Do Intelligence Games Improve Problem Posing Skill?

Abstract

In this study, it was aimed to determine whether intelligence games improve mathematics teachers' problem posing skills. The research, in which case study, one of the qualitative research methods, was preferred, was conducted with two mathematics teachers enrolled in the Mathematics Education Master's Program with Thesis at a state university. Criterion sampling method was used to determine the participants. The criterion was that the teachers did not have any interventions for intelligence games and problem posing. A problem posing test consisting of four tasks was used as a data collection tool. In the test, a visual of each task was included and teachers were asked to pose a problem of each degree of difficulty by giving easy, moderately difficult and difficult prompts for each visual before and after the application. The cognitive complexity analysis framework proposed by Kwek (2015) was used to analyze the mathematical complexity of the problems constructed by the teachers. In the study, it was found that the prompt given in problem posing tasks contributed to the construction of more complex problems. However, high level complex problems were generally posed in the final determination. It was determined that the problems posed by the teachers, especially after the intervention for intelligence games, were high level complex and they associated them with intelligence games. Therefore, in this study, it was concluded that intelligence games cause the problems to be more complex and intelligence games improve problem posing skills.

Keywords

• intelligence games
• problem posing
• problem posing prompts

Zekâ Oyunları Problem Kurma Becerisini Geliştirir Mi?

Öz

Bu araştırmada, zekâ oyunlarının matematik öğretmenlerinin problem kurma becerilerini geliştirip geliştirmediğini belirlemek amaçlanmıştır. Nitel araştırma yönteminden biri olan durum çalışmasının tercih edildiği araştırma, bir devlet üniversitesinin Matematik Eğitimi Tezli Yüksek Lisans programına kayıtlı iki matematik öğretmeni ile gerçekleştirilmiştir. Katılımcılarının belirlenmesinde ölçüt örnekleme yöntemi kullanılmıştır. Ölçüt olarak öğretmenlerin zekâ oyunları ve problem kurmaya yönelik müdahalelerinin olmamasıdır. Veri toplama aracı olarak dört görevden oluşan problem kurma testi kullanılmıştır. Testte her bir göreve ait bir görsele yer verilmiş ve öğretmenlerden uygulama öncesi ve sonrası her bir görsele ilişkin kolay, orta ve zor derecede birer problem kurmaları istenmiştir. Öğretmenlerin kurdukları problemlerin matematiksel karmaşıklığını analiz etmek için Kwek (2015) tarafından önerilen bilişsel karmaşıklık analiz çerçevesi kullanılmıştır. Araştırmada problem kurma görevlerinde verilen talimatın daha karmaşık problemlerin kurulmasına katkı sağladığı tespit edilmiştir. Ancak yüksek seviyede karmaşık problemler genellikle son tespit aşamasında kurulmuştur. Öğretmenlerin özellikle zekâ oyunlarına yönelik müdahaleden sonra kurdukları problemlerin yüksek seviyede karmaşık olduğu ve zekâ oyunları ile ilişkilendirdikleri belirlenmiştir. Dolayısıyla bu çalışmada zekâ oyunlarının kurulan problemlerin daha karmaşık olmasına neden olduğu ve zekâ oyunlarının problem kurma becerisini geliştirdiği sonucuna varılmıştır.

Anahtar Kelimeler

• zekâ oyunları
• problem kurma
• problem kurma talimatları

Kaynakça

1. Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In Mina, F.& Rogerson, A. (Eds.) The proceedings of the International Conference on Mathematical Education into the 21st Century: Societal Challenges, Issues and Approaches, (pp.1-8). Cairo, Egypt.
2. Alessi, S. M., & Trollip, S. R. (2001). Multimedia for learning: Methods and development (3rd ed.). Allyn and Bacon.
3. Baumanns, L., & Rott, B. (2024). Problem-posing tasks and their influence on pre-service teachers’ creative problem-posing performance and self-efficacy. The Journal of Mathematical Behavior, 73, 101130. https://doi.org/10.1016/j.jmathb.2024.1011304
4. Bayramin, T. (2020). Determining the 6th grade students' problem-solving strategies in intelligence games [Master’s thesis]. Istanbul University. Council of Higher Education National Thesis Center (Publication No. 636187).
5. Bottino, R. M., Ott, M., Tavella, M., & Benigno, V. (2010, October). Proceedings of the 4th ECGBL Conference on Games Based Learning Copenhagen (pp. 31-39).
6. Burgers, C., Eden, A., van Engelenburg, M. D., & Buningh, S. (2015). How feedback boosts motivation and play in a brain-training game. Computers in Human Behavior, 48, 94-103. https://doi.org/10.1016/j.chb.2015.01.038
7. 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. https://doi.org/10.1016/S0732-3123(02)00142-6
8. Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., ... & Song, N. (2020). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design. International Journal of Educational Research, 102, 101404. https://doi.org/10.1016/j.ijer.2019.02.004

