Pre-service Teachers’ Understanding of Graphs in Statistics in the Context of Lesson Study

Year 2024, Volume: 6 Issue: 1, 16 - 29, 30.06.2024

Nadide Yılmaz , İffet Yetkin

https://doi.org/10.51535/tell.1318693

Abstract

This study aims to examine pre-service teachers’ understandings of graphs and how their understandings about graphs have transformed into instructional practices as they participated in a lesson study. It was employed case study and three pre-service teachers participated. They initially viewed graphs as tools for organizing and representing data. As the lesson study progressed, they began to view graphs as tools to answer statistical questions. This fundamental transformation in their understanding resulted in a change in how they designed and implemented their lesson plans. They designed tasks around a statistical question and made connections with this question while deciding the type of graph and interpreting the graph. In addition, they anticipated students’ possible conceptions. Hence, for these pre-service teachers, understanding the role graphs as tools to answer statistical questions can be considered as a key development understanding (KDU), which was built on multiple experiences of designing, implementing and evaluating lessons.

Keywords

Pre-service teachers, key developmental understandings, graphs, lesson study.

Project Number

2211-A

References

• Ader, E. (2018). Programlardaki veri ve olasılık öğrenme alanı içeriklerine karşılaştırmalı bir bakış” [A comparative look at data and probability learning area contents in programs] In M. F. Özmantar, H. Akkoç, B. Kuşdemir Kayıran, & M. Özyurt (Ed.) Ortaokul Matematik Öğretim Programları: Tarihsel bir İnceleme (pp. 275-306). Pegem Akademi.
• Ari, E. (2010). The difficulties in learning the subject of probability and statistics in maths lessons of 6th, 7th and 8th grades in primary school and suggestions on solution. [Unpublished master thesis]. Afyon Kocatepe University.
• Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., and Spangler, D. (2020). Pre-K-12 Guidelines for assessment and instruction in statistics education (GAISE) report II. American Statistical Association and National Council of Teachers of Mathematics.
• Ben-Zvi, D. (2011). Statistical reasoning learning environment. Revista de Educação Matemática e Tecnológica Iberoamericana, 2, 1-13.
• Boote, S. K. (2014). Assessing and understanding line graph interpretations using a scoring rubric of organized cited factors. Journal of Science Teacher Education, 25(3), 333–354. https://doi.org/10.1007/s10972-012-9318-8.
• Bright, G. W. & Friel, S. N. (2011). Graphical Representations: Helping students interpret data. In S. P. Lajoie (Ed.) Reflections on statistics: Learning, teaching, and assessment in grades K-12. (pp. 63-88). Routledge.
• Buforn, A. & Fernández, C. (2014). The role of prospective teachers’ mathematical knowledge in recognizing students’ understanding: the process of unitizing, G. Adams. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 34(3) November 2014.
• Burgess, T. A. (2007). Investigating the nature of teacher knowledge needed and used in teaching statistics. [Unpublished doctoral dissertation]. Massey University.
• Chick, H. L. 2004. Tools for transnumeration: Early stages in the art of data representation. In I. Putt, R. Faragher, & M. McLean (Eds.), Mathematics Education for the Third Millennium: Towards 2010. Proceedings of the Twenty-seventh Annual Conference of the Mathematics Education Research Group of Australasia (pp. 167–174). MERGA.
• Chick, H. L. & Pierce, R. U. (2008). Teaching statistics at the primary school level: Beliefs, affordances, and pedagogical content knowledge. In C. Batanero, G. Burrill, C. Reading & A. Rossman (Ed.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008IASE Round Table Conference. Monterrey: ICMI and IASE.
• Cobb, P. & McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning, In D. Ben-Zvi and J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 375-396). Kluwer Academic Publishers
• Fernández, C.; Sánchez-Matamoros, G.; Valls, J. and Callejo, M., L. (2018). Noticing students’ mathematical thinking: characterization, development and contexts. Avances de Investigación en Educación Matemática, 13, 39-61. https://doi.org/10.35763/aiem.v0i13.229.
• Franklin, C. A., Bargagliotti, A. E., Case, C. A., Kader, G. D., Scheaffer, R. L., and Spangler, D. A. (2015). Statistical education of teachers (SET). VA: American Statistical Association
• Groth, R. E. (2013). Characterizing key developmental understandings and pedagogically powerful ideas within a statistical knowledge for teaching framework. Mathematical Thinking and Learning, 15, 121-145. https://doi.org/10.1080/10986065.2013.770718.
• Heaton, R. M. & Mickelson, W. T. (2002). The learning and teaching of statistical investigation teaching and teacher education. Journal of Mathematics Teacher Education, 5(1), 35–59. https://doi.org/10.1023/A:1013886730487.
• Huang, R. (2014). Prospective mathematics teachers’ knowledge of algebra: A comparative study in China and the United States of America. Springer.
• Ijeh, S. B. (2012). How competent mathematics teachers develop pedagogical content knowledge in statistics teaching. [Unpublished doctoral dissertation]. University of Pretoria.
