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수학과 교육과정에 관한 초등예비교사의 신념 연구

An analysis of beliefs held by preservice teachers about school mathematics curriculum

  • 투고 : 2025.10.09
  • 심사 : 2025.10.22
  • 발행 : 2025.10.31

초록

이 연구는 예비교사들이 수학과 교육과정에 관한 신념을 분석하고자 두 가지 연구문제를 설정하였다. 첫째, 예비교사들은 학교 교육과정에 대한 생산적 및 비생산적 신념에 어느 정도 동의하고 있는가, 둘째, 예비교사들은 어떤 근거에서 자신의 동의 수준을 설명하는가였다. 연구 대상은 미국의 중서부에 위치한 대학교의 초등수학교육방법론 과목을 수강하는 예비교사 64명이었다. NCTM(2014)이 제시한 성공적인 수학 수업을 위한 수학과 교육과정에 관한 생산적 신념과 비생산적 신념을 중심으로 설문 문항을 재구성하였다. 교육과정의 성취기준, 학년간 연계, 수업 진도표, 수학 학습 내용, 오픈 소스 등의 5가지 측면에서 생산적 신념과 비생산적 신념으로 총 10개 문항을 설문하였다. 리커트 척도에 따른 기술통계와 그 근거에 대한 세부 내용 분석을 실시하였다. 연구 결과는 전반적으로 생산적 신념(평균 3.39)을 더 강하게 지지하고, 비생산적 신념(평균 2.08)에는 낮은 동의를 보였다. 그러나 다른 신념과 비교해 볼 때, 성취 기준 및 학년 간 교육과정 연계 방식, 학습 진도 지침과 오픈 소스 교육과정 자료에 대한 신념은 다른 신념과 비교할 때 차이가 드러났다. 예비교사의 신념에서 교사 자율성과 외부 전문가 의존성, 유연성과 일관성, 형평성(equity)과 기회균등(equality) 등은 다른 입장들이 나타났다. 이 연구를 토대로 후속적으로 다양한 문화권의 예비교사를 비교하거나, 신념의 변화를 종단적으로 추적할 필요가 있다.

This study probed preservice teachers' (PSTs') beliefs about school mathematics curriculum. The participants were U.S. PSTs who completed a two-part questionnaire assessing their agreement with statements about productive and unproductive beliefs, along with their justifications for the levels of agreement they reported. We analyzed the PSTs' responses using a combination of descriptive statistics based on Likert scale data and inductive content analysis of written rationales. Most PSTs agreed or strongly agreed with productive belief statements and tended to disagree with the unproductive ones. However, the study revealed notable tensions, particularly in PSTs' understanding of standards and learning progressions, as well as in their perceptions of pacing guides and open-source curricula. This research highlights the essential skills that preservice teachers need to develop in order to effectively interpret, evaluate, and utilize curriculum materials. These insights can help teacher preparation programs focus on these necessary skills as they prepare future teachers to face the challenges of diverse classrooms.

