. We then illustrate this framework by a series of narratives from a project, in which the team of task-designers develops problem-solving resources aimed at reaching middle-school students via their teachers, who encounter these resources in professional development communities. We show how the problem-solving activity evolves along the implementation chain and then identify opportunities for mutual learning that emerge from tensions in perspectives on PS held by the different parties involved.
The impact sheet to this article can be accessed at
Purchase
Buy instant access (PDF download and unlimited online access):
Institutional Login
Log in with Open Athens, Shibboleth, or your institutional credentials
Personal login
Log in with your brill.com account
-
Aguilar, M. S., Kuzle, A., Wæge, K. & Misfeldt, M. (2019). Introduction to the papers of TWG23: Implementation of research findings in mathematics education. In U. T. Jankvist, M. Van den Heuvel-Panhuizen & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 4355–4362). Freudenthal Group & Freudenthal Institute, Utrecht University, Utrecht; ERME.
-
Akkerman, S. F. & Bakker, A. (2011). Boundary crossing and boundary objects. Review of Educational Research, 81(2), 132–169. https://doi.org/10.3102/0034654311404435.
-
Altrichter, H., Feldman, A., Posch, P. & Somekh, B. (2008). Teachers investigate their work: An introduction to action research across the professions (2nd edn.). Routledge, Abingdon.
-
Andžāns, A. & Johannesson, B. (2005). Dirichlet principle: Part I and II. Macibu gramata.
-
Arcavi, A. & Cooper, J. (2014). Summary tasks for central topics in the junior-high school curriculum (in Hebrew). Ministry of Education of Israel, Jerusalem. Available online at http://meyda.education.gov.il/files/Mazkirut_Pedagogit/matematika/osef_01.docx.
-
Brown, S. A., Pitvorec, K., Ditto, C. & Kelso, C. R. (2009). Reconceiving fidelity of implementation: An investigation of elementary whole-number lessons. Journal for Research in Mathematics Education, 40(4), 363–395. https://doi.org/10.5951/jresematheduc.40.4.0363.
-
Burkhardt, H. & Schoenfeld, A. (2021). Not just “implementation”: The synergy of research and practice in an engineering research approach to educational design and development. ZDM — Mathematics Education, 53(5), 991–1005. https://doi.org/10.1007/s11858-020-01208-z.
-
Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 19–36. https://doi.org/10.31129/lumat.v3i1.1049.
-
Cobb, P. & Jackson, K. (2021). An empirically grounded system of supports for improving the quality of mathematics teaching on a large scale. Implementation and Replication Studies in Mathematics Education, 1(1), 77–110. https://doi.org/10.1163/26670127-01010004.
-
Cooper, J. (2019). Mathematicians and teachers sharing perspectives on teaching whole number arithmetic: Boundary-crossing in professional development. ZDM — Mathematics Education, 51(1), 69–80. https://doi.org/10.1007/s11858-018-0995-4.
-
Cooper, J. & Koichu, B. (2022, February 2–February 5). Problem-solving implementation chain: From intended to experienced [Paper presentation]. 12th Congress of the European Society for Research in Mathematics Education, Bozen-Bolzano, Italy.
-
Cooper, J., Olsher, S. & Yerushalmy, M. (2020). Didactic metadata informing teachers’ selection of learning resources: boundary-crossing in professional development. Journal of Mathematics Teacher Education, 23(4), 363–384. https://doi.org/10.1007/s10857-019-09428-1.
-
Cuoco, A., Goldenberg, E. P. & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curriculum. The Journal of Mathematical Behavior, 15(4), 375–402. https://doi.org/10.1016/S0732-3123(96)90023-1.
-
Drijvers, P. & Trouche, L. (2008). From artifacts to instruments: A theoretical framework behind the orchestra metaphor. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Cases and perspectives (Vol. 2, pp. 363–392). NCTM, Reston, VA; Information Age, Charlotte, NC.
-
Felmer, P., Liljedahl, P. & Koichu, B. (Eds.). (2019). Problem solving in mathematics instruction and teacher professional development. Springer, Berlin. https://doi.org/10.1007/978-3-030-29215-7.
-
Goldin, G. A., Epstein, Y. M., Schorr, R. Y. & Warner, L. B. (2011). Beliefs and engagement structures: Behind the affective dimension of mathematical learning. ZDM — Mathematics Education, 43(4), 547–560. https://doi.org/10.1007/s11858-011-0348-z.
-
Gueudet, G. & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218. https://doi.org/10.1007/s10649-008-9159-8.
-
Jaworski, B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9(2), 187–211. https://doi.org/10.1007/s10857-005-1223-z.
