Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students

Aihui Peng; Li Cao; Bo Yu

doi:10.29333/ejmste/9130

Full Text (PDF)

Aihui Peng ¹ ^* , Li Cao ², Bo Yu ¹

More Detail

¹ Southwest University, CHINA² University of West Georgia, USA^* Corresponding Author

Abstract

The present study took a reciprocal learning approach to examine Canadian and Chinese elementary school students’ (N=40) mathematics problem posing and problem solving. Data included student performance, Skype meeting videos, meeting notes, and interviews transcripts through direct and indirect interactions between a pair of Canadian and Chinese sister schools. Qualitative and quantitative analyses show that the Chinese students and the Canadian students differed in the type of problems they posed to their counterparts, the performance of solving the problems posed by the counterparts, the strategies used to solve the problems, and the behavioral approach adopted to solve the problems. Possible sources of the differences and practical implications for mathematical teaching are discussed. The study proffered suggestions on what the Canadian and the Chinese can learn educationally from each other.

Keywords

cross cultural study
problem solving
problem posing
reciprocal learning

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 16, Issue 12, December 2020, Article No: em1913

https://doi.org/10.29333/ejmste/9130

Publication date: 03 Nov 2020

Article Views: 3028

Article Downloads: 1976

Open Access References How to cite this article

References

Bragg, L. A. (2012a). The effect of mathematical games on on-task behaviours in the primary classroom. Mathematics Education Research Journal, 24(4), 385-401. https://doi.org/10.1007/s13394-012-0045-4.
Bragg, L. A. (2012b). Testing the effectiveness of mathematical games as a pedagogical tool for children’s learning. International Journal of Science and Mathematics Education, 10(6), 1445-1467. https://doi.org/10.1007/s10763-012-9349-9
Cai, J. (2000). Mathematical thinking involved in U.S. and Chinese students’ solving process-constrained and process-open problems. Mathematical Thinking and Learning, 2, 309-340. https://doi.org/10.1207/S15327833MTL0204_4
Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving? Exploring the impact of early algebra learning and teachers’ beliefs. Journal of Mathematical Behavior, 23, 135-167. https://doi.org/10.1016/j.jmathb.2004.03.004
Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21, 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
Cai, J., & Hwang, S. (2019 in press). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research. https://doi.org/10.1016/j.ijer.2019.01.001
Cai, J., & Silver, E. A. (1995). Solution processes and interpretations of solutions in solving a division-with-remainder story problem: Do Chinese and U.S. students have similar difficulties? Journal for Research in Mathematics Education, 26(5), 491-497. https://doi.org/10.5951/jresematheduc.26.5.0491
Cai, J., Mok, I. A.C., Reddy, R., & Stacey, K. (2016). International comparative studies in mathematics: Lessons for improving students’ learning. New York: Springer. https://doi.org/10.1007/978-3-319-42414-9_1
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., &Hieber, J. (2018). Building and structuring knowledge that could actually improve instructional practice. Journal for Research in Mathematics Education, 49(3), 238-246. https://doi.org/10.5951/jresematheduc.49.3.0238
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57-69. https://doi.org/10.1007/s10649-012-9429-3
Cody, K. J., Rule, A. C., & Forsyth, B. R. (2015). Mathematical game creation and play assists students in practicing newly-learned challenging concepts. Creative Education, 6(14), 1484. https://doi.org/10.4236/ce.2015.614149
Connelly, F. M., & Xu, S. (2019). Reciprocal learning in the partnership project: Fromknowing to doing in comparative research models. Teachers and Teaching: Theory and Practice, 25(6), 1-20. https://doi.org/10.1080/13540602.2019.1601077
Corbin, J. M., & Strauss, A. (2015). Basics of qualitative research: Techniques and procedures for developing grounded theory (4^th Ed.). Los Angeles, California: SAGE Publications Inc.
Creswell, J. W. (2014). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (5th Ed.). Upper Saddle River, New Jersey: Pearson Education, Inc.
Dewey, J. (1897). Speech to Parents of Dewey School. In K. Mayhew, & A. C. Edwards (Eds.). The Dewey School: The laboratory school of the University of Chicago 1896-1903. NY: Atherton, 1966.
Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24, 8-40. https://doi.org/10.5951/jresematheduc.24.1.0008
Ellerton, N. F. (1986). Children’s made-up mathematics problems - A new perspective on talented mathematicians. Educational Studies in Mathematics, 17, 261-271. https://doi.org/10.1007/BF00305073
Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83, 87-101. https://doi.org/10.1007/s10649-012-9449-z
Huang, R., &Cai, J. (2010). Implementing mathematical tasks in US and Chinese Classrooms. In Y. Shimizu, B. Kaur, R. Huang, & D. Clarke (Eds.), Mathematical tasks in classrooms around the world (pp. 145-164). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789460911507_009
Jiang, C., Hwang, S., & Cai, J. (2014). Chinese and Singaporean sixth-grade students’ strategies for solving problems about speed. Educational Studies in Mathematics, 87, 27-50. https://doi.org/10.1007/s10649-014-9559-x
Lambdin, D. V. (2003). Benefits of teaching through problem solving. In F. K. Lester (Ed.), Teaching mathematical through problem solving: Prekindergarten-Grade 6 (pp. 3-13). Reston, VA: National Council of Teachers of Mathematics.
Levasseur, K., & Cuoco, A. (2003) Mathematical habits of mind. In H. L. Schoen (Ed.), Teaching mathematics through problem solving: Grades 6-12 (pp. 27-37). Reston, VA: National Council of Teachers of Mathematics.
Ministry of Education. (2016). Mathematics curriculum standards for compulsory education in China. Beijing: The People’s Education Press.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
Ontario. (2005). The Ontario curriculum, grades 1-8: mathematics. Ontario: Toronto Publication.
Peng, A, Ezeife, A. N., & Yu, B. (2018). Reciprocal learning in mathematics education: An interactive study between two Canadian and Chinese elementary schools. Comparative and International Education / Éducation Comparée et Internationale, 47(1), Article 4.
Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press. https://doi.org/10.1515/9781400828678
Russo, J., & Russo, T. (2020). Transforming mathematical games into investigations. Australian Primary Mathematics Classroom, 25(2), 14-19. https://doi.org/10.29333/iejme/5843
Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. https://doi.org/10.5951/jresematheduc.27.5.0521
Singer, F. M, Ellerton, N. F, & Cai, J. (2015). Mathematical problem posing: from research to effective practice. New York, NY: Springer. https://doi.org/10.1007/978-1-4614-6258-3
Silver, E. A., Leung, S. S., & Cai, J. (1995). Generating multiple solutions for a problem: A comparison of the responses of U.S. and Japanese students. Educational Studies in Mathematics, 28(1), 35-54. https://doi.org/10.1007/BF01273855
Stanic, G. M. A., & Kilpatrick, J. (1988). Historical perspectives on problem solving in mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), Research agenda for mathematics education: The teaching and assessing of mathematical problem solving (pp. 1-22). Reston, VA: National Council of Teachers of Mathematics.
Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488. https://doi.org/10.3102/00028312033002455
Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: An analysis of high school students’ mathematical problem posing in China and USA. Educational Studies in Mathematics, 82(2), 201-221. https://doi.org/10.1007/s10649-012-9419-5
Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96, 101-118. https://doi.org/10.1007/s10649-017-9760-9
Xu, S., & Connelly, M. (2019). Partnership Grant Reciprocal learning in teacher education and school education between Canada and China. https://doi.org/10.1080/13540602.2019.1659766
Yeo, J. B. (2007). Mathematical tasks: clarification, classification and choice of suitable tasks for different types of learning and assessment. Report No. ME 2007-02, Nanyang Technological University, Singapore.

