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Chinese junior high school students’ mathematical problem-posing performance

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Abstract

The study of mathematical problem posing (MPP) from the perspective of a learning trajectory is a new and thriving research field. The latest Chinese Compulsory Mathematics Curriculum Standards stipulate the developmental requirements of students’ MPP ability at three different stages: Grades 1 − 3, Grades 4 − 6, and Grades 7 − 9. However, in this study, we found that there were irregular changes in MPP as the grade level advanced for junior middle school students in Grades 7 − 9. In addition, the results were not the same for different situations. Moreover, it was difficult for students to pose extended mathematical problems. The sample consisted of 904 Chinese students in seventh, eighth, and ninth grades. They each faced the same three tasks involving a real-life situation, a medicine situation, and a mathematics situation. The evaluation of students’ MPP ability was based on fluency, flexibility, and profundity evaluation indexes for the three tasks. How to scientifically and reasonably formulate the learning trajectory of MPP is an important research topic for the future.

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References

  • Bicer, A., Lee, Y., Perihan, C., et al. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-09995-8.

    Article  Google Scholar 

  • Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83, 37–55.

    Google Scholar 

  • Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Mathematical Notes, 35(1), 153.

    Google Scholar 

  • Cai, J. (2003). Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719–737.

    Google Scholar 

  • Cai, J. (Ed.). (2017). Compendium for research in mathematics education. Reston, VA: National Council of Teachers of Mathematics.

    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.

    Google Scholar 

  • Cai, J., & Silver, E. A. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521–539.

    Google Scholar 

  • Cai, J., & Yao, Y. (2019). Teaching through mathematical problem posing: Theoretical bases and practical strategies. The Journal of Mathematics Education, 4, 42–47.

    Google Scholar 

  • 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.

    Google Scholar 

  • Cai, J., Hwang, S., Jing, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered question. In F. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing. New York, NY: Springer.

    Google Scholar 

  • Confrey, J., Maloney, A. P., & Corley, A. K. (2014). Learning trajectories: A framework for connecting standards with curriculum. ZDM-Mathematics Education, 46(5), 719–733.

    Google Scholar 

  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243–270.

    Google Scholar 

  • Duncan, R. G., & Hmelo-Silver, C. E. (2009). Learning progressions: Aligning curriculum, instruction, and assessment. Journal of Research in Science Teaching, 46(6), 606–609.

    Google Scholar 

  • Ellerton, N. F. (1986). Children’s made-up mathematics problems—A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261–271.

    Google Scholar 

  • Empson, S. (2011). On the idea of learning trajectories: Promises and pitfalls. The Mathematics Enthusiast, 8(3), 571–596.

    Google Scholar 

  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183–217.

    Google Scholar 

  • Goodlad, J. J. (1979). Curriculum inquiry: The study of curriculum practice. NY: McGraw-Hill.

    Google Scholar 

  • Hashimotto, Y. (1987). Classroom practice of problem solving in Japanese elementary schools. In J. P. Becker & T. Miwa (Eds.), Proceeding of the US-Japan seminar on mathematical problem solving (pp. 94–119). Carbondale, IL: Southern Illinois University.

    Google Scholar 

  • Hu, D., Cai, J., & Nie, B. (2015). Mathematics question posing and curriculum evolution: Comparison between two editions of primary mathematics textbooks. Curriculum, Teaching Material and Method, 7, 75–79.

    Google Scholar 

  • Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the Billiard Task. Educational Studies in Mathematics, 83, 71–86.

    Google Scholar 

  • Kotsopoulos, D., & Cordy, M. (2009). Investigating imagination as a cognitive space for learning mathematics. Educational Studies in Mathematics, 70, 259–274.

    Google Scholar 

  • Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5–24.

    Google Scholar 

  • Li, H., & Zhang, W. (2019). Research on the development of pupils’ mathematical problem posing ability. The Journal of Mathematics Education, 28(5), 2–8.