-
Koichu, B. (2018). Mathematical problem solving in choice-affluent environments. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt & B. Xu (Eds.), Invited lectures from the 13th International Congress on Mathematics Education (pp. 307–324). Springer, Berlin. https://doi.org/10.1007/978-3-319-72170-5_18.
-
Koichu, B. (in press). The art of being specific while theorizing for and from practice of mathematics teachers’ collaboration. In H. Borko & D. Potari (Eds.), Teachers of mathematics working and learning in collaborative groups. An ICMI Study 25. Springer, Berlin.
-
Koichu, B. & Keller, N. (2019). Creating and sustaining online problem solving forums: Two perspectives. In P. Liljedahl & L. M. Santos-Trigo (Eds.), Mathematical problem solving: Current themes, trends, and research (pp. 263–287). Springer. https://doi.org/10.1007/978-3-030-10472-6_12.
-
Koichu, B., Berman, A. & Moore, M. (2007). Heuristic literacy development and its relation to mathematical achievements of middle school students. Instructional Science, 35(2), 99–139. https://doi.org/10.1007/s11251-006-9004-3.
-
Koichu, B., Aguilar, M. S. & Misfeldt, M. (2021). Implementation-related research in mathematics education: the search for identity. ZDM — Mathematics Education, 53(5), 975–989. https://doi.org/10.1007/s11858-021-01302-w.
-
Krainer, K. (2021). Implementation as interaction of research, practice, and policy. Considerations from the Austrian initiative IMST. ZDM — Mathematics Education, 53(5), 1175–1187. https://doi.org/10.1007/s11858-021-01300-y.
-
Krainer, K., Zehetmeier, S., Hanfstingl, B., Rauch, F. & Tscheinig, T. (2019). Insights into scaling up a nationwide learning and teaching initiative on various levels. Educational Studies in Mathematics, 102(3), 395–415. https://doi.org/10.1007/s10649-018-9826-3.
-
Lester, F. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1–2), 245–278.
-
Lester, F. K. & Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. In P. Felmer, E. Pehkonen & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 117–135). Springer, Berlin. https://doi.org/10.1007/978-3-319-28023-3_8.
-
Liljedahl, P. & Cai, J. (2021). Empirical research on problem solving and problem posing: A look at the state of the art. ZDM — Mathematics Education, 53(4), 723–735. https://doi.org/10.1007/s11858-021-01291-w.
-
Mamona-Downs, J. & Downs, M. (2005). The identity of problem solving. The Journal of Mathematical Behavior, 24(3–4), 385–401. https://doi.org/10.1016/j.jmathb.2005.09.011.
-
Mason, J. (2016a). Part 1 reaction: Problem posing and solving today. In P. Felmer, E. Pehkonen & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 109–113). Springer, Berlin. https://doi.org/10.1007/978-3-319-28023-3_7.
-
Mason, J. (2016b). When is a problem …? “When” is actually the problem! In P. Felmer, E. Pehkonen & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 263–285). Springer, Berlin. https://doi.org/10.1007/978-3-319-28023-3_16.
-
National Council of Teachers of Mathematics. (2000). Principles and standards for teaching mathematics. NCTM, Reston, VA.
-
Niss, M. (2007). Reflections on the state of and trends in research on mathematics teaching and learning: From here to utopia. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 1293–1312). Information Age.
-
Organization for Economic Co-operation and Development. (2018). PISA 2022 mathematics framework (draft). Available online at https://pisa2022-maths.oecd.org/files/PISA%202022%20Mathematics%20Framework%20Draft.pdf.
-
Palatnik, A. & Koichu, B. (2019). Flashes of creativity. For the Learning of Mathematics, 39(2), 8–12.
-
Pólya, G. (1973). How to solve it. Princeton University Press, Princeton, NJ. (Original work published 1945).
-
Potari, D., Psycharis, G., Sakonidis, C. & Zachariades, T. (2019). Collaborative design of a reform-oriented mathematics curriculum: Contradictions and boundaries across teaching, research, and policy. Educational Studies in Mathematics, 102(3), 417–434. http://doi.org/10.1007/s10649-018-9834-3.
-
Prediger, S. (2020). Content-specific theory elements for explaining and enhancing teachers’ professional growth in collaborative groups. In H. Borko & Potari, D. (Eds.), Proceedings of the 25th ICMI Study “Teacher of mathematics working and learning in collaborative groups” (pp. 2–14). National and Kapodistrian University of Athens, Athens.