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참고문헌

  1. Abtahi, Y., & Planas, N. (2024). Mathematics teaching and teacher education against marginalisation, or towards equity, diversity and inclusion. ZDM Mathematics Education 56, 307–318. https://doi.org/10.1007/s11858-024-01602-x
  2. Alonzo, A. C., & Gotwals, A. W. (Eds.). (2012). Learning progressions in science: Current challenges and future directions. Sense Publishers.
  3. Anderson, R. K., Boaler, J., & Dieckmann, J. A. (2018). Achieving elusive teacher change through challenging myths about learning: A blended approach. Education Sciences, 8(3), 98. https://doi.org/10.3390/educsci8030098
  4. Assiri, E. A., & Alnatheer, M. A. (2019). Utilization of open educational resources in mathematics instruction for the intermediate school. Journal of Educational Issues, 5(2), 193-207. https://doi.org/10.5296/jei.v5i2.15898
  5. Au, W. (2007). High-stakes testing and curricular control: A qualitative metasynthesis. Educational Researcher, 36(5), 258–267. https://doi.org/10.3102/0013189X07306523
  6. Ball, D. L.,Thames, M. H, & Phelps, G.(2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
  7. Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. Educational Studies in Mathematics, 79(1), 127–147. https://doi.org/10.1007/s10649-011-9333-2
  8. Brown, R. (2009). Teaching for social justice: Exploring the development of student agency through participation in the literacy practices of a mathematics classroom. Journal of Mathematics Teacher Education, 12(2), 171–185. https://doi.org/10.1007/s10857-009-9110-7
  9. Choppin, J., Davis, J., McDuffie, A. R. & Drake, C. (2021). Influence of features of curriculum materials on the planned curriculum. ZDM: Mathematics Education, 53(6), 1249-1263. https://doi.org/10.1007/s11858-021-01305-7
  10. Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning. The Elementary School Journal, 103(3), 287–311. https://doi.org/10.1086/499727
  11. Confrey, J., Maloney, A. P., & Corley, A. K. (2014). Learning trajectories: A framework for connecting standards with curriculum. ZDM: Mathematics Education, 46, 719–733. https://doi.org/10.1007/s11858-014-0598-7
  12. Corcoran, T., Mosher, F. A., & Rogat, A. (2009). Learning progressions in science: An evidence-based approach to reform. Consortium for Policy Research in Education.
  13. Darling-Hammond, L., Hyler, M. E., & Gardner, M. (2017). Effective teacher professional development. Learning Policy Institute.
  14. Datnow, A., & Park, V. (2009). Conceptualizing policy implementation: Large-scale reform in an era of complexity. In G. Sykes, B. Schneider, D. N. Plank, & T. Ford (Eds.), Handbook of Education Policy Research(pp. 348–361). Routledge.
  15. Davis, B., & Simmt, E. (2006). Mathematics‑for‑teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293–319. https://doi.org/10.1007/s10649-006-2372-4
  16. Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34(3), 3–14.https://doi.org/10.3102/0013189X034003003
  17. De Corte, E., Verschaffel, L., & Depaepe, F. (2008). Unraveling the relationship between students' mathematics‑related beliefs and the classroom culture. European Psychologist, 13(1), 24–36. https://doi.org/10.1027/1016-9040.13.1.24
  18. diSessa, A. A. (2004). Metarepresentation: Native competence and targets for instruction. Cognition and Instruction, 22(3), 293–331. https://doi.org/10.1207/s1532690xci2203_2
  19. Duschl, R.A. (2019). Learning progressions: framing and designing coherent sequences for STEM education. Disciplinary and Interdisciplinary Science Education Research, 1, 4. https://doi.org/10.1186/s43031-019-0005-x
  20. Ernest, P. (1991). The philosophy of mathematics education. Routledge Falmer.
  21. Frykholm, J. A. & Glasson, G. (2005). Connecting science and mathematics instruction: Pedagogical context knowledge for teachers. School Science and Mathematics, 105(3), 127–141. https://doi.org/10.1111/j.1949-8594.2005.tb18047.x
  22. Hale, J. A. (2008). A guide to curriculum mapping: Planning, implementing, and sustaining the process. Corwin Press.
  23. Harvey, P., & Bond, J. (2022). The effects and implications of using open educational resources in secondary schools. The International Review of Research in Open and Distributed Learning, 23(2), 107–119. https://doi.org/10.19173/irrodl.v22i3.5293
  24. Hilton III, J. (2020). Open educational resources, student efficacy, and user perceptions: a synthesis of research published between 2015 and 2018. Education Technology Research and Development, 68, 853–876. https://doi.org/10.1007/s11423-019-09700-4
  25. Hyde, R., Archer, R. & Bamber, S. (2024). Beginning mathematics teachers' values and beliefs about pedagogy during a time of policy flux. Journal of Mathematics Teacher Education. Advance online publication. https://doi.org/10.1007/s10857-024-09647-1
  26. Jacobs, H. H. (1997). Mapping the big picture: Integrating curriculum and assessment K–12. ASCD.
  27. Kimmons, R. (2015). OER quality and adaptation in K–12: Teacher and student perspectives. Educational Technology Research and Development, 63, 453–478. https://doi.org/10.19173/irrodl.v16i5.2341
  28. Kimmons, R. (2016). Expansive openness in teacher practice. Teachers College Record, 118(9), 1-34. https://doi.org/10.1177/016146811611800901
  29. LaVenia, M., Cohen-Vogel, L., & Lang, L. B. (2015). The Common Core State Standards initiative: An event history analysis of state adoption. American Journal of Education, 121(2), 145–182. https://doi.org/10.1086/679389
  30. Lee, J., & Kim, S. (2025). Preservice teachers' beliefs and views on curriculum and teacher guide components, In Kwon, O., Kaur, B., Pang, J., Noh, J., Lee, S., Han, S., Yeo, S., & Lim, M. (Eds.), Proceedings of the 9 th ICMI-East Asia Regional Conference on Mathematics Education, Vol. 3, 5-9.
