Enhancing the Development of Chinese Fifth-Graders’ Problem-Posing and Problem-Solving Abilities, Beliefs, and Attitudes: A Design Experiment

Part of the Research in Mathematics Education book series (RME)


The present study reports the design, implementation, and evaluation of a training program aimed at developing Chinese students’ problem-posing abilities, problem-solving abilities, and their beliefs about, and attitudes toward, mathematical problem posing and problem solving. In this study, a framework for teaching and assessing problem posing was developed. Results revealed that the training program had a significant positive effect on the originality of the problems posed by the students (but not on the appropriateness, complexity, and diversity of the problems posed), as well as on their problem-solving abilities and on their problem-posing and problem-solving beliefs and attitudes.


Problem posing Problem solving Mathematics education Chinese students 


  1. Bonotto, C., & Baroni, M. (2008). Using maths in a daily context: Experiences in Italian compulsory education. In H. W. Henn & S. Meier (Eds.), Planting mathematics. First Annual Publication of the Comenius-Network Developing Quality in Mathematics Education II—DQME II (pp. 19–47). Dortmund, Germany: TU Dortmund.Google Scholar
  2. Brown, S. I., & Walter, M. I. (1990). The art of problem posing. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  3. Brown, S. I., & Walter, M. I. (1993). Problem posing in mathematics education. In S. I. Brown & M. I. Walter (Eds.), Problem posing: Reflections and applications (pp. 16–27). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  4. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behaviour, 21, 401–421. doi: 10.1016/j.bbr.2011.03.031.CrossRefGoogle Scholar
  5. Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2005). The relationship between posing and solving division with remainder problems among Chinese elementary school children. Mediterranean Journal for Research in Mathematics Education, 4(2), 85–109.Google Scholar
  6. Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2007). The relationship between posing and solving arithmetic word problems among Chinese elementary school children. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 11(1), 1–31.Google Scholar
  7. Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2011). An investigation on Chinese teachers’ realistic problem posing and problem solving ability and beliefs. International Journal of Science and Mathematics Education, 9, 919–948. doi: 10.1007/s10763-010-9259-7.CrossRefGoogle Scholar
  8. Chen, L., Verschaffel, L., & Van Dooren, W. (2011). The relationship between posing and solving (realistic) mathematical problems in elementary school in China (Doctoral dissertation). Center for Instructional Psychology and Technology, Katholieke Universiteit Leuven, Leuven, Belgium.Google Scholar
  9. Chen, Z., & Ye, X. (2007). 数学课堂教学中学生问题提出能力培养的研究 [The research on developing students’ ability to put forward questions in math class] (Master’s thesis). Fujian Normal University, Fuzhou, China.Google Scholar
  10. Çildir, S., & Sezen, N. (2011). Skill levels of prospective physics teachers on problem posing. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Hacettepe University Journal of Education], 40, 105–116.Google Scholar
  11. Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.Google Scholar
  12. Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the craft of reading, writing and mathematics. In L. B. Resnick (Ed.), Knowing, learning and instruction: Essays in honor of Robert Glaser (pp. 453–494). Hillsdale, NJ: Erlbaum.Google Scholar
  13. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334. doi: 10.1007/BF02310555.CrossRefGoogle Scholar
  14. Ellerton, N. F. (1986). Children’s made-up mathematical problems: A new perspective on talented mathematicians. Educational Studies in Mathematics, 17, 261–271.CrossRefGoogle Scholar
  15. English, L. D. (1997a). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183–217. doi: 10.1023/A:1002963618035.CrossRefGoogle Scholar
  16. English, L. D. (1997b). Development of seven-grade students’ problem posing. In E. Pehkonen (Ed.), 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 241–248). Lahti, Finland.Google Scholar
  17. English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.CrossRefGoogle Scholar
  18. Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). New York, NY: Macmillan.Google Scholar
  19. 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: Lawrence Erlbaum.Google Scholar
  20. Lavy, I., & Bershadsky, I. (2003). Problem posing via “What if not?” strategy in solid geometry—A case study. Journal of Mathematics Behavior, 22, 369–387. doi: 10.1016/j.jmathb.2003.09.007.CrossRefGoogle Scholar
  21. 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. doi: 10.1007/BF03217299.CrossRefGoogle Scholar
  22. Lowrie, T. (2002). Young children posing problems: The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14(2), 87–98. doi: 10.1007/BF03217355.CrossRefGoogle Scholar
  23. Ma, Y. (2003). 小学数学教学论 [Instructional theory on elementary school mathematics]. Beijing, China: People’s Education Press.Google Scholar
  24. Ministry of Education of The People’s Republic of China. (2012). 义务教育数学课程标准 [Compulsory education mathematics curriculum standards]. 北京, 中国: 北京师范大学出版社 [Beijing, China: Beijing Normal University Publishing House].Google Scholar
  25. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  26. Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York, NY: McGraw-Hill.Google Scholar
  27. Rudnitsky, A., Etheredge, S., Freeman, S., & Gilbert, T. (1995). Learning to solve addition and subtraction word problems through a structure-plus-writing approach. Journal for Research in Mathematics Education, 26, 467–486. doi: 10.2307/749433.CrossRefGoogle Scholar
  28. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.Google Scholar
  29. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and posing. ZDM: International Reviews on Mathematical Education, 29(3), 75–80. doi: 10.1007/s11858-997-0003-x.CrossRefGoogle Scholar
  30. Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.CrossRefGoogle Scholar
  31. Silver, E. A., Mamona-Downs, J., Leung, S. S., & Kenney, P. A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27, 293–309.CrossRefGoogle Scholar
  32. Verschaffel, L., & De Corte, E. (1996). Number and arithmetic. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education. Part I (pp. 99–138). Dordrecht, The Netherlands: Kluwer.Google Scholar
  33. Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1, 195–229. doi: 10.1207/s15327833mtl0103_2.CrossRefGoogle Scholar
  34. Verschaffel, L., De Corte, E., Lowyck, J., Dhert, S., & Vandeput, L. (2000). Supporting mathematical problem solving and posing in upper elementary school children by means of knowledge forum (deliverable of project no. 2017 CL-Net: Computer supported collaborative learning networks in primary and secondary education). Leuven, Belgium: Center for Instructional Psychology and Technology, Katholieke Universiteit Leuven.Google Scholar
  35. Verschaffel, L., Van Dooren, W., Chen, L., & Stessens, K. (2009). The relationship between posing and solving division-with-remainder problems among Flemish upper elementary school children. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 143–160). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  36. Winograd, K. (1997). Ways of sharing student-authored story problems. Teaching Children Mathematics, 4(1), 40–47.Google Scholar
  37. Xia, X., Lü, C., Wang, B., & Song, Y. (2007). Experimental research on mathematics teaching of “situated creation and problem-based instruction” in Chinese primary and secondary schools. Frontiers of Education in China, 2, 366–377.CrossRefGoogle Scholar
  38. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.CrossRefGoogle Scholar
  39. Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’ creativity and mathematical problem posing abilities. In B. Sriraman & K. H. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5–28). Rotterdam, The Netherlands: Sense Publishers. doi: 10.1007/978-94-6091-439-3_2.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Limin Chen
    • 1
  • Wim Van Dooren
    • 2
  • Lieven Verschaffel
    • 2
  1. 1.Liaoning Research and Training Center for Basic EducationShenyang Normal UniversityShenyangChina
  2. 2.Faculty of Psychology and Educational SciencesUniversity of LeuvenLeuvenBelgium

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