Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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The Effects of Mathematical Problem Posing Activities on 10th Grade Students' Mathematics Achievement and Affective Characteristic of Mathematics

수학적 문제제기 활동을 반영한 수업이 고등학교 1학년 학생들의 수학 학업 성취도 및 수학 교과에 대한 정의적 특성에 미치는 영향

  • Received : 2018.08.13
  • Accepted : 2018.09.07
  • Published : 2018.09.30
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Abstract

The purpose of this study is to investigate the effect of mathematics classes focused on mathematical problem posing activities on 10th grade students' mathematics achievement and affective characteristics of mathematics. This study was conducted in a total of 45 regular mathematics classrooms with 81 students from two classes through a nonequivalent control group design. The results of the study showed that the teaching method based on mathematical problem posing activities had a more positive effect on students' mathematics achievement and the affective characteristics of mathematics than the teaching method that focuses on problem solving. The teaching method based on problem posing activities proposed in this study could induce students' self-reflective learning motivation, which in turn gave them a more solid understanding of the mathematical concepts they had learned. In addition, it was found that students' problem solving ability, mathematical communication ability, and mathematical thinking ability were positively influenced by problem posing activities. Regarding the affective characteristics of mathematics, the mathematical problem-posing activity suggested in this study turned out to be a very effective strategy for improving students' interest in mathematics.

본 연구에서는 수학적 문제제기 활동을 반영한 수학 수업이 고등학교 1학년 학생들의 수학 학업 성취도 및 수학 교과에 대한 정의적 특성에 미치는 영향에 대해서 알아보았다. 본 연구는 이질통제집단 설계(nonequivalent control group design)를 통해 고등학교 1학년 2개 학급의 81명의 학생들을 대상으로 총 45차시의 정규 수학 수업 시간에 이루어졌다. 연구 결과에 의하면, 수학적 문제제기 활동을 반영한 수업 방식이 전통적인 문제해결에 중점을 둔 수업 방식보다 학생들의 수학 학업 성취 및 수학 교과에 대한 정의적 특성에 보다 긍정적인 영향을 미치는 것으로 나타났다. 본 연구에서 제안한 문제제기 활동을 반영한 수업은 학생들의 자기성찰적 학습 동기를 유발시킬 수 있었고, 이를 통해 학생들은 학습한 수학적 개념에 대한 이해를 보다 확고히 할 수 있는 것으로 나타났다. 이와 더불어 문제제기 활동은 학생들의 문제해결력, 수학적 의사소통 능력, 수학적 사고력 발달에도 긍정적인 영향을 미친 것으로 나타났다. 정의적 특성과 관련해서는 본 연구에서 제안한 수학적 문제제기 활동은 학생들의 수학 교과에 대한 흥미 향상에 매우 효과적인 전략으로 나타났다.

