[논문]중등 예비교사의 교과서 과제 변형 및 수업 실행 중 나타난 과제의 특징 변화: 수학적 모델링 관점을 중심으로

정혜윤; 이지현

doi:10.7468/mathedu.2024.63.3.527

[국내논문] 중등 예비교사의 교과서 과제 변형 및 수업 실행 중 나타난 과제의 특징 변화: 수학적 모델링 관점을 중심으로
Investigating how the tasks' characteristics change according to modifying the textbook tasks and implementing the lesson by secondary preservice teachers: Focused on the mathematical modeling perspectives 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.63 no.3, 2024년, pp.527 - 547

정혜윤 (한국교육과정평가원) , 이지현 (인천대학교)

초록
AI-Helper

수학 교사가 수학적 모델링 수업을 위해 과제를 개발하고 수업을 설계하여 실행하는 데에는 많은 어려움이 있으며, 이와 같은 어려움은 학교수학에서 수학적 모델링 수업이 잘 실행되지 않는 원인으로 작용한다. 본 연구에서는 이와 같은 교사의 어려움을 개선하기 위하여, 중등 예비교사들이 수학 교과서 실세계 맥락 과제를 수학적 모델링 과제로 변형하고, 변형된 과제를 적용하여 수업을 실행하는 과정을 살펴보았다. 특히, 과제 변형과 수업 실행 과정에서, 수학적 모델링 과제의 특징이라고 할 수 있는 수학적 모델링 과정의 각 단계 및 과제의 개방성과 현실성이 어떻게 변화하는지 살펴보았다. 이를 위해, 중등 예비교사 의한 변형 전후 과제, 변형 전 과제 분석 결과 보고서, 과제 변형 보고서, 수업 실행 장면을 녹화, 녹음 및 전사한 자료, 수업 실행에 대한 동료평가와 자기평가를 수집하였으며, 사례 분석 절차에 따라 자료를 분석하였다. 연구 결과는 다음과 같다. 첫째, 예비교사들은 과제 변형 시 개방성과 변수 정의하기 단계 및 수학적 모델 도출하기 단계에 주목하는 경향을 보였으며, 이에 따라 변형된 과제에서는 변형 전과 비교하여 개방성과 변수 정의하기, 수학적 모델 도출하기 단계에 대한 학습 기회가 증진되었다. 둘째, 예비교사의 수업 실행 과정에서 변형된 과제의 개방성과 변수 정의하기, 수학적 모델 도출하기 단계가 다시 제한되는 경향이 나타났다. 셋째, 예비교사들은 위에서 언급한 수학적 모델링 과정의 단계들 외에 나머지 단계에 대하여 과제 변형과 수업 실행 과정에서 크게 주목하지 않았다. 이상의 연구결과를 토대로 예비교사들이 수학적 모델링 과제의 변형과 수업 실행 시 갖는 어려움을 확인하고 향후 수학적 모델링에 대한 예비교사교육의 시사점을 제안하였다.

Abstract ▼ AI-Helper

It is difficult for mathematics teachers to develop mathematical modeling tasks and implement mathematical modeling lessons for their students. These difficulties serve as a reason why mathematical modeling lessons are not implemented well in school mathematics. In this study, we aimed to examine how preservice mathematics teachers (PMTs) modify mathematical modeling tasks in mathematics textbooks as a way to develop mathematical modeling tasks and how they implement the mathematical modeling lesson. In particular, we focused on how the openness and reality reflected in the task and the mathematical modeling process change as PMTs modify the tasks. We collected data through PMTs' evaluation reports on analyzing textbook tasks, task modification, lesson plans and implementations, peer evaluation, and self-evaluation. Then, we analyzed these data according to the case analysis process. The findings revealed that when PMTs modified the textbook task, they focused on and improved the openness and the defining variables and the model stages of mathematical modeling process. However, when PMTs implemented lesson, the openness and the defining variables and the model stages of mathematical modeling process were restricted again. PMTs did not focus on other stages. Based on these results, the theoretical and practical implications of the study was discussed.

