Teachers’ Creativity in Posing Statistical Problems from Discrete Data

Affiliation(s)

Department of Methodology and Educational Practice, Faculty of Education, Universiti Kebangsaan Malaysia, Bangi, Malaysia.

Department of Methodology and Educational Practice, Faculty of Education, Universiti Kebangsaan Malaysia, Bangi, Malaysia.

ABSTRACT

Choosing a quality problem in mathematics is a challenge for many teachers. Teachers cannot rely on textbooks for good problems. They have to be able to pose their own problems in order to promote mathematical thinking among students. This study was conducted to explore the creativity of 175 teachers in terms of fluency, flexibility, and originality in posing statistical problems. Participants consisted of secondary school teachers from twenty schools in Peninsular Malaysia. Teaching experience was ranged from 1 to 33 years. The features of the problems posed by these teachers were also studied. The participants were provided a stimulus, which was a set of ungrouped discrete data, and they were asked to pose as many problems as they could. The posed statistical problems were supposed to promote mathematical thinking and to increase students’ understanding. Findings showed that participants were able to pose a total of 270 (74%) statistical problems within the time given. The mean of the creativity score was 11.08 (s.d. = 6.76). Analysis showed no significant difference in creativity between gender and the value of t = –.346, p = .73, where p > .05. Analysis showed significant differences in the teachers’ creativity scores for three groups of teachers: F (2172) = 6.83, p = .001, p < .05.The results also showed that 115 (31.5%) posed problems focuses on the statistical content measure of central tendency. The study provided expo- sure to the teachers to pose problems that can trigger students’ thinking in solving statistical problems.

Choosing a quality problem in mathematics is a challenge for many teachers. Teachers cannot rely on textbooks for good problems. They have to be able to pose their own problems in order to promote mathematical thinking among students. This study was conducted to explore the creativity of 175 teachers in terms of fluency, flexibility, and originality in posing statistical problems. Participants consisted of secondary school teachers from twenty schools in Peninsular Malaysia. Teaching experience was ranged from 1 to 33 years. The features of the problems posed by these teachers were also studied. The participants were provided a stimulus, which was a set of ungrouped discrete data, and they were asked to pose as many problems as they could. The posed statistical problems were supposed to promote mathematical thinking and to increase students’ understanding. Findings showed that participants were able to pose a total of 270 (74%) statistical problems within the time given. The mean of the creativity score was 11.08 (s.d. = 6.76). Analysis showed no significant difference in creativity between gender and the value of t = –.346, p = .73, where p > .05. Analysis showed significant differences in the teachers’ creativity scores for three groups of teachers: F (2172) = 6.83, p = .001, p < .05.The results also showed that 115 (31.5%) posed problems focuses on the statistical content measure of central tendency. The study provided expo- sure to the teachers to pose problems that can trigger students’ thinking in solving statistical problems.

Cite this paper

Zakaria, E. & Salleh, F. (2012). Teachers’ Creativity in Posing Statistical Problems from Discrete Data.*Creative Education, 3,* 1380-1383. doi: 10.4236/ce.2012.38201.

Zakaria, E. & Salleh, F. (2012). Teachers’ Creativity in Posing Statistical Problems from Discrete Data.

References

[1] Anderson, L. W., & Krathwohl, D. R. (Eds.) (2001). A taxonomy for Learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. New York: Addison Wesley Longman.

[2] Balka, D. S. (1974). The development of an instrument to measure creative ability in mathematics. Ph.D. Thesis, Main St. Durham, NH: University of New Hampshire.

[3] Bloom, B. S. (1976). Human characteristics and school learning. New York: McGraw-Hill.

[4] Brown, S. I., & Walter. M. I. (1983). The art of problem posing. Philadelphia: The Franklin Institute Press.

[5] Brumbaugh, D. K., & Rock, D. (2006). Teaching secondary mathematics (3th ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

[6] Chua, Y. P. (2004). Creative and critical thinking styles. New York: University Putra Malaysia Press.

[7] Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243-270. doi:10.1023/A:1024364304664

[8] Cunningham, R. F. (2004). Problem posing: An opportunity for increasing students responsibility. Mathematics and Computer Education, 38, 83-89

[9] English, L. D. (1997). Promoting a problem posing classroom. Teaching Children mathematics, 4, 172-180

[10] Gonzales, N. A. (1996). Problem formulation: Insights from student generated questions. School Science and Mathematics, 96, 152-157. doi:10.1111/j.1949-8594.1996.tb15830.x

[11] Grundmeier, T. A. (2002). University students’ problem posing and attitudes towards mathematics. Primus: Problem, Resources, and Issues in Mathematics Undergraduate Studies, 12, 122-134.

