Abstract
The goal of the present study is to investigate the relationship between pupils’ problem posing and problem solving abilities, their beliefs about problem posing and problem solving, and their general mathematics abilities, in a Chinese context. Five instruments, i.e., a problem posing test, a problem solving test, a problem posing questionnaire, a problem solving questionnaire, and a standard achievement test, were administered to 69 Chinese fifth-grade pupils to assess these five variables and analyze their mutual relationships. Results revealed strong correlations between pupils’ problem posing and problem solving abilities and beliefs, and their general mathematical abilities.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Brown. S. I., & Walter. M. I. (1990). The art of problem posing. Hillsdale, NJ: Lawrence Erlbaum Associates.
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 Associates.
Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behaviour, 21(4), 401–421.
Cai, J., & Nie, B. (2007). Problem solving in Chinese mathematics education: Research and practice. ZDM: The International Journal on Mathematics Education, 39(5–6), 459–473. doi: 10.1007/s11858-007-0042-3
Chen, L. M., 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.
Chen, L. M., 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.
Chen, L. M., 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(4), 919–948.
Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM: International Reviews on Mathematical Education, 37(3), 149–158.
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334.
Ellerton, N. F. (1986). Children’s made-up mathematical problems: A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261–271.
English, L. D. (1997a). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183–217. doi: 10.1023/ A:1002963618035
English, L. D. (1997b). Development of seven-grade students’ problem posing. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. ii, pp. 241–248). Lahti, Finland: University of Helsinki, Lahti Research and Training Centre.
English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.
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.
Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education, 20(3), 261–273.
He, X. Y. (1998). 小学生数学自我效能, 自我概念与数学成绩关系的研究 [Research on the relationship between elementary school pupils’ math self-efficacy, self-concept and their mathematics academic achievement]. 心理发展与教育 [Psychological Development and Education], (1), 45–48.
House, J. D. (2006). Mathematics beliefs and achievement of elementary school students in Japan and the United States: Results from the third international mathematics and science study. The Journal of Genetic Psychology, 167(1), 31–45.
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 Associates.
Leung, F. K. S. (2002). Behind the high achievement of East Asian students. Educational Research and Evaluation: An International Journal on Theory and Practice, 8(1), 87–108. doi: 10.1076/edre.8.1.87.6920
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.
Liu, Z. (2009). 大学生数学自我效能, 自我概念与数学学业成绩关系的研究 [Research on the relationship between college students’ math self-efficacy and self-concept and their mathematics academic achievement]. 数学教育学报 [Journal of Mathematics Education], 18(6), 37–41.
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].
Mullis, I. V. S., Martin, M. O., Beaton, A., Gonzalez, E., Kelly, D., & Smith, T. A. (1997). Mathematics achievement in the primary school years: IEA’s third international mathematics and science study (TIMSS). Chestnut Hill, MA: Center for the Study of Testing, Evaluation and Educational Policy, Boston College.
Mullis, I. V. S., Martin, M. O., & Foy, P. (2008). TIMSS 2007 international mathematics report: Findings from IEA’s trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Nicolaidou, M., & Philippou, G. N. (2003). Attitudes towards mathematics, self-efficacy and achievement in problem solving. In M. A. Mariotti (Ed.), European Research in Mathematics III (pp. 1–11). Pisa, Italy: University of Pisa.
Nicolaou, A. A., & Philippou, G. N. (2007). Efficacy beliefs, problem posing, and mathematics achievement. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the V Congress of the European Society for Research in Mathematics Education (pp. 308–317). Larnaca, Cyprus: Department of Education, University of Cyprus.
Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York, NY: McGraw-Hill.
Pajares, F., & Kranzler, J. (1995). Role of self-efficacy beliefs and general mental ability in mathematical problem solving. Contemporary Educational Psychology, 20(4), 426–443. doi: 10.1006/ceps.1995.1029
Rao, N., Moely, B., & Sachs, J. (2000). Motivational beliefs, study strategies and mathematics attainment in high-and low-achieving Chinese secondary school students. Contemporary Educational Psychology, 25(3), 287–316. doi: 10.1006/ceps.1999.1003
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
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.
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(3), 293–309.
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, Netherlands: Kluwer.
Verschaffel, L., Van Dooren, W., Chen, L. M., & 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.
Zhang, D., & Dai, Z. (2004, July). The “Two basics”: Mathematics teaching approach and open-ended problem-solving in China. Regular lecture in the 10th International Congress on Mathematics Education, Copenhagen, Denmark.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Limin, C., Van Dooren, W. & Verschaffel, L. The Relationship between Students’ Problem Posing and Problem Solving Abilities and Beliefs: A Small-Scale Study with Chinese Elementary School Children. Front Educ China 8, 147–161 (2013). https://doi.org/10.1007/BF03396966
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03396966