-
Pruner, M. & Liljedahl, P. (2021). Collaborative problem solving in a choice-affluent environment. ZDM — Mathematics Education, 53(4), 753–770. https://doi.org/10.1007/s11858-021-01232-7.
-
Robutti, O., Aldon, G., Cusi, A., Olsher, S., Panero, M., Cooper, J., Carante, P. & Prodromou, T. (2020). Boundary objects in mathematics education and their role across communities of teachers and researchers in interaction. In G. M. Lloyd & O. Chapman (Eds.), International handbook of mathematics teacher education: Participants in mathematics teacher education (Vol. 3, 2nd edn.) (pp. 211–240). Brill/Sense, Leiden. https://doi.org/10.1163/9789004419230_009.
-
Rowland, T. & Zazkis, R. (2013). Contingency in the mathematics classroom: Opportunities taken and opportunities missed. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 137–153. https://doi.org/10.1080/14926156.2013.784825.
-
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press, San Diego, CA.
-
Schoenfeld, A. H. (2011). How we think: A theory of goal-oriented decision making and its educational applications. Routledge, Abingdon.
-
Schoenfeld, A. H. (2013). Reflections on problem solving theory and practice. The Mathematics Enthusiast, 10(1–2), 9–34.
-
Schoenfeld, A. H. (2022). Why are learning and teaching mathematics so difficult? In M. Danesi (Ed.), Handbook of cognitive mathematics (pp. 1–35). Springer, Berlin. https://doi.org/10.1007/978-3-030-44982-7_10-1.
-
Schroeder, T. & Lester, F. (1989). Developing understanding in mathematics via problem solving. In P. Traffon & A. Shulte (Eds.), New directions for elementary school mathematics: 1989 yearbook (pp. 31–42). NCTM, Reston, VA.
-
Stein, M., Remillard, J. & Smith, M. (2007). How curriculum influences student learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Information Age, Charlotte, NC.
-
Stein, M. K., Engle, R. A., Smith, M. S. & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. https://doi.org/10.1080/10986060802229675.
-
Törner, G., Schoenfeld, A. H. & Reiss, K. M. (Eds.). (2008). Problem solving around the world: Summing up the state of the art [Special Issue]. ZDM — Mathematics Education, 39(5–6).
-
Tripp, S. D. & Bichelmeyer, B. (1990). Rapid prototyping: An alternative instructional design strategy. Educational Technology Research and Development, 38(1), 31–44. https://doi.org/10.1007/BF02298246.
-
Trouche, L., Gueudet, G. & Pepin, B. (2020). Documentational approach to didactics. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed., pp. 237–247). Springer, Berlin. https://doi.org/10.1007/978-3-319-77487-9_100011-1.
-
Vinner, S. (2014). The irrelevance of research mathematicians’ problem solving to school mathematics. In Koichu, B. (2014) Reflections on problem solving. In M. N. Fried & T. Dreyfus (Eds.), Mathematics & mathematics Education: Searching for common ground (pp. 113–135). Springer, Berlin. https://doi.org/10.1007/978-94-007-7473-5_8.
| All Time | Past Year | Past 30 Days | |
|---|---|---|---|
| Abstract Views | 992 | 398 | 81 |
| Full Text Views | 83 | 21 | 3 |
| PDF Views & Downloads | 186 | 51 | 8 |
Implementation of Problem Solving in School: From Intended to Experienced
In: Implementation and Replication Studies in Mathematics EducationSearch for other papers by Boris Koichu in
Current site
Google Scholar
PubMed
Search for other papers by Jason Cooper in
Current site
Google Scholar
PubMed
Search for other papers by Mirela Widder in
Current site
Google Scholar
PubMed
Abstract
The importance of mathematical problem solving has long been recognized, yet its implementation in classrooms remains a challenge. In this paper we put forth the notion of problem-solving implementation chain as a dynamic sequence of intended, planned, enacted and experienced activity, shaped by researchers, teachers and students, where the nature of the activity and its aims may change at the links of the chain. We propose this notion as an analytical framework for investigating implementation of problem-solving resources. We then illustrate this framework by a series of narratives from a project, in which the team of task-designers develops problem-solving resources aimed at reaching middle-school students via their teachers, who encounter these resources in professional development communities. We show how the problem-solving activity evolves along the implementation chain and then identify opportunities for mutual learning that emerge from tensions in perspectives on PS held by the different parties involved.
The impact sheet to this article can be accessed at
| All Time | Past Year | Past 30 Days | |
|---|---|---|---|
| Abstract Views | 992 | 398 | 81 |
| Full Text Views | 83 | 21 | 3 |
| PDF Views & Downloads | 186 | 51 | 8 |