    Google Scholar 

  • Maher, C. A., Goldin, G. A. & Davis, R. B. (1989). Proceedings of the eleventh annual meeting, North American chapter of the International Group for the Psychology of Mathematics Education. In Silver, E. A. & Mamona, J, Problem posing by middle school teachers (pp. 263–269). New Brunswick.

  • Merritt, J. D., Krajcik, J., & Shwartz, Y. (2008). Development of a learning progression for the particle model of matter. Cre8ing A Learning World: International Conference for the Learning Sciences. DBLP.

  • Ministry of Education of the People’s Republic of China. (2012). Chinese 2011 compulsory education mathematics curriculum standards. Beijing: Beijing Normal University Publishing Group.

    Google Scholar 

  • Moser, C. J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179–202.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • National Governors Association Center for Best Practices. (2010). Common core state standards for mathematics. Washington, DC: Author.

    Google Scholar 

  • National Research Council. (2007). Taking science to school: Learning and teaching science in grades K-8. In R. A. Duschl, H. A. Schweingtuber, & A. W. Shouse (Eds.), Committee on science learning, kindergarten through eighth grade. Washington DC: The National Academies Press.

    Google Scholar 

  • Roseman, J. E., Caldwell, A., Gogos, A., & Kurth, L. (2006). Mapping a coherent learning progression for the molecular basis of heredity. Presented at the National Association for Research in Science Teaching Annual Meeting.

  • Si, H., (2014). Developing and refining the developing progressions for mathematics problem posing in grades 10–11 (Unpublished doctoral dissertation). East China Normal University.

  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.

    Google Scholar 

  • Singer, F.M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7.

    Google Scholar 

  • Steffe, L. P., Cobb, P., & von Glasersfeld, E. (1988). Construction of arithmetical meanings and strategies. New York, NY: Springer.

    Google Scholar 

  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. Technology in Mathematics Education, 518–525.

  • Tichá, M., & Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143.

    Google Scholar 

  • Torrance, E. P. (1988). The nature of creativity as manifest in its testing. In R. J. Sternberg (Ed.), The nature of creativity: Contemporary psychological perspectives (p. 43–75). Cambridge University Press.

  • 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.

    Google Scholar 

  • Wu, Y., Deng, S., & Yang, J. (2017). Progress and implications of learning progression research in mathematics education. The Journal of Mathematics Education, 26(6), 40–46.

    Google Scholar 

  • Xia, X., & Wang, K. (2011). Investigation and analysis of mathematics questions proposed by the 5th graders of the Shui ethnic Group. Journal of Research on Education for Ethnic Minorities, 22(06), 21–26.

    Google Scholar 

  • Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’ creativity and mathematical problem posing abilities—Comparing Chinese and US students. In B. Sriraman & K. H. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5–28). AW Rotterdam: Sense Publisher.

    Google Scholar 

  • Zeng, X., Lv, C., & Wang, B. (2006). Actuality and countermeasure of ‘posing mathematical problem’ on junior high school student. The Journal of Mathematics Education, 15(3), 51–53.

    Google Scholar 

  • Zhang, Y. (2016). New idea of science curriculum design: Nature, elements and theoretical tracing of learning progressions. Curriculum, Teaching Material and Method, 36(6), 115–120.

    Google Scholar 

  • Zhang, D., & Wu, Z. (2017). An empirical study on cultivating pupils’ ability to pose problem——Taking primary school mathematics teaching as an example. Journal of the Chinese Society of Education, 5, 100–104.

    Google Scholar 

  • Zhou, F. (2014). The Investigation and analysis for mathematical problem posing ability of Junior high students (Unpublished Master’s dissertation). East China Normal University.

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Funding

This research was supported by Ministry of Education (Grant 19JA880009).

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Correspondence to Yufeng Guo.

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Guo, Y., Yan, J. & Men, T. Chinese junior high school students’ mathematical problem-posing performance. ZDM Mathematics Education 53, 905–917 (2021). https://doi.org/10.1007/s11858-021-01240-7

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