[12] Grundmeier, T. A. (2003). The effects of mathematical problem posing providing experiences for k-8 pre-service teachers: Investigating teachers’ beliefs and characteristics of posed problems. Ph.D. Thesis, Main St. Durham, NH: Universty of New Hampshire.

[13] Harpster, D. L. (1999). A study of possible factors that influence the construction of teacher-made problem that assess higher-order thinking skill. Ph.D. Thesis, Bozeman: Montana State University.

[14] Jensen, L. R. (1973). The relationships among mathematical creativity, numerical aptitute and mathematical achievement. Ph.D. Thesis. Austin: University of Texas.

[15] Kilpatrick, J. (1987). Formulating the problem: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 123-147). Hillsdale, NJ: Lawrence Erlbaum Associates.

[16] Leung, S. S. (1993). Mathematical problem posing: The influence of task formats, mathematics knowledge, and creative thinking. In I. Hirabayashi, N. Nohda, k. Shigematsu, & F. Lin (Eds.), Proceedings of 17th International conference of International Group for the Psychology of Mathematics Education (pp. 33-40). Tsukuba, Japan.

[17] Leung, S. K., & 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, 5-24. doi:10.1007/BF03217299

[18] Lowrie, T. (2002). Designing a framework for problem posing young children generating open-ended task. Contemporary Issues in Early Childhood, 3, 354-364. doi:10.2304/ciec.2002.3.3.4

[19] Ministry of Malaysian Education (2008). Inspectorate and quality assurance. Annual Report, Putra Jaya.

[20] NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.

[21] Noraini, I. (2001). Pedagogy in mathematics education. Kuala Lumpur: Utusan Publications & Distributors Sdn Bhd.

[22] Perez, J. A. (1985). Effects of students generated problems on problem solving performance (writing word problems). Ph.D. Thesis, New York: Columbia University College.

[23] Perrin, J. R. (2007). Problem posing at all levels in the calculus classroom. School Science and Mathematics, 107, 182-192. doi:10.1111/j.1949-8594.2007.tb17782.x

[24] Polya, G. (1973). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton, New Jersey: Princeton Univeversity Press.

[25] Senk, S. L., Beckmann, C. E., & Thompson, D. R. (1997). Assessment and grading in high school mathematics classroom. Journal for Research in Mathematics Education, 28, 187-215. doi:10.2307/749761

[26] Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14, 19-28.

[27] 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. doi:10.2307/749366

[28] Slavin, R. E. (2000). Educational psychology: Theory and practice (6th ed.). Boston: Allyn & Bacon.

[29] Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical problem posing. Ph.D. Thesis, Bloomington: University of Indiana.

[30] Tengku Zawawi, T. Z. (2005). Pedagogical content knowledge of fraction among primary school mathematics teacher. Ph.D. Thesis, Bangi: Faculty of Education, Universiti Kebangsaan Malaysia.

[31] TIMSS (2007). International mathematics report. Boston: International Study Center.

[32] Thompson, T. (2008). Mathematics teachers’ interpretation of higherorder thinking in Bloom’s taxomomy. Electronic International Journal of Mathematics Education, 3, 96-109.

[33] Winograd, K. (1991). Writing, solving and sharing original math story problem. Case studies of fifth grade children’s cognitive behaviour. The Annual Meeting of the American Educational Research Association, Chicago, 3-7 April 1991.

[34] Yusminah, M. Y. (2009). A case study of teachers’ pedagogical content knowledge of functions. Proceedings of the 3th International Conference on Science and Mathematics Education. Penang, 10-12 November 2009.

[35] Zakaria, E., & Iksan, Z. (2007). Promoting cooperative learning. Eurasia Journal of Mathematics, Science & Technology Education, 3, 35- 39.

[36] Zakaria, E., & Ngah, N. (2011). A preliminary analysis of students’ problem-posing ability and its relationship to attitudes towards problem solving. Research Journal of Applied Sciences, Engineering and Technology, 3, 866-870.

[1] Anderson, L. W., & Krathwohl, D. R. (Eds.) (2001). A taxonomy for Learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. New York: Addison Wesley Longman.

[2] Balka, D. S. (1974). The development of an instrument to measure creative ability in mathematics. Ph.D. Thesis, Main St. Durham, NH: University of New Hampshire.

[3] Bloom, B. S. (1976). Human characteristics and school learning. New York: McGraw-Hill.

[4] Brown, S. I., & Walter. M. I. (1983). The art of problem posing. Philadelphia: The Franklin Institute Press.

[5] Brumbaugh, D. K., & Rock, D. (2006). Teaching secondary mathematics (3th ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

[6] Chua, Y. P. (2004). Creative and critical thinking styles. New York: University Putra Malaysia Press.