Keyword

표/그림 (14)

표 Table 1. Framework for analysis and modification of tasks and analysis of implemented tasks
그림 Figure 1. Textbook task selected by group A for modification (Lee et al., 2023, p. 127).
그림 Figure 2. Textbook task selected by group B for modification (Lew et al., 2023, p. 114).
그림 Figure 3. Textbook task selected by group C for modification (Koh, 2023, p. 48).
그림 Figure 4. Part of the report on task analysis and task modification.
그림 Figure 5. Part of preservice teachers' peer evaluation.
그림 Figure 6. Part of preservice teachers' self-assessment.
표 Table 2. The focus of the task modification
표 Table 3. The strategy of task modification
그림 Figure 7. Mathematical modeling task developed by group A.
그림 Figure 8. Mathematical modeling task developed by group B.
그림 Figure 9. Mathematical modeling task developed by group C.
표 Table 4. Characteristics of tasks before and after the modification for each group
표 Table 5. Characteristics of the planned and implemented tasks for each group

참고문헌 (61)

Alhammouri, A. M., & DiNapoli, J. (2023). Secondary teachers' perspectives on mathematical modeling and modeling？mathematics: Discovery, appreciation, and conflict. Research in Mathematical Education, 26(3), 203-233.
Alwast, A., & Vorhoelter, K. (2022). Measuring pre-service teachers' noticing competencies within a mathematical modeling context-an analysis of an instrument. Educational Studies in Mathematics, 109(2), 263-285.

상세보기
Andersson, A., Ryan, U., Herbel-Eisenmann, B., Huru, H. L., & Wagner, D. (2022). Storylines in public news media about？mathematics education and minoritized students. Educational Studies in Mathematics, 111(2), 323-343.

상세보기
Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation.？Journal of Mathematics Teacher Education, 19, 523-545.

상세보기
Baek, D. H., & Lee. K. H. (2018). Role and significance of abductive reasoning in mathematical modeling, Journal of Educational Research in Mathematics, 28(2), 221-240.

상세보기
Barquero, B., & Jessen, B. E. (2020). Impact of theoretical perspectives on the design of mathematical modelling task.？Avances de Investigacion en Educacion Matematica, 17, 98-113.
Berget, I. K. L. (2022). Mathematical modelling in textbook tasks and national examination in Norwegian upper secondary？school. Nordic Studies in Mathematics Education, 27(1), 51-70.
Bliss, K. M., Kavanagh, K. R., & Galluzzo, B. J. (2019). GAIMME-guidelines for assessment & instruction in mathematical？modeling education. Society for Industrial and Applied Mathematics.
Blomhoj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123-139.

상세보기
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The？proceedings of the 12th international congress on mathematical education - Intellectual and attitudinal challenges (pp.？73-96). Springer.
Borromeo Ferri, R. (2007). Modeling from a cognitive perspective: Individual modeling routes of pupils. In C. Haines, P.？Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 260-270).？Horwood.
Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in psychology, 3(2), 77-101.

상세보기
Burkhardt, H. (2018). Ways to teach modelling. A 50 year study. ZDM Mathematics Education, 50(1-2), 61-75.
Cai, J., Cirillo, M., Pelesko, J., Bommero Ferri, R., Borba, M., Geiger, V., Stillman, G., English, L. D., Wake, G., Kaiser, G.,？& Kwon, O. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional, and？teacher education perspectives. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of PME38. Vol. 1. (pp.？145-172). Vancouver, Canada: PME.
Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modelling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational？Studies in Mathematics, 109(2), 205-236.

상세보기
Choi, J. S. (2017). Prospective teachers' perception of mathematical modeling in elementary class. Journal of Educational？Research in Mathematics, 27(2), 313-328.
Creswell, J. W. (2016). Qualitative inquiry and research design (2nd ed.): Choosing among five approaches. Sage publications.
Dan, Q., & Xie, J. (2011). Mathematical modelling skills and creative thinking levels: An experimental study. In G. Kaiser, W.？Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 457-466).？Springer.
English, L. D. (2006). Mathematical modeling in the primary school: Children's construction of a consumer guide. Educational Studies in Mathematics, 63, 303-323.

