Students’ Reasoning about Variability in Graphs during an Introductory Statistics Course

Rachel Chaphalkar; Ke Wu

doi:10.29333/iejme/7602

Full Text (PDF)

Rachel Chaphalkar ¹ ^* , Ke Wu ²

More Detail

¹ University of Wisconsin – Whitewater, USA² University of Montana, USA^* Corresponding Author

Abstract

Variation and variability are key concepts in K-16 statistics education. Prior research has investigated students’ reasoning about variability in different contexts. However, there is a lack of research on students’ development of understanding of variability when comparing distributions in bar graphs, dot plots, and histograms as they took an introductory college-level statistics course. This exploratory case study conducted three interviews with each of the ten participants through a four-month period, at the beginning, middle, and end of the course. The Structure of Observed Learning Outcomes (SOLO) taxonomy was used to analyze participants’ responses. Results indicated that overall the group of participants demonstrated a stable understanding of variability over the semester (i.e. lack of improvement). However, when examining each student’s reasoning, four types of reasoning development paths were found: improvement, lack of change, decline, and inconsistent. This study provides implications in teaching college introductory statistics course and recommendations for future research.

Keywords

statistical reasoning
college introductory statistics
distribution comparisons
qualitative case study

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 15, Issue 2, May 2020, Article No: em0580

