A preservice middle school mathematics teacher’s knowledge of student thinking about line graphs
Aytug Ozaltun Celik 1 *
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1 Pamukkale University, Turkey
* Corresponding Author

Abstract

Interpreting statistical graphs and making inferences based on the graphs are a precursor for formal statistical inferences. To support student inferences, both teachers and future teachers should have adequate knowledge regarding students’ thinking on graphs as well as their potential misinterpretations and difficulties in interpreting graphs. In this qualitative case study, I examined a preservice middle school mathematics teacher’s knowledge of student thinking about interpretation of line graphs. During her practicum course, preservice teacher planned a lesson to teach creating and interpreting line graphs. I first interviewed with her on the lesson plan and then observed her teaching the subject. The data indicated that the preservice mathematics teacher’s actions regarding knowledge of student thinking before and during the lesson supported the students in interpreting graphs beyond reading. Preservice and in-service teachers with more knowledge of student thinking would provide teaching practices to support students’ learning of statistical graphs. I thus suggest that a curriculum may be designed for improving preservice mathematics teachers’ knowledge of student thinking about statistical concepts and informal statistical inferences.

Keywords

References

  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172. https://doi.org/10.1023/b:jmte.0000021943.35739.1c
  • Ball, D. L., Sleep, L., Boerst, T., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. The Elementary School Journal, 109(5), 458-474. https://doi.org/10.1086/596996
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal for Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
  • Ben-Zvi, D., & Makar, K. (2016). International perspectives on the teaching and learning of statistics. In D. Ben-Zvi & K. Makar (Eds.), The teaching and learning of statistics: International perspectives (pp. 1-10). Springer. https://doi.org/10.1007/978-3-319-23470-0_1
  • Brendefur, J.L., Thiede, K., Strother, S., Bunning, K., & Peck, D. (2013). Developing mathematical thinking: Changing teachers’ knowledge and instruction. Journal of Curriculum and Teaching, 2(2), 62-75. https://doi.org/10.5430/jct.v2n2p62
  • Bruno, A., & Espinel, M. C. (2009). Construction and evaluation of histograms in teacher training. International Journal of Mathematical Education in Science and Technology, 40(4), 473-493. https://doi.org/10.1080/00207390902759584
  • Catman Aksoy, E., & Isiksal Bostan, M. (2020). Seventh graders’ statistical literacy: an investigation on bar and line graphs. International Journal of Science and Mathematics Education, 19, 397-418. https://doi.org/10.1007/s10763-020-10052-2
  • Chaphalkar, R., & Wu, K. (2020). Students’ reasoning about variability in graphs during an introductory statistics course. International Electronic Journal of Mathematics Education, 15(2), em0580. https://doi.org/10.29333/iejme/7602
  • Chapman, O. (2004). Facilitating peer interactions in learning mathematics: teachers’ practical knowledge. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2, 191–198.
  • Chick, H. L., & Pierce, R. (2011). Teachers’ beliefs about statistics education. In C. Batanero, G. Burrill, & C. Reading (Eds.), New ICMI study series: Vol. 14. Teaching statistics in school mathematics-challenges for teaching and teacher education: A joint ICMI/IASE study: The 18th ICMI Study (pp. 151–162). Springer. https://doi.org/10.1007/978-94-007-1131-0_17
  • Chick, H. L., & Pierce, R. (2013). The statistical literacy needed to interpret school assessment data. Mathematics Teacher Education and Development, 15(2), 5–26.
  • Common Core State Standards Initiative (CCSSI). (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • Conference Board of the Mathematical Sciences (CBMS) (2012). The mathematical education of teachers II. American Mathematical Society and Mathematical Association of America.
  • Creswell, J. W. (2013). Qualitative inquiry and research design: Choosing among five approaches. (3rd ed.). Sage.
  • Çakıroğlu, Ü., & Güler, M. (2021). Enhancing statistical literacy skills through real life activities enriched with gamification elements: An experimental study. E-Learning and Digital Media, 18(5), 441-459. https://doi.org/10.1177/2042753020987016
  • da Ponte, J. P. (2011). Preparing teachers to meet the challenges of statistics education. In C. Batanero, G. Burill, C. Reading (Eds.), Teaching statistics in school mathematics-Challenges for teaching and teacher education (pp. 299-309). Springer. https://doi.org/10.1007/978-94-007-1131-0_29
  • de Vetten, A., Schoonenboom, J., Keijzer, R., & van Oers, B. (2018). The development of informal statistical inference content knowledge of preservice primary school teachers during a teacher college intervention. Educational studies in Mathematics, 99(2), 217-234. https://doi.org/10.1007/s10649-018-9823-6
