Skip to main content
SpringerLink
Log in

Assessing impact of a Teacher professional development program on student problem-solving performance

  • Original Paper
  • Published:
ZDM – Mathematics Education Aims and scope Submit manuscript

Abstract

In this paper we report on the impact of a year-long teacher professional development (PD) workshop on student problem-solving skills. The PD workshop was held in Chile and promoted the use of collaborative problem-solving activities in the classroom, through monthly sessions during the school year. Participant teachers met with a monitor to solve a new problem collaboratively, plan a problem-solving activity for their next lesson, and reflect on their activities from their previous lesson. The study documents the performance of two groups of students when solving non-routine mathematics problems in two similar and non-equal tests consisting of three problems each, before and after the year of application of the workshop. The first group of students was the experimental group with collaborative problem-solving activities, as proposed in the PD workshop. The second group was the control group, composed of students whose teachers followed traditional teaching. In the first part of the paper we present the results of pre- and post-tests in which the students in the experimental group improved their problem-solving performance in a significant way compared with the control group. In the second part, we present a sample of representation strategy used by successful students in both groups and we discuss, in general, student strategies in solving test problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. ARPA is the Spanish acronym for Activating PS in the Classrooms.

  2. Names of students used here and thereafter are pseudonyms.

References

  • Alibali, M. W., Phillips, K. M., & Fischer, A. D. (2009). Learning new problem-solving strategies leads to changes in problem representation. Cognitive Development, 24(2), 89–101.

    Article  Google Scholar 

  • Blumenfeld, P. C., Marx, R. W., Soloway, E., & Krajcik, J. (1996). Learning with peers: From small group cooperation to collaborative communities. Educational Researcher, 25(8), 37–39.

    Article  Google Scholar 

  • Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15.

    Article  Google Scholar 

  • Borko, H., Jacobs, J., & Koellner, K. (2010). Contemporary approaches to teacher professional development. In P. Peterson, E. Baker, & B. McGaw (Eds.), International encyclopedia of education (Vol. 7, pp. 548–556). Oxford: Elsevier.

    Chapter  Google Scholar 

  • Cai, J. (2000). Understanding and representing the arithmetic averaging algorithm: An analysis and comparison of US and Chinese students’ responses. International Journal of Mathematical Education in Science and Technology, 31(6), 839–855.

    Article  Google Scholar 

  • Cai, J. (2002). Assessing and understanding US and Chinese students’ mathematical thinking. ZentralblattfürDidaktik der Mathematik, 34(6), 278–290.

    Google Scholar 

  • Cai, J., & Cifarelli, V. (2005). Exploring mathematical exploration: How two college students formulated and solved their own mathematical problems. Focus on Learning Problems in Mathematics, 27(3), 43.

    Google Scholar 

  • Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401–421.

    Article  Google Scholar 

  • Chandia, E., Rojas, D., Rojas, F., & Howard, S. (2016). Creencias de formadores de profesores de matemáticasobreresolución de problemas (Mathematics teacher educators’ beliefs on problem solving). Bolema, 30(55), 605–624.

    Article  Google Scholar 

  • Dahl, H. (2019). “He’s so fast at drawing”—Children’s use of drawings as a tool to solve word problems in multiplication and division. In Eleventh Congress of the European Society for Research in Mathematics Education (Vol. 3, pp. 4475–4482. Freudenthal Group, Freudenthal Institute: ERME.

  • Dahl, H., Klemp, T., & Nilssen, V. (2018). Collaborative talk in mathematics–contrasting examples from third graders. Education 3–13, 46(5), 599–611.

  • Darling-Hammond, L., Hyler, M. E., & Gardner, M. (2017). Effective teacher professional development. Palo Alto, CA: Learning Policy Institute.

    Google Scholar 

  • Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181–199.

    Article  Google Scholar 

  • Desimone, L. M., Porter, A. C., Garet, M. S., Yoon, K. S., & Birman, B. F. (2002). Effects of a professional development on teachers’ instruction: Results from a three-year longitudinal study. Educational Evaluation and Policy Analysis, 24(2), 81–112.

    Article  Google Scholar 

  • Duijzer, C., den Heuvel-Panhuizen, V., Veldhuis, M., & Doorman, M. (2019). Moving towards understanding graphical representations of motion. In Eleventh Congress of the European Society for Research in Mathematics Education (Vol. 3, pp. 4491–4497). Freudenthal Group, Freudenthal Institute: ERME.

  • Elia, I., den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM, 41(5), 605.

    Article  Google Scholar 

  • Fawcett, L., & Garton, A. (2005). The effect of peer collaboration on children’s problem-solving ability. British Journal of Educational Psychology, 75(2), 157–169.

    Article  Google Scholar 

  • Felmer, P., & Perdomo-Díaz, J. (2016). Novice Chilean secondary mathematics teachers as problem solvers. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems, Research in Mathematics Education Series (pp. 287–308). Cham: Springer.

    Chapter  Google Scholar 

  • Felmer, P., Perdomo-Díaz, J., & Reyes, C. (2019). The ARPA experience in Chile: Problem solving for teachers’ professional development. In Liljedahl, P., and Santos-Trigo, M. (Eds.) Mathematical problem solving. ICME-13 Monographs (pp. 311–337). Springer, Cham.

  • Francisco, J. M. (2013). Learning in collaborative settings: Students building on each other’s ideas to promote their mathematical understanding. Educational Studies in Mathematics, 82(3), 417–438.

    Article  Google Scholar 

  • Gick, M. L. (1986). Problem-solving strategies. Educational Psychologist, 21(1–2), 99–120.