https://doi.org/10.29333/iejme/7602

Publication date: 26 Jan 2020

Article Views: 2386

Article Downloads: 1639

Open Access References How to cite this article

References

Battista, M. T. (2011). Conceptualizations and issues related to learning progressions, learning trajectories, and levels of sophistication. The Mathematics Enthusiast, 8(3), 507-570.
Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal, 3(2), 42-63.
Biggs, J. B., & Collis, K. F. (1991). Multimodal learning and the quality of intelligent behaviour. Intelligence: Reconceptualization and Measurement, 57-76.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York, NY: NCTM/Macmillan Publishing Co.
Common Core State Standards Initiative. (2010). Common core state standards for mathematics, Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
Cooper, L. L., & Shore, F. S. (2008). Students’ misconceptions in interpreting center and variability of data represented via histograms and stem-and-leaf plots. Journal of Statistics Education, 16(2), 1-13. https://doi.org/10.1080/10691898.2008.11889559
Cooper, L. L., & Shore, F. S. (2010). The effects of data and graph type on concepts and visualizations of variability. Journal of Statistics Education, 18(2), 1-16. https://doi.org/10.1080/10691898.2010.11889487
Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches (4^th ed.), Los Angeles, CA: Sage Publications.
delMas, R., & Liu, Y. (2005). Exploring students’ conceptions of the standard deviation. Statistics Education Research Journal, 4(1), 55-82.
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.
DeVeaux, R. D., Velleman, P. F., & Bock, D. E. (2013). Intro Stats (4^th custom ed.), Boston, MA: Addison Wesley.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K -12 curriculum framework. Alexandria, VA: American Statistical Association.
Friel, S. N., & Bright, G. W. (1995). Graph knowledge: Understanding how students interpret data using graphs. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH. Retrieved from https://files.eric.ed.gov/fulltext/ED391661.pdf
GAISE College Report ASA Revision Committee (2016). Guidelines for assessment and instruction in statistics education college report 2016. Retrieved from www.amstat.org/education/gaise
Garfield, J., & Alhgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for Research in Mathematics Education, 19(1), 44-63. https://doi.org/10.2307/749110
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1- 27). Hilladale, NJ: Lawrence Erlbaum Associates, Inc.
Jones, D. L., & Scariano, S. M. (2014). Measuring the variability of data from other values in the set. Teaching Statistics, 36(3), 93-96. https://doi.org/10.1111/test.12056
Kadar, G. D., & Perry, M. (2007). Variability for Categorical Variables. Journal of Statistics Education, 15(2). https://doi.org/10.1080/10691898.2007.11889465
Kaplan, J. J., Gabrosek, J. G., Curtiss, P., & Malone, C. (2014). Investigating student understanding of histograms. Journal of Statistics Education, 22(2). https://doi.org/10.1080/10691898.2014.11889701
Kaplan, J., Fisher, D., & Rogness, N. (2010). Lexical ambiguity in statistics: How students use and define the words: Association, average, confidence, random and spread. Journal of Statistics Education, 18(2), 1-22. https://doi.org/10.1080/10691898.2010.11889491
Leavy, A. M., & Middleton, J. A. (2011). Elementary and middle grades students’ constructions of typicality. Journal of Mathematical Behavior. 30(3), 235-254. https://doi.org/10.1016/j.jmathb.2011.03.001
Lunsford, M. L., Rowell, G. H., & Goodson-Espy, T. (2006). Classroom research: Assessment of student understanding of sampling distributions of means and the central limit theorem in post-calculus probability and statistics classes. Journal of Statistics Education, 14(3). https://doi.org/10.1080/10691898.2006.11910587
Onwuegbuzie, A. J., & Leech, N. L. (2007). A call for qualitative power analyses. Quality & Quantity, 41(1), 105-121. https://doi.org/10.1007/s11135-005-1098-1
Peters, S. A. (2011). Robust understanding of statistical variation. Statistics Education Research Journal, 10(1), 52-88.
Pfaff, T. J., & Weinberg, A. (2009). Do hands-on activities increase student understanding?: A case study. Journal of Statistics Education, 17(3). https://doi.org/10.1080/10691898.2009.11889536
Reading, C. (2004). Student description of variation while working with weather data. Statistics Education Research Journal, 3(2), 84-105.
Shaughnessy, J. M., Ciancetta, M., & Canada, D. (2004, July). Types of student reasoning on sampling tasks. In Proceedings of the 28th International Group for the Psychology of Mathematics Education (pp. 177-184), Vol. 4.
Watson, J. M. (2001). Longitudinal development of inferential reasoning by school students. Educational Studies in Mathematics, 47(3), 337-372. https://doi.org/10.1023/A:1015158813656
Watson, J. M. (2002). Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics, 51(3), 225-256. https://doi.org/10.1023/A:1023622017006
Watson, J. M. (2009). The influence of variation and expectation on the developing awareness of distribution. Statistics Education Research Journal, 8(1), 32-61.
Watson, J. M., & Moritz, J. B. (1999). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37(2), 145-168. https://doi.org/10.1023/A:1003594832397
Watson, J. M., Callingham, R. A., & Kelly, B. A. (2007). Students’ appreciation of expectation and variation as a foundation for statistical understanding. Mathematical Thinking and Learning, 9(2), 83-130. https://doi.org/10.1080/10986060709336812
Watson, J. M., Collis, K. F., Callingham, R. A., & Moritz, J. B. (1995). A model for assessing higher order thinking in statistics. Educational Research and Evaluation, 1(3), 247-275. https://doi.org/10.1080/1380361950010303
Watson, J. M., Kelly, B. A. Callingham, R. A., & Shaughnessy, J. M. (2003). The measurement of school students’ understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1-29. https://doi.org/10.1080/0020739021000018791
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. (2017). Case study research and applications: Design and methods. Los Angeles, CA: Sage publications. https://doi.org/10.1002/col.22052
Zieffler, A. S., & Garfield, J. B. (2009). Modeling the growth of students’ covariational reasoning during an introductory statistics course. Statistics Education Research Journal, 8(1), 7-31.

How to cite this article

APA

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

Vancouver

Chaphalkar R, Wu K. Students’ Reasoning about Variability in Graphs during an Introductory Statistics Course. INT ELECT J MATH ED. 2020;15(2):em0580. https://doi.org/10.29333/iejme/7602

AMA

Chaphalkar R, Wu K. Students’ Reasoning about Variability in Graphs during an Introductory Statistics Course. INT ELECT J MATH ED. 2020;15(2), em0580. https://doi.org/10.29333/iejme/7602

Chicago

Chaphalkar, Rachel, and Ke Wu. "Students’ Reasoning about Variability in Graphs during an Introductory Statistics Course". International Electronic Journal of Mathematics Education 2020 15 no. 2 (2020): em0580. https://doi.org/10.29333/iejme/7602

Harvard

Chaphalkar, R., and 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

MLA

Chaphalkar, Rachel et al. "Students’ Reasoning about Variability in Graphs during an Introductory Statistics Course". International Electronic Journal of Mathematics Education, vol. 15, no. 2, 2020, em0580. https://doi.org/10.29333/iejme/7602