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References

  1. Kang. M. S.(2000). The effect of problem posing activities on the improving problem solving ability in high school mathematics classes. Unpublished master's thesis. Graduate school of education, Sogang university.
  2. Kim, K. O., & Rye, S. R. (2009). The effects of the situation-based mathematical problem posing activity on problem solving ability and mathematical attitudes. School Mathematics, 11(5), 665-683.
  3. Kim, S, Kim, D..& Seo, H. (2017). An Effect of Problem-solving Lessons with Problem-posing on Mathematical Creativity. East Asian Mathematical Journal, 33(4), 381-411 https://doi.org/10.7858/EAMJ.2017.028
  4. Kim, E. (2016). The effect of problem posing activity on mathematics learning attitude and academic achievement-Focused on high school students underachieving in mathematics-.Unpublished master's thesis. Graduate school of education, Korea university.
  5. Kim, J. K., & Lim, M. K. (2001). An effect coming to the problem solving ability from the problem posing activity by presenting the problem situation. Journal of Elementary Mathematics Education in Korea, 5, 77-98.
  6. Park, S. H., Kim, M. H., & Ju, M. K. (2010). A Study on Affective Characteristics Toward Mathematics. Research Report RRI 2010-9, Seoul: Korea Institute of Curriculum and Evaluation
  7. Park, Y. (2014). The Effect of Problem Making Activities on Academic Achievement and Learning Attitude. Unpublished master's thesis. Graduate school of education, Korea university.
  8. Park, H. (2012). The effect of problem posing activity on academic achievement and mathematical attitude of middle graded students. Unpublished master's thesis. Graduate school of education, Korea university.
  9. Bae, J. H., & Park, M. (2016). The Effects of Reflective Problem Posing Activities on Students’Problem Solving Ability and Attitudes toward Mathematics. Journal of Elementary Mathematics Education in Korea, 20(2), 311-331.
  10. Sang, K., Kim, S., Kim, K., Kim, S., Si, K., & Han, J (2015). The Influence of Educational Context Variables on students' Mathematics Achievement and Affective Characteristics. Research Report RRE 2015-8. Seoul: Korea Institute of Curriculum and Evaluation
  11. Song, M. J., & Park, J. S. (2005). The effects of development and application of problem posing program on mathematics learning achievements, attitude and interest. Journal of Elementary Mathematics Education in Korea, 9(1), 1-18.
  12. Song, M. Rim, H., Choi, H., Park, H. Y., & Son, S.(2013). OECD Programme for International Students Assessment: Analyzing PISA 2012 Results. Research Report RRE-2013-6-1. Seoul: Korea Institute of Curriculum and Evaluation
  13. Shin, S. J., & Lim, M. K. (2010). An Analytic Study of Mathematical Problem-Posing Activities for Two-hour Classes - Focusing on 3rd Grade Elementary School children -. Journal of Elementary Mathematics Education in Korea, 14(1), 43-64.
  14. Yang, M. J. (2010). The effect of mathematics education through guided self problem - posing -Focusing on the subject of function in the first year high school-. Unpublished master's thesis. Graduate school of education, Hanyang university.
  15. Oh, D. G., & Kim, S. L (2010). The effect of problem posing activities using fairy tale on mathematical attitude and academic achievement. East Asian Mathematical Journal, 26(4), 509-533.
  16. Oh, Y., & Jeon, Y.(2018). The Effect of Problem-posing Activities on the Affective Domain of Mathematics. Journal of the Korea Contents Association, 18(2), 541-552 https://doi.org/10.5392/JKCA.2018.18.02.541
  17. Yun, M. R., & Park, J. S. (2008). The effects of problem posing program throuth structure-centered cooperative learning on mathematics learning achievements and mathematical disposition. Journal of Elementary Mathematics Education in Korea, 12(2), 101-124.
  18. Yoon, S. A., & Paik, S. (2010). A study to improve teaching methods of mathematical problem posing in elementary mathematics. The Journal of Korea Elementary Education, 21(1), 25-47. https://doi.org/10.20972/kjee.21.1.201007.25
  19. Lee, S. (2005). The effect of problem posing teaching on mathematical problem-solving ability and creativity. Mathematical Education, 44(3), 361-374.
  20. Lim, M. K. (1996). Investigation and analysis of thinking activities in problem posing. Mathematical Education, 35(1), 1-13.
  21. Jeon, M., & Heo, H. (1998). A study of the effects of problem posing strategies on mathematics achievement. Journal of Educational Research in Mathematics, 8(2), 709-722.
  22. Jung, S. G., & Park, M. (2010). The effects of the mathematical problem generating program on problem solving ability and learning attitude. Journal of Elementary Mathematics Education in Korea, 14(2), 315-335.