[7] Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243-270. doi:10.1023/A:1024364304664

[8] Cunningham, R. F. (2004). Problem posing: An opportunity for increasing students responsibility. Mathematics and Computer Education, 38, 83-89

[9] English, L. D. (1997). Promoting a problem posing classroom. Teaching Children mathematics, 4, 172-180

[10] Gonzales, N. A. (1996). Problem formulation: Insights from student generated questions. School Science and Mathematics, 96, 152-157. doi:10.1111/j.1949-8594.1996.tb15830.x

[11] Grundmeier, T. A. (2002). University students’ problem posing and attitudes towards mathematics. Primus: Problem, Resources, and Issues in Mathematics Undergraduate Studies, 12, 122-134.

[12] Grundmeier, T. A. (2003). The effects of mathematical problem posing providing experiences for k-8 pre-service teachers: Investigating teachers’ beliefs and characteristics of posed problems. Ph.D. Thesis, Main St. Durham, NH: Universty of New Hampshire.

[13] Harpster, D. L. (1999). A study of possible factors that influence the construction of teacher-made problem that assess higher-order thinking skill. Ph.D. Thesis, Bozeman: Montana State University.

[14] Jensen, L. R. (1973). The relationships among mathematical creativity, numerical aptitute and mathematical achievement. Ph.D. Thesis. Austin: University of Texas.

[15] Kilpatrick, J. (1987). Formulating the problem: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 123-147). Hillsdale, NJ: Lawrence Erlbaum Associates.

[16] Leung, S. S. (1993). Mathematical problem posing: The influence of task formats, mathematics knowledge, and creative thinking. In I. Hirabayashi, N. Nohda, k. Shigematsu, & F. Lin (Eds.), Proceedings of 17th International conference of International Group for the Psychology of Mathematics Education (pp. 33-40). Tsukuba, Japan.

[17] Leung, S. K., & 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, 5-24. doi:10.1007/BF03217299

[18] Lowrie, T. (2002). Designing a framework for problem posing young children generating open-ended task. Contemporary Issues in Early Childhood, 3, 354-364. doi:10.2304/ciec.2002.3.3.4

[19] Ministry of Malaysian Education (2008). Inspectorate and quality assurance. Annual Report, Putra Jaya.

[20] NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.

[21] Noraini, I. (2001). Pedagogy in mathematics education. Kuala Lumpur: Utusan Publications & Distributors Sdn Bhd.

[22] Perez, J. A. (1985). Effects of students generated problems on problem solving performance (writing word problems). Ph.D. Thesis, New York: Columbia University College.

[23] Perrin, J. R. (2007). Problem posing at all levels in the calculus classroom. School Science and Mathematics, 107, 182-192. doi:10.1111/j.1949-8594.2007.tb17782.x

[24] Polya, G. (1973). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton, New Jersey: Princeton Univeversity Press.

[25] Senk, S. L., Beckmann, C. E., & Thompson, D. R. (1997). Assessment and grading in high school mathematics classroom. Journal for Research in Mathematics Education, 28, 187-215. doi:10.2307/749761

[26] Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14, 19-28.

[27] 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. doi:10.2307/749366

[28] Slavin, R. E. (2000). Educational psychology: Theory and practice (6th ed.). Boston: Allyn & Bacon.

[29] Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical problem posing. Ph.D. Thesis, Bloomington: University of Indiana.

[30] Tengku Zawawi, T. Z. (2005). Pedagogical content knowledge of fraction among primary school mathematics teacher. Ph.D. Thesis, Bangi: Faculty of Education, Universiti Kebangsaan Malaysia.

[31] TIMSS (2007). International mathematics report. Boston: International Study Center.

[32] Thompson, T. (2008). Mathematics teachers’ interpretation of higherorder thinking in Bloom’s taxomomy. Electronic International Journal of Mathematics Education, 3, 96-109.

[33] Winograd, K. (1991). Writing, solving and sharing original math story problem. Case studies of fifth grade children’s cognitive behaviour. The Annual Meeting of the American Educational Research Association, Chicago, 3-7 April 1991.

[34] Yusminah, M. Y. (2009). A case study of teachers’ pedagogical content knowledge of functions. Proceedings of the 3th International Conference on Science and Mathematics Education. Penang, 10-12 November 2009.

[35] Zakaria, E., & Iksan, Z. (2007). Promoting cooperative learning. Eurasia Journal of Mathematics, Science & Technology Education, 3, 35- 39.

[36] Zakaria, E., & Ngah, N. (2011). A preliminary analysis of students’ problem-posing ability and its relationship to attitudes towards problem solving. Research Journal of Applied Sciences, Engineering and Technology, 3, 866-870.