상세보기
Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2022). Developing a task design and implementation framework for？fostering mathematical modelling competencies. Educational Studies in Mathematics, 109(2), 313-336.

상세보기
Goksen-Zayim, S., Pik, D., Dekker, R., & van Boxtel, C. (2021). Mathematical modelling in Dutch lower secondary education: An explorative study zooming in on conceptualization. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong？(Eds.), Mathematical modelling education in East and West (pp. 227-237). Cham: Springer International Publishing.
Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1), 111-129.
Gravemeijer, K., Stephan, M., Julie, C., Lin, F-L., & Ohtani, M. (2017). What mathematics education may prepare students？for the society of the future? International Journal of Science and Mathematics Education, 15(1), 105-123.
Han, S., & Hwang, J. (2023). Exploring mathematical modeling in classrooms: Insights from diverse studies. Research in？Mathematical Education, 26(3), 121-125.
Hartmann, L. M., & Schukajlow, S. (2021). Interest and emotions while solving real-world problems inside and outside the？classroom. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.) Mathematical modelling education in East？and West (pp. 153-163). Springer International Publishing.
Hartmann, L. M., Krawitz, J., & Schukajlow, S. (2021). Create your own problem! When given descriptions of real-world？situations, do students pose and solve modelling problems?. ZDM-Mathematics Education, 53(4), 919-935.

상세보기
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support？and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549.

상세보기
Hwang, S., & Han, S. (2023a). A study on mathematical modeling trends in Korea. Journal of Educational Research in？Mathematics, 33(3), 639-666.
Hwang, S., & Han, S. (2023b). In-service teacher's perception on the mathematical modeling tasks and competency for？designing the mathematical modeling tasks: Focused on reality. The Mathematical Education, 62(3), 381-400.
Jones, K., & Pepin, B. (2016). Research on mathematics teachers as partners in task design. Journal of Mathematics？Teacher Education, 19, 105-121.

상세보기
Jung, H. Y. & Lee, K. H. (2021). Promoting in-service teacher's mathematical modeling teaching competencies by implementing and modifying mathematical modeling tasks. Journal of Educational Research in Mathematics, 31(1), 35-62.

상세보기
Jung, H. Y. (2023). Analyzing an elementary school teacher's difficulties and knowledge improvement in the process of？modifying a mathematics textbook task to a mathematical modeling task: Focused on an experienced teacher. The？Mathematical Education, 62(3), 363-380.
Jung, H. Y., Lee, K. H., & Jung, J. H. (2020). Analyzing real world tasks of 6th grade textbook from a mathematical modeling perspective: Focused on the curriculum for revised 2011 and 2015. The Journal of Learner-Centered Curriculum？and Instruction, 20(18), 1313-1340.

상세보기
Jung, H., Stehr, E. M., & He, J. (2019). Mathematical modeling opportunities reported by secondary mathematics preservice teachers and instructors. School Science and Mathematics, 119(6), 353-365.

상세보기
Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.),？Mathematical modelling: Education, engineering and economics (pp. 110-119). Horwood Publishing.
Kaiser, G., & Schukajlow, S. (2022). Innovative perspectives in research in mathematical modelling education. In C.？Fernandez, S. Llinares, A. Gutierrez, & N. Planas (Eds.), Proceedings of the 45th conference of the international group？for the Psychology of Mathematics Education (Vol. 1, pp. 147-176). PME.
Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM, 38, 196-208.
Kim, H. S., & Pang, S. J. (2005). An analysis of cognitive demands of tasks in elementary mathematical instruction: Focusing on 'Ratio and Proportion'. Journal of Educational Research in Mathematics, 15(3), 251-272.
Kim, S. (2021). Analyzing tasks in the statistics area of Korean and Singaporean textbooks from the perspective of mathematical modeling: Focusing on 7th grade. Journal of the Korean School Mathematics Society, 24(3), 283-308.
Koh, S. E., Lee, J., Lee, S., Cha, S., Kim, Y., Oh, T., & Cho, S. (2022). High school mathematics 1. Sinsago.
Kohen, Z., & Gharra-Badran, Y. (2023). A rubric for assessing mathematical modelling problems in a scientific-engineering？context. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(3), 266-288.
Krawitz, J., Chang, Y. P., Yang, K. L., & Schukajlow, S. (2021). The role of reading comprehension in mathematical modelling: Improving the construction of a real model and interest in Germany and Taiwan. Educational Studies in Mathematics, 109, 337-359.
Lee, J. Y., Choi, B., Kim, D., Kim, S., Won, Y., Kang., H., Kim, S., & Kang, S. (2022). Middle school mathematics 2. Cheonjae Education.
Lew, H. C., Sunwoo, H., Shin, B., Cho, J., Kim, Y., Lee, B., Lim, M., Han, M., Nam, S., Kim, M., & Cheong, S. (2022). High？school mathematics 1. Cheonjae Education.
Maass, J., O'Meara, N., & Patrick Johnson, J. O. (2018). Mathematical modelling for teachers. Springer.
Maass, K. (2010). Classification scheme for modelling tasks. Journal Fur Mathematik-Didaktik, 31(2), 285-311.