  23. Chung, J. H. (2013). The effect of the problem generating programs of the unit of proposition on mathematical academic achievement, tendency and learning attitude for high school students. Unpublished master's thesis. Graduate school of education, Kyungpook national university.
  24. Joo, H., & Han, H. (2016). The analysis of middle school students’ problem posing types and strategies. Mathematical Education, 55(1), 73-89. https://doi.org/10.7468/mathedu.2016.55.1.73
  25. Choi, S. H. (2016). An Effect of Learning Task by Problem Posing Activities on Academic Achievement and Attitude of Learning Mathematics: Focused on Differentiation in The second-year High-School Mathematics. Unpublished master's thesis. Graduate school of education, Hanyang university.
  26. Chok, Y. S., & Bae, J. S. (2004). Effects of teaching with problem posing on mathematical problem solving ability and attitude in elementary school mathematics. Journal of Elementary Mathematics Education in Korea, 8(1), 23-43.
  27. Choi, H. J., & Kim, S. L. (2011). Activities of Mathernatical Problern Posing Using Real-Life Materials. Journal of Elementary Mathematics Education in Korea, 15(1), 121-139.
  28. Han, H., Choi, H., Kim, S., & Lee, J. (2017). The Perceptions of Pre-Service Mathematics Teachers’ Mathematical Problem Posing and Problem Posing Strategies. Journal of Learner-Centered Curriculum and Instruction, 17(22), 325-352. https://doi.org/10.22251/jlcci.2017.17.22.325
  29. Huh, N. (2011). Elementary teachers’ perceptions and applications about problem-posing in the mathematics instruction. Journal of the Korean school mathematics society, 14(4), 539-564.
  30. Hwang, D. J. (2006). Difference between gifted and regular students in mathematical problem solving ability. Journal of the Korean school mathematics society, 9(3), 287-308.
  31. Hwang, H. J., Na, G. S., Choi, S. H., Park, K. M., & Yim, J. H. (2007). The theory of mathematics education. Seoul: Moon-Um-Sa.
  32. Abu-Elwan, Reda (2002). Effectiveness of problem posing strategies on prospective mathematics teachers' problem solving performance. Journal of science and mathematics education in Southeast Asia, 25(1), 56-69.
  33. Brown, S. I., & Walter, M. I. (2005). The art of problem posing. Psychology Press.
  34. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21(4), 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
  35. Campbell, D., & Stanley, J. (1963). Experimental and quasi-experimental designs for research. Boston: Houghton Mifflin.
  36. English, L. D. (1997). Promoting a problem-posing classroom. Teaching Children Mathematics, 4(3), 172.
  37. Guvercin, S., Cilavdaroglu, A. K., & Savas, A. C. (2014). The effect of problem posing instruction on 9th grade students‟ mathematics academic achievement and retention. Anthropologist, 17(1), 129-136. https://doi.org/10.1080/09720073.2014.11891422
  38. Guvercin, S., & Verbovskiy, V. (2014). The effect of problem posing tasks used in mathematics instruction to mathematics academic achievement and attitudes toward mathematics. International Online Journal of Primary Education, 3(2), 59-65.
  39. Kesan, C., Kaya, D., & Guvercin, S. (2010). The effect of problem posing approach to the gifted student’s mathematical abilities. International Online Journal of Educational Sciences, 2, 677-687.
  40. Kilic, C. (2013). Turkish primary school teachers’ opinions about problem posing applications: Students, the mathematics curriculum and mathematics textbooks. Australian Journal of Teacher Education, 38(5), 144-155
  41. Moses, B. M., Bjork, E., & Goldenberg, E. P. (1993). Beyond problem solving: Problem posing. In S. I. Brown & M. I. Walter(Eds.), Problem posing: Reflections and applications (pp. 178-188). Hillsdale, NJ: LEA.
  42. NCTM (1991). Professional standards for teaching mathematics. Reston, VA: National Council of Teacher of Mathematics.
  43. Silver, E. A. (1997). Fostering creativity though instruction rich in mathematical problem solving and problem posing. International Reviews on Mathematical Education, 29, 75-80.
  44. 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. https://doi.org/10.2307/749846
  45. Suib, A. F., Rosli, R., & Capraro, M. M. (2016). A primary school mathematics teachers' perspectives about problem posing activity. The Social Sciences, 11, 4992-4997
  46. 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). Sense Publishers.
  47. Xia, X., Lu, C., & Wang, B. (2008). Research on mathematics instruction experiment based on problem posing. Journal of Mathematics Education, 1(1), 153-163.