• Lee, H. S., Kersaint, G., Harper, S. R., Driskell, S. O., Jones, D. L., Leatham, K. R., Angotti, R. L. and Adu-Gyamfi, K. (2014). Teachers' use of transnumeration in solving statistical tasks with dynamic statistical software. Statistics Education Research Journal, 13(1), 25-52.
• Litke, E., & Hill, H. C. (2020). Exploring central tendencies: The teaching of data and statistics in elementary mathematics classrooms. The Elementary School Journal, 120(3), 480–506. https://doi.org/10.1086/707007.
• Llinares, S., Fernández, C., & Sánchez-Matamoros, G. (2016). Changes in How Prospective Teachers Anticipate Secondary Students’ Answers. Eurasia Journal of Mathematics, Science and Technology Education, 12(8), 2155-2170. https://doi.org/10.12973/eurasia.2016.1295a.
• Matthews, M., Hlas, C. S. and Finken, T. M. 2009. Using lesson study and four-column lesson planning with preservice teachers: Lessons from lessons. Mathematics Teacher, 102(7), 504- 509. https://doi.org/10.5951/MT.102.7.0504.
• Mercimek, O. (2013). Assessment of preservice mathematics teachers’ knowledge for teaching statistics. [Unpublished doctoral dissertation]. Middle East Technical University.
• Ministry of National Education [MoNE]. (1968). İlkokul matematik programı [Primary school mathematics curricula]. Milli Eğitim Basımevi
• Ministry of National Education [MoNE]. (1983). İlkokul matematik programı [Primary school mathematics curricula]. Milli Eğitim Basımevi
• Ministry of National Education [MoNE]. (1990). İlköğretim matematik dersi programı [Elementary school mathematics curricula]. Milli Eğitim Basımevi
• Ministry of National Education [MoNE]. (1998). İlköğretim okulu matematik dersi öğretim programı [Elementary school mathematics curricula]. Milli Eğitim Basımevi
• Ministry of National Education [MoNE]. (2005). İlköğretim matematik programı [Elementary school mathematics curricula]. Milli Eğitim Basımevi. Ministry of National Education [MoNE]. (2013). Ortaokul Matematik Dersi (5,6,7, ve 8. Sınıf) Öğretim Programı [Middle school mathematics (5,6,7, and 8. grades) curricula]. Milli Eğitim Yayınevi.
• Ministry of National Education [MoNE]. (2018). Matematik dersi (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar) öğretim programı [Primary and middle school mathematics curricula for grades 1, 2, 3, 4, 5, 6, 7, and 8]. Milli Eğitim Basımevi.
• Monk, S. (2003). Representation in school mathematics: Learning to graph and graphing to learn. In J. Kilpatrick (Ed.), A research companion to principles and standards for school mathematics (pp. 250–262). VA: NCTM.
• National Council of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. VA: Author.
• Patahuddin, S.M., Lowrie, T. (2019) Examining Teachers’ Knowledge of Line Graph Task: a Case of Travel Task. International Journal of Science and Mathematics Education, 17, 781–800. https://doi.org/10.1007/s10763-018-9893-z.
• Pfannkuch, M. & Wild, C. J. (2004). Towards an understanding of statistical thinking. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 17–46). Kluwer Academic Publishers.
• Reston, E., Jala, L., & Edullantes, T. (2006). Probing college statistics teachers’ instructional goals and classroom practices within a statistical literacy framework. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education: Proceedings of the 7th International Conference on Teaching Statistics, Salvador, Brazil. International Association for Statistical Education and International Statistical Institute: Voorburg, The Netherlands.
• Rhee, K. L. (2012). Teachers’ explanations of a key developmental understandings of multiplicative reasoning. [Unpublished doctoral dissertation]. Drexel University.
• Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing preservice teachers' noticing of students' understanding of the derivative concept. International Journal of Science and Mathematics Education, 13(6), 1305-1329. https://doi.org/10.1007/s10763-014-9544-y.
• Shah, P. & Hoeffner, J. (2002). Review of graph comprehension research: Implications for instruction. Educational Psychology Review, 14, 47–69. https://doi.org/10.1023/A:1013180410169.
• Silverman, J. (2005). An investigation of content knowledge for teaching: Understanding its development and its influence on pedagogy. [Unpublished doctoral dissertation]. Vanderbilt University.
• Silverman, J. & Thompson, P. W. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499–511. https://doi.org/10.1007/s10857-008-9089-5.
• Simon, M. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical Thinking and Learning, 8(4), 359– 371.https://doi.org/10.1207/s15327833mtl0804_1.
• Sorto, M. A. (2004). Prospective middle school teachers’ knowledge about data analysis and its application to teaching. [Unpublished doctoral dissertation]. Michigan State University.
• Şeker-Akın, V. (2023). How do mathematics teachers teach statistics? A comprehensive examination of statistical problem-solving process and instructional quality [Unpublished doctoral dissertation]. Middle East Technical University.
• Van de Walle, J. A., Karp, K. S., and Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally. Pearson Education. Wild, C. J. & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x.
• Zhang, S. and Cheng, Q. (2011). Learning to Teach Through a Practicum-Based Microteaching Model. Action in Teacher Education, 33(4), 343-358. https://doi.org/10.1080/01626620.2011.620523.