상세보기
Meyer, D. (2015). Missing the promise of mathematical modeling. The Mathematics Teacher, 108(8), 578-583.

상세보기
Na, G. S., Park, M., Kim, D. W., Kim, Y., & Lee, S. J. (2018). Exploring the direction of mathematics education in the future？age. Journal of Educational Research in Mathematics, 28(4), 437-478.

상세보기
Park, E. Y., & Kwon, O. N. (2023). Comparison and analysis of middle school trigonometry textbook tasks and teacher design tasks: From the perspective of mathematical modelling. Journal of Learner-Centered Curriculum and Instruction,？23(7), 817-838.

상세보기
Park, S., & Han, S. (2018). Reconstruction and application of reforming textbook problems for mathematical modeling process. The Mathematical Education, 57(3), 289-309.
Park, W. H., & Choi-Koh, S. S. (2022). A comparative study on International Baccalaureate Diploma Programme (IBDP)？textbooks and Korean textbooks by the 2015 revised curriculum: Focus on function from a mathematical modeling perspective. Journal of the Korean School Mathematics Society, 25(2), 125-148.
Pepin, B., & Haggarty, L. (2001). Mathematics textbooks and their use in English, French and German classrooms: A way？to understand teaching and learning cultures. Zentralblatt fur Didaktik der Mathematik, 33, 158-175.
Song, H. J., Ka, Y., & Hwang, J. (2023). Exploring opportunities for mathematical modeling in Korean high school textbooks: An analysis of exponential and logarithmic function tasks. Research in Mathematical Education, 26(3), 253-270.
Stein, M. K., & Kaufman, J. H. (2010). Selecting and supporting the use of mathematics curricula at scale. American Educational Research Journal, 47, 663-693.

상세보기
Suh, J., Matson, K., Seshaiyer, P., Jamieson, S., & Tate, H. (2021). Mathematical modeling as a catalyst for equitable？mathematics instruction: Preparing teachers and young learners with 21st century skills. Mathematics, 9(2), 162.

상세보기
Tekin-Dede, A., & Bukova-Guzel, E. (2018). A Rubric Development Study for the Assessment of Modeling Skills. The？Mathematics Educator, 27(2), 33-72.
Vorholter, K., Greefrath, G., Borromeo Ferri, R., Leiss, D., & Schukajlow, S. (2019). Mathematical modelling. In H. N. Jahnke, & L. Hefendehl-Hebeker (Eds.), Traditions in German-speaking mathematics education research (pp. 91-114).？Cham, Switzerland: Springer.
Wegerif, R., & Dawes, L. (2004). Thinking and learning with ICT: Raising achievement in primary classrooms. Routledge？Falmer.
Yang, X., Schwarz, B., & Leung, I. K. (2022). Pre-service mathematics teachers' professional modeling competencies: A？comparative study between Germany, Mainland China, and Hong Kong. Educational Studies in Mathematics, 109(2),？409-429.

상세보기
Yin, R. K. (2003). Case study research: Design and methods. Sage Publications.

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