9. Cai, J., Ran, H., Hwang, S., Ma, Y., Han, J., & Muirhead, F. (2023). Impact of prompts on students’ mathematical problem posing. The Journal of Mathematical Behavior, 72, 101087. https://doi.org/10.1016/j.jmathb.2023.101087
10. Candiasa, I. M., Santiyadnya, N., & Sunu, G. K. A. (2018, June). Using puzzle to encourage students to do problem posing. In Journal of Physics: Conference Series (Vol. 1040, No. 1, p. 012025). IOP Publishing.
11. Chen, S. Y., Tsai, J. C., Liu, S. Y., & Chang, C. Y. (2021). The effect of a scientific board game on improving creative problem solving skills. Thinking Skills and Creativity, 41, 100921. https://doi.org/10.1016/j.tsc.2021.100921
12. Chen, T., & Cai, J. (2020). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. International Journal of Educational Research, 102, 101420. https://doi.org/10.1016/j.ijer.2019.03.004
13. Christou, C., Pitta-Pantazi, D., & Chimoni, M. (2024). Teachers' mathematical problem posing: The role of processes and complexity levels in posing problems on the fraction part-whole concept. The Journal of Mathematical Behavior, 73, 101134. https://doi.org/10.1016/j.jmathb.2024.101134
14. Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415. https://doi.org/10.1007/s10857-008-9081-0
15. Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry & research design: choosing among five approaches (4th ed.). SAGE.
16. Çağan, B. (2022). The effect of teaching activities carried out using mathematical mind and intelligence games on secondary school students' mathematics achievement, motivation and problem-solving skills [Master’s thesis]. Bartin University. Council of Higher Education National Thesis Center (Publication No. 725197)
17. Çomarlı, S. K. (2018). Examining the problem posing skills of secondary school mathematics teachers regarding data processing learning field (Publication No. 525365) [Master’s thesis]. Bartin University. Council of Higher Education National Thesis Center
18. Dahalan, F., Alias, N., & Shaharom, M. S. N. (2024). Gamification and game based learning for vocational education and training: A systematic literature review. Education and Information Technologies, 29(2), 1279-1317. https://doi.org/10.1007/s10639-022-11548-w
19. Doğan-Coşkun, S. (2019). The analysis of the problems posed by pre-service elementary teachers for the addition of fractions. International Journal of Instruction, 12(1), 1517-1532. https://doi.org/10.29333/iji.2019.12197a
20. 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(1), 87-101. https://doi.org/10.1007/s10649-012-9449-z
21. Goldstein, J. (2003). Contributions of play and toys to child development. Key studies. For the Toy Industries of Europe, Brussels.
22. Grundmeier, T. A. (2003). The effects of providing mathematical problem posing experiences for K-8 preservice teachers: Investigating teachers’ beliefs’ and characteristics of posed problems [Doctoral dissertation]. Retrieved from ProQuest Dissertations & Theses (PQDT) Global. (3083732)
23. Kalmpourtzis, G. (2019). Connecting game design with problem posing skills in early childhood. British Journal of Educational Technology, 50(2), 846-860. https://doi.org/10.1111/bjet.12607
24. Kar, T. (2014). Investigating middle school mathematics teachers’ mathematical knowledge for teaching in the context of problem posing: the example of addition operation with fractions [Doctoral dissertation]. Ataturk University. Council of Higher Education National Thesis Center (Publication No. 366543).
25. Kar, T., & Işık, C. (2015). The investigation of middle school mathematics teachers' views on the difficulty levels of posed problems. Ahi Evran University Journal of Kırşehir Education Faculty, 16(2), 63-81. Retrieved from http://kefad.ahievran.edu.tr/
26. Kiili, K. (2007). Foundation for problem-based gaming. British Journal of Educational Technology, 38(3), 394-404. https://doi.org/10.1111/j.1467-8535.2007.00704.x
27. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. Shoenfeld (Ed.), Cognitive science and mathematics education (1st ed., pp. 123–148). Lawrance Erlbaum Associates.
28. Kinach, B. M. (2002). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18, 51–71. https://doi.org/10.1016/S0742-051X(01)00050-6
29. Kirriemuir, J., & McFarlane, A. (2004). Literature review in games and learning (Futurelab Series, Report 8). Futurelab.
30. Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, … Capraro, R. M. (2019). The effects of problem-posing intervention types on elementary students’ problem-solving, Educational Studies, 45(6), 708-725. https://doi.org/10.1080/03055698.2018.1509785
31. Kurbal, M. S. (2015). An investigation of sixth grade students’ problem solving strategies and underlying reasoning in the context of a course on general puzzles and games [Master’s thesis]. Middle East Technical University. Council of Higher Education National Thesis Center (Publication No. 399985).
