Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

Students' mathematical noticing in arithmetic sequence lesson

등차수열 수업에서 나타나는 학생의 수학 주목하기

  • Received : 2024.02.05
  • Accepted : 2024.03.19
  • Published : 2024.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

This study analyzed students' mathematical noticing in high school sequence classes based on students' two perceptions of sequence. Specifically, mathematical noticing was analyzed in four aspects: center of focus, focusing interaction, task features, and nature of mathematics activities, and the following results were obtained. First of all, the change pattern of central of focus could not be uniquely described by any one component among 'focusing interaction', 'task features', and 'the nature of mathematical activities'. Next, the interactions between the components of mathematical noticing were identified, and the teacher's individual feedback during small group activities influenced the formation of the center of focus. Finally, students showed two different modes of reasoning even within the same classroom, that is, focusing interaction, task features, and nature of mathematics activities that resulted in the same focus. It is hoped that this study will serve as a catalyst for more active research on students' understanding of sequence.

본 연구는 수열에 대한 학생의 두 가지 인식을 바탕으로 고등학교 수열 수업에서 나타나는 학생의 수학 주목하기를 분석하였다. 구체적으로 수학 주목하기를 초점의 중심, 초점을 유발하는 상호작용, 수학 과제의 특징, 수학 활동의 본질의 네 가지 측면에서 분석하여 다음의 결과를 얻었다. 우선 초점의 중심 변화 양상은 '초점을 유발하는 상호작용', '물질적 자원', '수학 활동의 본질' 중 어떤 한 구성요소만으로는 유일하게 묘사될 수 없었다. 다음으로 수학 주목하기 구성요소 간의 상호작용이 식별되었으며, 소집단 활동에서의 교사의 개별 피드백은 초점의 중심 형성에 영향을 주었다. 마지막으로 학생들은 동일 교실, 즉 동일 초점을 유발하는 상호작용, 물질적 자원, 수학 활동의 본질 내에서도 서로 다른 두 가지 추론 양상을 보였다. 본 연구가 마중물이 되어 수열에 대한 학생의 이해 연구가 더욱 활발히 진행되길 기대한다.