    Article  Google Scholar 

  • Heinze, A., Star, J., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM, 41, 535–540.

    Article  Google Scholar 

  • İmre, S., & Akkoç, H. (2012). Investigating the development of prospective mathematics teachers’ pedagogical content knowledge of generalising number patterns through school practicum. Journal of Mathematics Teacher Education, 15(3), 207–226.

    Article  Google Scholar 

  • Jacob, R., Hill, H., & Corey, D. (2017). The impact of a professional development program on teachers’ mathematical knowledge for teaching, instruction, and student achievement. Journal of Research on Educational Effectiveness, 10(2), 379–407.

    Article  Google Scholar 

  • Liljedahl, P. (2014). The affordances of using visually random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 127–144). New York, NY: Springer.

    Google Scholar 

  • MINEDUC [Ministry of Education Republic of Chile] (2012). Bases Curriculares Matemática; Ficha Bases Curriculares 2012. http://www.curriculumenlineamineduc.cl/605/w3-article-21321.html.

  • National Agency of Quality of Education [Agencia de Calidad de la Educación] (2018). SIMCE. https://www.agenciaeducacion.cl/evaluaciones/que-es-el-simce.

  • National Research Council. (2011). Successful K-12 STEM education: Identifying effective approaches in science, technology, engineering, and mathematics. National Academies Press.

  • Nistal, A., Van Dooren, W., Clarebout, G., Elen, J., & Verschaffel, L. (2009). Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: a critical review. ZDM, 41(5), 627–636.

    Article  Google Scholar 

  • OECD (2016). Low-performing students: Why they fall behind and how to help them succeed. PISA, OECD Publishing, Paris. doi: https://doi.org/10.1787/9789264250246-en.

  • OECD. (2017). PISA 2015 Results (Volume V): Collaborative problem solving. PISA: OECD Publishing, Paris.

    Book  Google Scholar 

  • Paas, F., & Sweller, J. (2012). An evolutionary upgrade of cognitive load theory: Using the human motor system and collaboration to support the learning of complex cognitive tasks. Educational Psychology Review, 24(1), 27–45. https://doi.org/10.1007/s10648-011-9179-2.

    Article  Google Scholar 

  • Pijls, M., Dekker, R., & Van Hout-Wolters, B. (2007). Reconstruction of a collaborative mathematical learning process. Educational Studies in mathematics, 65(3), 309–329.

    Article  Google Scholar 

  • Polotskaia, E., Savard, A., & Freiman, V. (2016). Investigating a case of hidden misinterpretations of an additive word problem: structural substitution. European Journal of Psychology of Education, 31(2), 135–153.

    Article  Google Scholar 

  • Polya, G. (1957). How to solve it. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Radovic, D., & Preiss, D. (2010). Discourse patterns observed in middle-school level mathematics classes in Chile. Psykhe, 19, 65–79.

    Article  Google Scholar 

  • Reynolds, D., & Muijs, D. (1999). The effective teaching of mathematics: a review of research. School Leadership & Management, 19(3), 273–288.

    Article  Google Scholar 

  • Saadati, F., & Reyes, C. (2019). Collaborative learning to improve problem-solving skills: A relation affecting through attitude toward mathematics. In Felmer, P., Liljedahl, P., and Koichu, B. (Eds.) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education Series (pp. 187–202). Springer, Cham.

  • Schoenfeld, A. H. (1982). Measures of problem-solving performance and of problem-solving instruction. Journal for Research in Mathematics Education, 31–49.

  • Sofroniou, A., & Poutos, K. (2016). Investigating the effectiveness of group work in mathematics. Education Sciences, 6(3), 30.

    Article  Google Scholar 

  • SoucyMcCrone, S. (2005). The development of mathematical discussions: an investigation in a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.

    Article  Google Scholar 

  • Stein, M., Engle, R., Smith, M., & Hughes, E. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.

    Article  Google Scholar 

  • Suydam, M. (1980). Untangling clues from research on problem solving. Problem solving in school mathematics, 34–50.

  • Swan, M. (2006). Collaborative learning in mathematics: a challenge to our beliefs and practices. Leicester: National Institute of Adult Continuing Education.

    Google Scholar 

  • Tambunan, H. (2019). The effectiveness of the problem-solving strategy and the scientific approach to students’ mathematical capabilities in high order thinking skills. International Electronic Journal of Mathematics Education, 14(2), 293–302.

    Article  Google Scholar 

  • TNTP. (2015). The mirage: Confronting the hard truth about our quest for teacher development. Brooklyn, NY: TNTP.

    Google Scholar 

  • Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379–402.

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referees for their useful comments and suggestions, which improved the paper considerably. Funding from PIA-CONICYT Basal Funds for Centers of Excellence Project FB0003 and Grant PAI AFB-170001 is gratefully acknowledged. FS is also grateful for the support of CONICYT/Fondecyt Postdoctoral Project 3170673.

Author information

Authors and Affiliations

  1. Centro de Investigación Avanzada en Educación, Universidad de Chile, Santiago, Chile

    Farzaneh Saadati & Patricio Felmer

  2. Center for Mathematical Modeling, Universidad de Chile, Santiago, Chile

    Patricio Felmer

Authors
  1. Farzaneh Saadati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patricio Felmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Patricio Felmer.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saadati, F., Felmer, P. Assessing impact of a Teacher professional development program on student problem-solving performance. ZDM Mathematics Education 53, 799–816 (2021). https://doi.org/10.1007/s11858-020-01214-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-020-01214-1

Keywords

Search

Navigation