Abstract
Research on the effectiveness of collaborative learning approaches usually concentrates on individual performance as the primary indicator for a successful learning outcome. However, inconsistent success has been demonstrated for students’ outcomes after participating in a collaborative learning. In order to seek the reasons for this inconsistency, it is necessary to move beyond simple descriptions of the positive or negative impact of collaborative learning on students’ outcomes. This study aims to investigate whether students’ attitudes toward mathematics can affect their learning to solve non-routine mathematical problems through a collaborative learning approach. A group of 12 elementary teachers who participated in a professional development program for activating collaborative problem solving in mathematics classrooms voluntarily joined this study. The data were obtained from their 214 students (grades 3–8) at the beginning and the end of the school year. Results indicated that students with very positive or moderately positive levels of attitude performed better in comparison with students having negative attitudes toward mathematics, in all four stages of Polya’s problem-solving model, which includes understanding the problem, devising a plan, carrying out the plan, and looking back. Furthermore, students with different degrees of positive and negative attitudes toward mathematics showed meaningful differences in choosing the strategies and being aware of evaluating their solutions. The influence of attitude on learning is then a factor to be taken into account by educators and policymakers for considering appropriate strategies in order to improve the effectiveness of collaborative learning.
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
Notes
- 1.
Spanish acronym for Activando la Resolución de Problemas en las Aulas (Activating Problem Solving in Classrooms).
References
Birman, B., Desimone, L., Garet, M., & Porter, A. (2000). Designing professional development that works. Educational Leadership, 57(8), 28–33.
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.
Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15.
Bossert, S. T. (1988). Cooperative activities in the classroom. Review of Research in Education, 15(1), 225–252.
Davidson, N., & Kroll, D. L. (1991). An overview of research on cooperative learning related to mathematics. Journal for Research in Mathematics Education, 22(5), 362–365.
De Corte, E. (2004). Mainstreams and perspectives in research on learning (mathematics) from instruction. Applied Psychology, 53, 279–310. https://doi.org/10.1111/j.1464-0597.2004.00172.x
Fawcett, L. M., & Garton, A. F. (2005). The effect of peer collaboration on children’s problem-solving ability. British Journal of Educational Psychology, 75(2), 157–169.
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 (pp. 287–308). Cham, Switzerland: Springer International Publishing.
Felmer, P., Perdomo-Díaz, J., & Reyes, C. (2019). The ARPA experience in Chile: Problem solving for teachers’ professional development. In Mathematical problem solving (pp. 311–337). Cham, Switzerland: Springer.
Geary, D. C. (2008). An evolutionarily informed education science. Educational Psychologist, 43(4), 179–195.
Hannula, M. S. (2015). Emotions in problem solving. In Selected regular lectures from the 12th international congress on mathematical education (pp. 269–288). Cham, Switzerland: Springer.
Krawec, J. L. (2014). Problem representation and mathematical problem solving of students of varying math ability. Journal of Learning Disabilities, 47(2), 103–115. https://doi.org/10.1177/0022219412436976
Leroy, N., & Bressoux, P. (2016). Does amotivation matter more than motivation in predicting mathematics learning gains? A longitudinal study of sixth-grade students in France. Contemporary Educational Psychology, 44, 41–53.
Marrongelle, K., Sztajn, P., & Smith, M. (2013). Scaling up professional development in an era of common state standards. Journal of Teacher Education, 64(3), 202–211.
Mayer, R. E. (1992). Thinking, problem solving, cognition. New York: WH Freeman, Times Books, Henry Holt & Co.
Mevarech, Z. R. (1999). Effects of metacognitive training embedded in cooperative settings on mathematical problem solving. The Journal of Educational Research, 92(4), 195–205.
MINEDUC. (2012). Bases Curriculares Matemática; Ficha Bases Curriculares 2012. Ministry of Education Republic of Chile: Ministerio de Educación. Retrieved 2018 from http://www.curriculumenlineamineduc.cl/605/w3-article-21321.html
Naizer, G. L., Bell, G. L., West, K., & Chambers, S. (2003). Inquiry science professional development with a science summer camp for immediate application. The Journal of Elementary Science Education, 15(2), 31–37.
NCTM. (1980). An agenda for action: Recommendations for school mathematics. Retrieved, 2018, from http://www.nctm.org/standards/content.aspx?id=17279
NCTM. (2000). In V. A. Reston (Ed.), Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
O’Donnell, A. M. (2006). The role of peers and group learning. In P. Alexander & P. Winne (Eds.), Handbook of educational psychology (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.
OECD. (2015). Chile: Policy priorities for stronger and more equitable growth, OECD Series. Better Policies. Paris: OECD Publishing.
Organisation for Economic Co-operation and Developmen. (2012). Development co-operation report 2012. Paris: OECD Publishing. https://doi.org/10.1787/dcr-2012-en
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
Polya, G. (1957). How to solve it. Princeton, NJ: Princeton University Press.
Power, M., & Dalgleish, T. (2008). Cognition and emotion. From order to disorder (2nd ed.). Hove, UK: Psychology Press.
Retnowati, E., Ayres, P., & Sweller, J. (2017). Can collaborative learning improve the effectiveness of worked examples in learning mathematics? Journal of Educational Psychology, 109(5), 666–678.
Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics. Educational Studies in Mathematics, 35(1), 1–18.
Saadati, F., & Cerda, M. (2019). Exploring strategies used to solve a non-routine problem by Chilean students; an example of “sharing chocolates”. Proceedings of the 11th congress of the European Society for Research in Mathematics Education. Utrecht, The Netherlands (in press).
Schoenfeld, A. H. (1985). Metacognitive and epistemological issues in mathematical understanding. Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, 89(4), 361–380.
Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Thousand Oaks, CA: Corwin Press.
Webb, N. (1975). An exploration of mathematical problem-solving processes, ERIC. http://files.eric.ed.gov/fulltext/ED106148.pdf
Webb, N. L. (1979). Processes, conceptual knowledge, and mathematical problem-solving ability. Journal for Research in Mathematics Education, 10(2), 83–93.
Webb, N. M. (2009). The teacher’s role in promoting collaborative dialogue in the classroom. British Journal of Educational Psychology, 79(1), 1–28.
Zan, R., & Di Martino, P. (2007). Attitude toward mathematics: Overcoming the positive/negative dichotomy. The Montana Mathematics Enthusiast, Monograph, 3(2007), 157–168.
Acknowledgment
Funding from FONDEF ID14I20338 and PIA-CONICYT Basal Funds for Centers of Excellence Project FB0003 is gratefully acknowledged. FS is grateful to the support of CONICYT/Fondecyt Postdoctoral Project 3170673.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Saadati, F., Reyes, C. (2019). Collaborative Learning to Improve Problem-Solving Skills: A Relation Affecting Through Attitude Toward Mathematics. In: Felmer, P., Liljedahl, P., Koichu, B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-29215-7_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29214-0
Online ISBN: 978-3-030-29215-7
eBook Packages: EducationEducation (R0)