Keywords

References

  1. Ministry of Education. (2015). Mathematics curriculum. Notification of the Ministry of Education No. 2015-74.
  2. Ministry of Education. (2022). Mathematics curriculum. Notification of the Ministry of Education No. 2022-33.
  3. Kim, D. H. (2023). Study on errors and leading learning caused by sequence unit in the students [Master's thesis, Konkuk University].
  4. Kim, S. K. (2003). Comparative study of teacher's group feedback and individual feedback on high school English formative test [Master's thesis, Busan National University].
  5. Kim, S. B. (2019). A Study on differences of mathematical noticing and teaching strategies [Ewha Woman University Doctoral dissertation].
  6. Kim, Y., & Kim, D. W. (2022). A study on mathematical knowledge for teaching: Patterns in elementary school. Journal for Philosophy of Mathematics Education, 4(2), 63-76.
  7. Kim, Y. H., & Hwang, W. H. (2011). An analysis of student's understanding of mathematical terminology and symbols suggested in mathematical series and its limits. KU Center for Curriculum and Instruction Studies, 4(2), 21-47.
  8. Kim, H. S., Park, J. M., Park, J. S., Bae, H. S., & Bang, S. J. (2007). The Realities of Mathematics and Creativity Development. Kyungmoon.
  9. Kim, H. J. (2022). Pre-service mathematics teachers' noticing competency: Focusing on teaching for robust understanding of mathematics. The Mathematical Education, 61(2), 339-357. https://doi.org/10.7468/MATHEDU.2022.61.2.339
  10. Ryu, H. C. Sunwoo, H. S., Shin, B. M., Jo, J. M., Lee, B. M., Kim, Y. S., ..., Jung, S. Y. (2018). High school math I teacher's guidebook. Chunjae.
  11. Park, D. S. (2017). A study on analysis of students' algebraic thinking habits of mind and generalization level in problem solving process of high school sequence unit [Doctoral dissertation, Ewha Woman University].
  12. Sunwoo, J., & Pang, J. S. (2020). A study on the responsive teaching practices of an elementary school teacher teaching pattern generalization. School Mathematics, 22(2), 445-465.
  13. An, J. S. (2023). The Effects of Creative and Personality Activities on Academic Achievement and Mathematical Learning Attitudes. The Journal of Learner-Centered Curriculum and Instruction, 23(8), 775-791.
  14. Oh, Y. S., & Kim, D. J. (2023). An analysis of characteristics of open-ended tasks presented in sequences of high school mathematics textbooks: Focusing on cognitive demands. The Mathematical Education, 62(2), 257-268. https://doi.org/10.7468/MATHEDU.2023.62.2.257
  15. Yu, K. W., Jung, J. W., Kim, Y. S., & Kim, H. B. (2012). An understanding of qualitative research methods. PYbook.
  16. Lee, K. H. (2022). 2022 revised mathematics curriculum proposal (Final Draft) development policy study. Korea Foundation for the Advancement of Science & Creativity.
  17. Lee, S. J., & Shin, J. (2022). The actor-oriented transfer perspective and radical constructivism. Journal for Philosophy of Mathematics Education, 4(2), 97-116.
  18. Lee, W. J. (2021). A study on the effect of teacher repetition on beginning level Korean class: Based on interaction between teacher and learners. Teaching Korean as a Foreign Language, 63, 141-163. https://doi.org/10.21716/TKFL.63.6
  19. Lee, Y. J. (2023). Analysis of student noticing in a lesson that emphasizing relational understanding of equals sign. The Mathematical Education, 62(3), 341-362.
  20. Lee, J. A., & Lee, S. J. (2019). Mathematical noticing of two prospective secondary teachers in the course of planning, implementing, and reflecting on lessons. School Mathematic, 21(3), 561-589.
  21. Jang, H. S., Lee, S. H., & Lee, D. W. (2022). A survey on the connection of high school students' perception to a sequence and the limit of sequence. School Mathematic, 22(1), 69-83.
  22. Jung, D. M. (2022). Introduction to real analysis. Kyungmoon.
  23. Jo, H. M., & Lee, E. J. (2021). Prospective teachers' noticing about concept of variables. Communications of Mathematical Education, 35(3), 257-275.
  24. Ji, H. O. (2021). Mathematical noticing of prospective secondary mathematics teachers through analyzing the task dialogue writing activity [Master's thesis, Korea National University of Education].
  25. Choi, Y. H., & Lee, S. J. (2023). Teachers' mathematical noticing in elementary school mathematics classroom during remote learning. Journal of Educational Research in Mathematic, 33(4), 951-974.
  26. Han, H. J. (2022). 2022 revised curriculum coordination study (I). Korea Institute for Curriculum and Evaluation.
  27. Hong, J. G., & Kim, Y. G. (2008). On the students' understanding of mathematical induction. Journal of Educational Research in Mathematic, 18(1), 123-135.
  28. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190.
  29. Hohensee, C. (2011). Backward transfer: How mathematical understanding changes as one builds upon it [Published doctoral dissertation, University of California].
  30. Janvier, C. (Ed.). (1897). Problems of representation in the teaching and learning of mathematics. Lawrence Erlbaum.
  31. Lobato, J. (2003). How design experiments can inform a rethinking of transfer and vice versa. Educational Researcher, 32(1), 17-20.
  32. Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students' mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809-850.
  33. Lobato, J., Rhodehamel, B., & Hohensee, C. (2012). "Noticing" as an alternative transfer of learning process. Journal of the Learning Sciences, 21(3), 433-482.
  34. Mamona, J. (1990). Sequences and series-sequences and functions: Students' confusions. International Journal of Mathematical Education in Science and Technology, 21(2), 333-337.
  35. McDonald, M. A., Mathews, D. M., & Strobel, K.H. (2000). Understanding sequences: A tale of two objects, In A. H. Schoenfeld and J. Kaput (Eds.), Research in collegiate mathematics education No. 4 (pp. 77-102). American Mathematical Society.
  36. O'Connor, M. C., & Michaels, S. (1993). Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy. Anthropology and Education Quarterly, 24(4), 318-335.
  37. Przenioslo, M. (2005). Introducing the concept of convergence of a sequence in secondary school. Educational Studies in Mathematics, 60, 71-93. doi:10.1007/s10649-005-5325-4
  38. Przenioslo, M. (2006). Conceptions of a sequence formed in secondary schools. International Journal of Mathematical Education in Science and Technology, 37(7), 805-823. doi:10.1080/00207390600733832
  39. Sievert, H., van den Ham, A. K., & Heinze, A. (2021). The role of textbook quality in first graders' ability to solve quantitative comparisons: A multilevel analysis. ZDM-Mathematics Education, 53(6), 1417-1431.
  40. Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Mmiddle School, 3(4), 268-275.
  41. Stein, M. K., Smith, M. S., Hennignsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development (2nd ed.). Teachers College Press.
  42. Sierpinska, A. (1990). Some remarks on understanding in mathematics. For the Learning of Mathematics, 10(3), 24-36.
  43. Thorndike, E. L. (1906). Principles of teaching. Seiler.
  44. Wagner, J. F. (2006). Transfer in pieces. Cognition and Instruction, 24(1), 1-71. https://doi.org/10.1207/s1532690xci2401_1