How to cite this article

APA

Peng, A., Cao, L., & Yu, B. (2020). Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students. Eurasia Journal of Mathematics, Science and Technology Education, 16(12), em1913. https://doi.org/10.29333/ejmste/9130

Vancouver

Peng A, Cao L, Yu B. Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students. EURASIA J Math Sci Tech Ed. 2020;16(12):em1913. https://doi.org/10.29333/ejmste/9130

AMA

Peng A, Cao L, Yu B. Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students. EURASIA J Math Sci Tech Ed. 2020;16(12), em1913. https://doi.org/10.29333/ejmste/9130

Chicago

Peng, Aihui, Li Cao, and Bo Yu. "Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students". Eurasia Journal of Mathematics, Science and Technology Education 2020 16 no. 12 (2020): em1913. https://doi.org/10.29333/ejmste/9130

Harvard

Peng, A., Cao, L., and Yu, B. (2020). Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students. Eurasia Journal of Mathematics, Science and Technology Education, 16(12), em1913. https://doi.org/10.29333/ejmste/9130

MLA

Peng, Aihui et al. "Reciprocal Learning in Mathematics Problem Posing and Problem Solving: An Interactive Study between Canadian and Chinese Elementary School Students". Eurasia Journal of Mathematics, Science and Technology Education, vol. 16, no. 12, 2020, em1913. https://doi.org/10.29333/ejmste/9130