  • delMas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing students’ conceptual understanding after a first course in statistics. Statistics Education Research Journal, 6(2), 28–58.
  • Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70, 1-51. https://doi.org/10.1111/j.1751-5823.2002.tb00336.x
  • Gal, I. (2004). Statistical literacy. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 47-78). Springer. https://doi.org/10.1007/1-4020-2278-6_3
  • Galesic, M., & Retamero-Garcia, R. (2011). Graph literacy: A cross-cultural comparison. Medical Decision Making, 31(3), 444-457.
  • Glazer, N. (2011). Challenges with graph interpretation: A review of the literature. Studies in Science Education, 47(2), 183-210. https://doi.org/10.1080/03057267.2011.605307
  • Guest, G., MacQueen, K. M., & Namey, E. E. (2012). Validity and reliability (credibility and dependability) in qualitative research and data analysis. In G. Guest, K. M. MacQueen & E. E. Namey (Eds.), Applied thematic analysis (pp. 79–106). Sage.
  • Guler, M., Gursoy, K., & Guven, B. (2016). Critical views of 8th grade students toward statistical data in newspaper articles: Analysis in light of statistical literacy. Cogent Education, 3(1), 1268773. https://doi.org/10.1080/2331186X.2016.1268773
  • Hiebert, J., Berk, D., Miller, E., Gallivan, H., & Meikle, E. (2019). Relationships between opportunity to learn mathematics in teacher preparation and graduates' knowledge for teaching mathematics. Journal for Research in Mathematics Education, 50(1), 23-50. https://doi.org/10.5951/jresematheduc.50.1.0023
  • Hill, H., Ball, D., & Schilling, S. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400. https://doi.org/10.5951/jresematheduc.39.4.0372
  • Leavy, A. M. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9(1), 46–67.
  • Lee, K. (2006). Teachers’ knowledge of middle school students’ mathematical thinking in algebra word problem solving [Unpublished doctoral dissertation]. Oregon State University, Corvallis, USA.
  • Makar, K., & Rubin, A. (2009). A framework for thinking about informel statistical inference. Statistics Education Research Journal, 8(1), 82-105.
  • Monteiro, C., & Ainley, J. (2004). Interpretation of media graphs and critical sense: Implications for teaching and teachers [Paper presentation]. 10th International Congress on Mathematics Education, Copenhague, Denmark.
  • National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Author.
  • Ozaltun, A. (2014). Professional development of mathematics teachers: Reflection of knowledge of student thinking on teaching [Unpublished master’s thesis]. Dokuz Eylül University, İzmir, Turkey.
  • Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Developing young students’ informal inference skills in data analysis. Statistics Education Research Journal, 7(2), 83-106.
  • 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(4), 781-800. https://doi.org/10.1007/s10763-018-9893-z
  • Patton, M. Q. (2002). Qualitative research & evaluation methods. Sage.
  • Pfannkuch, M. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13(1-2), 27-46. https://doi.org/10.1080/10986065.2011.538302
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189x015002004.
  • 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
  • Smith, M., Bill, V., & Hughes, E. (2008). Thinking through a lesson: Successfully implementing high level tasks. Mathematics Teaching in the Middle School, 14(3), 132-138. https://doi.org/10.5951/mtms.14.3.0132
  • Takker, S., & Subramaniam, K. (2012). Understanding teacher's knowledge of and responses to students' mathematical thinking. In S. J. Cho (Ed.), Proceedings of the 12th international congress on mathematical education (ICME-12) (pp. 4906-4915). SpringerOpen.
  • Tchoshanov, M. A. (2010). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76, 141–164. https://doi.org/10.1007/s10649-010-9269-y
  • Van Zoest, L. R., & Stockero, S. L. (2008). Using a video-case curriculum to develop preservice teachers’ knowledge and skills. AMTE Monograph, 4, 117-132.
  • Wallman, K. K. (1993). Enhancing statistical literacy: Enriching our society. Journal of the American Statistical Association, 88(421), 1-8. https://doi.org/10.2307/2290686
  • Watson, J., & Moritz, J. (1998). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37, 145-168. https://doi.org/10.1023/A:1003594832397
  • Whitaker, D., & Jacobbe, T. (2017). Students' understanding of bar graphs and histograms: Results from the LOCUS assessments. Journal of Statistics Education, 25(2), 90-102. https://doi.org/10.1080/10691898.2017.1321974
  • Yin, R. K. (2014). Case study research: Design and methods (5th ed.). SAGE Publications.
  • Zeichner, K., & Conklin, H. G. (2008). Teacher education programs as sites for teacher preparation. In M. Cochran-Smith, S. Feiman-Nemser, J. D. McIntyre, & K. E. Demers (Eds.) Handbook of research on teacher education: Enduring questions in changing contexts, (pp. 269-289). Routledge/Association of Teacher Educators.

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