32. Kwek, M. L. (2015). Using problem posing as a formative assessment tool. In F. M. Singer, N. F. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 273-292). Springer. https://doi.org/10.1007/978-1-4614-6258-3
33. Leavy, A., & Hourigan, M. (2020). Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23(4), 341-361. https://doi.org/10.1007/s10857-018-09425-w
34. 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. https://doi.org/10.1007/BF03217299
35. Leung, S.S. (2016). Mathematical problem posing: A case of elementary school teachers developing tasks and designing instructions in Taiwan. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 327-344). Springer.
36. Lin, C., Shao, Y., Wong, L., Li, Y., & Niramitranon, J. (2011). The impact of using synchronous col¬laborative virtual tangram in children’s geometric. The Turkish Online Journal of Educational Tecnology, 10(2), 250-258.
37. Lowrie, T. (1999). Free problem posing: Year 3/4 students constructing problems for friends to solve. In J. Truran & K. Truran (Eds.), Making a difference (Proceedings of the 22nd annual conference of the Mathematics Education Research Group of Australasia, Adelaide, pp. 328–335). MERGA.
38. McFarlane, A., Sparrowhawk, A., & Heald, Y. (2002). Report on the educational use of games. TEEM (Teachers Evaluating Educational Multimedia). Cambridge.
39. Ministry of National Education [MONE]. (2013). Middle school and imam hatip middle school intelligence games course (5th, 6th, 7th, 8th grades) teaching program. MONE Publications.
40. Michalewicz, Z., Falkner, N. ve Sooriamurthi, R. (2011). Puzzle-based learning: An introduction to critical thinking and problem-solving. Decision Line, 42(5), 6–9. Retrieved from https://www.andrew.cmu.edu/user/sraja/papers/2011-decsionline-oct-paper.pdf
41. Moursund, D. G. (2006). Introduction to using games in education: A guide for teachers and parents. https://uoregon.edu/~moursund/Books/Games/games.html
42. Örnek, T., & Soylu, Y. (2021). The assessment of problem posing learning model designed for the development of problem posing skill. Journal of Computer and Education Research, 9(18), 929-960. https://doi.org/10.18009/jcer.949572
43. Příhonská, J. (2008). Brain-teasers as an instrument for development the creativity of future teachers. In Scientific Issues, Teaching Mathematıcs: Innovation, New Trends, Research (pp. 229-234). Catholic University, Ružomberok.
44. Reiter, H. B., Thornton, J., & Vennebush, G. P. (2014). Using kenken to build reasoning skills. The Mathematics Teacher, 107(5), 341-347. https://doi.org/10.5951/mathteacher.107.5.0341
45. Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing. International Journal of Mathematical Education in Science and Technology, 48(2), 163-184. https://doi.org/10.1080/0020739X.2016.1232843
46. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28. Retrieved from https://www.jstor.org/journal/forlearningmath
47. 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/10.2307/749846
48. Şanlıdağ, M., & Aykaç, N. (2021). The effect of mind games on students’ attitudes of solving mathematical problems and reflective thinking skills for solving mathematical problems. MSKU Journal of Education, 8(2), 597-611. https://doi.org/10.21666/muefd.846312
49. Şişman, Ş. (2022). The effect of mind games on 8th grade students' success in solving non-routine problems and their attitudes to mathematics [Master’s thesis]. Kocaeli University. Council of Higher Education National Thesis Center (Publication No. 763324).
50. Terzi, A. (2024). The impact of intelligence game-based applications on developing non-routine problem-solving skills of elementary school students [Doctoral dissertation]. Trabzon University. Council of Higher Education National Thesis Center (Publication No. 863259).
51. Tichá, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 1941–1950). Institut National de Recherche Pédagogique.
52. Ulusoy, F. (2024). Problem posing as an assessment tool. In K. Özgen, T. Kar, S. Çenberci, & Y. Zengin (Eds.), Problem solving and problem posing in mathematics (3rd ed., pp. 283-307). Pegem Academy. Yıldırım, A., & Şimşek, H. (2018). Qualitative research methods in social sciences (11th Edition). Seçkin Publishing.
53. Yıldırım, B. (2023). Investigation of the effect of intelligence games on 7th grade students' mathematical problem solving skills and attitudes [Master’s thesis]. Kafkas University. Council of Higher Education National Thesis Center (Publication No. 802068).
54. Zengin-Kılavuz, P. (2024). The effect of intelligence games used in mathematics lessons on the problem solving skills of 7th grades students [Master’s thesis]. Hacettepe University. Council of Higher Education National Thesis Center (Publication No. 857155).