Problem Solving in Mathematics Instruction and Teacher Professional Development pp 187-202 | Cite as

# Collaborative Learning to Improve Problem-Solving Skills: A Relation Affecting Through Attitude Toward Mathematics

## 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.

## Keywords

Attitude toward mathematics Collaborative learning Problem-solving skills## Notes

### 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.

## References

- Birman, B., Desimone, L., Garet, M., & Porter, A. (2000). Designing professional development that works.
*Educational Leadership, 57*(8), 28–33.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.CrossRefGoogle Scholar - Borko, H. (2004). Professional development and teacher learning: Mapping the terrain.
*Educational Researcher, 33*(8), 3–15.CrossRefGoogle Scholar - Bossert, S. T. (1988). Cooperative activities in the classroom.
*Review of Research in Education, 15*(1), 225–252.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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.xCrossRefGoogle Scholar - 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.CrossRefGoogle 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*(pp. 287–308). Cham, Switzerland: Springer International Publishing.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - Geary, D. C. (2008). An evolutionarily informed education science.
*Educational Psychologist, 43*(4), 179–195.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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/10.1177/0022219412436976CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - Mayer, R. E. (1992).
*Thinking, problem solving, cognition*. New York: WH Freeman, Times Books, Henry Holt & Co.Google Scholar - 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.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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.Google Scholar - 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.Google Scholar - OECD. (2015).
*Chile: Policy priorities for stronger and more equitable growth*,*OECD Series. Better Policies*. Paris: OECD Publishing.Google Scholar - Organisation for Economic Co-operation and Developmen. (2012).
*Development co-operation report 2012*. Paris: OECD Publishing. https://doi.org/10.1787/dcr-2012-enCrossRefGoogle 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/s10648-011-9179-2CrossRefGoogle Scholar - Polya, G. (1957).
*How to solve it*. Princeton, NJ: Princeton University Press.Google Scholar - Power, M., & Dalgleish, T. (2008).
*Cognition and emotion. From order to disorder*(2nd ed.). Hove, UK: Psychology Press.Google Scholar - 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.CrossRefGoogle Scholar - Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics.
*Educational Studies in Mathematics, 35*(1), 1–18.CrossRefGoogle Scholar - 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).Google Scholar - Schoenfeld, A. H. (1985). Metacognitive and epistemological issues in mathematical understanding.
*Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, 89*(4), 361–380.Google Scholar - Smith, M. S., & Stein, M. K. (2011).
*Five practices for orchestrating productive mathematics discussions*. Thousand Oaks, CA: Corwin Press.Google Scholar - 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.CrossRefGoogle Scholar - Webb, N. M. (2009). The teacher’s role in promoting collaborative dialogue in the classroom.
*British Journal of Educational Psychology, 79*(1), 1–28.CrossRefGoogle Scholar - Zan, R., & Di Martino, P. (2007). Attitude toward mathematics: Overcoming the positive/negative dichotomy.
*The Montana Mathematics Enthusiast, Monograph, 3*(2007), 157–168.Google Scholar