  31. Lerman, S.(1990). lternative perspectives of the nature of mathematics and their influence on the teaching of mathematics. British Educational Research Journal, 16(1), 53–61. https://doi.org/10.1080/0141192900160105
  32. Lloyd, G. M. (2008). Curriculum use while learning to teach: One student teacher's appropriation of mathematics curriculum materials. Journal for Research in Mathematics Education, 39(1), 63-94. http://www.jstor.org/stable/30034888.
  33. Lynch, S. (2023, June 26). It's time to give teachers realistic pacing guides. Instruction Partners.
  34. Maher, C. A., Maher, J. A., Palius, M. F., & Wilkinson, L. C. (2023). Teachers attending to student reasoning: Do beliefs matter? Journal of Mathematical Behavior, 69, 101050. https://doi.org/10.1016/j.jmathb.2023.101050
  35. Marsh, J. A., & Farrell, C. (2015). How leaders can support teachers with data-driven decision-making: A framework for understanding capacity building. Educational Management Administration & Leadership, 43(2), 269–289. https://doi.org/10.1177/1741143214537229
  36. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
  37. National Council of Teachers of Mathematics. (2000). Principles and standards for school Mathematics.
  38. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.
  39. National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common Core State Standards for Mathematics.
  40. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. National Academy Press.
  41. Patrick, S., & Sturgis, C. (2015). Maximizing competency education and blended learning: Insights from experts. CompetencyWorks Issue Brief. International Association for K-12 Online Learning.
  42. Pepin, B., Gueudet, G., & Trouche, L. (2013). Re-sourcing teachers' work and interactions: A collective perspective on resources, their use and transformation. ZDM The International Journal on Mathematics Education, 45(7), 929–943. https://doi.org/10.1007/s11858-013-0534-2
  43. Pepin, B., Biehler, R., & Gueudet, G. (2021). Mathematics in engineering education: A review of the recent literature with a view towards innovative practices. International Journal of Research in Undergraduate Mathematics Education, 7(2), 163-188. https://doi.org/10.1007/s40753-021-00139-8
  44. Philipp, R. A. (2007). Mathematics teachers' beliefs and affect. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning(pp. 257–318). Information Age Publishing.
  45. Polikoff, M. S., Rabovsky, S. J., Silver, D., & Lazar-Wolfe, R. (2021). The equitable distribution of opportunity to learn in mathematics textbooks. AERA Open, 7. https://doi.org/10.1177/23328584211065712
  46. Poulton, P. (2025). Preservice teachers as curriculum deliverers or curriculum-makers? Exploring curriculum-making conceptions and opportunities in professional experiences. Austrian Educational Researcher. 52, 2201–2227. https://doi.org/10.1007/s13384-025-00808-6
  47. Purnomo, Y. W. (2017). The complex relationship between teachers' mathematics‑related beliefs and their practices in mathematics class. The New Educational Review, 47(1), 200–210. https://doi.org/10.15804/tner.2017.47.1.16
  48. Reeves, D. B. (2003). High performance in high poverty schools: 90/ 90/ 90 and beyond. Center for Performance Assessment.
  49. Remillard, J. T. (2000). Can curriculum materials support teachers' learning? Two fourth-grade teachers' use of a new mathematics text. The Elementary School Journal, 100(4), 331–350. https://doi.org/10.1086/499645
  50. Schmidt, W. H., McKnight, C. C., & Raizen, S. A. (1997). A splintered vision: An investigation of U.S. science and mathematics education. Kluwer Academic Publishers.
  51. Schmidt, W. H., Wang, H. C., & McKnight, C. C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525–559. https://doi.org/10.1080/0022027042000294682
  52. Schoenfeld, A. H. (2010). How we think: A theory of goal‑oriented decision making and its educational applications. Routledge.
  53. Seaman, J. E., & Seaman, J. (2020). What we teach: K-12 educators' perceptions of curriculum quality. Bay View Analytics. https://www.onlinelearningsurvey.com/reports/k-12_whatweteach.pdf
  54. Short, D., & Fitzsimmons, S. (2007). Double the work: Challenges and solutions to acquiring language and academic literacy for adolescent English language learners. Carnegie Corporation of New York.
  55. Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  56. Stein, M. K., Remillard, J. T., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning(pp. 319–369). Information Age Publishing.
  57. Tanase, M., & Dinsmore, D. L. (2022). Mapping the interrelations between pre-service teachers' beliefs and knowledge of learning to their principles of effective instruction. Journal of School and Educational Psychology, 3(1), 1–21. https://doi.org/10.47602/josep.v3i1.28
  58. Tarr, J. E., Chávez, Ó., Reys, R. E., & Reys, B. J. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students' opportunity to learn. School Science and Mathematics, 106(4), 191–201. https://doi.org/10.1111/j.1949-8594.2006.tb18075.x
  59. Taylor, M. W. (2016). From effective curricula toward effective curriculum use. Journal for Research in Mathematics Education, 47(5), 440–453. https://doi.org/10.5951/jresematheduc.47.5.0440
  60. Thompson, A. G. (1984). The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105–127. https://doi.org/10.1007/BF00305892
  61. Thompson, L., Lantz, J., Sullivan, B. (2019). Pre-service teacher awareness of open educational resources. International Journal of Open Educational Resources, 1(2), 91-114. https://doi.org/10.18278/ijoer.1.2.6
  62. Wellberg, S. (2024). An examination of pre-service mathematics teachers' course-taking, beliefs, and preferred assessment practices. Journal of Mathematics Teacher Education. Advance online publication. https://doi.org/10.1007/s10857-024-09640-8