Educational Studies in Mathematics

, Volume 92, Issue 2, pp 163–177 | Cite as

Students’ use of slope conceptualizations when reasoning about the line of best fit

  • Stephanie A. CaseyEmail author
  • Courtney Nagle


Learning experiences regarding the line of best fit are typically students’ first encounters with the fundamental topic of statistical association. Students bring with them into these learning experiences prior knowledge and experiences about mathematical lines and their properties, namely slope. This study investigated the role students’ conceptions of slope play in their conceptualization of the line of best fit and approaches to placing it informally (i.e., by eye). Task-based interviews concerning the meaning and placement of the line of best fit conducted with seven grade 8 students were analyzed for this study. The results showed that students’ conceptualizations of slope can play a significant role in their reasoning about the line of best fit, in both productive and unproductive ways. Analysis of associations between slope conceptualizations and students’ criteria for placing the line, accuracy of the placed line, and meaning of the line of best fit are presented. The discussion highlights implications of the study for the teaching of lines in both mathematical and statistical settings.


Statistics education Statistical association Slope Line of best fit Linear regression 


  1. Akkerman, S. F., & Bakker, A. (2011). Boundary crossing and boundary objects. Review of Educational Research, 81(2), 132–169.CrossRefGoogle Scholar
  2. Arbaugh, F., Herbel-Eisenmann, B., Ramirez, N., Knuth, E., Kranendonk, H., & Quander, J. R. (2010). Linking research and practice: The NCTM research agenda conference report. Reston, VA: NCTM. Retrieved from
  3. Bakker, A. (2004). Reasoning about shape as a pattern in variability. Statistics Education Research Journal, 3(2), 64–83.Google Scholar
  4. Casey, S. (2015). Examining student conceptions of covariation: A focus on the line of best fit. Journal of Statistics Education, 23(1).Google Scholar
  5. Cobb, P., McClain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21, 1–78.CrossRefGoogle Scholar
  6. Common Core Standards Writing Team. (2013). Progressions for the common core state standards in mathematics (draft). Front matter, preface, introduction. Grade 8, High School, Functions. Tucson, AZ: Institute for Mathematics and Education, University of Arizona. Retrieved from
  7. Common Core State Standards Initiative (CCSSI). (2010). Common core state standards for mathematics. Washington, D.C.: Author.Google Scholar
  8. Estepa, A., & Batanero, C. (1996). Judgments of correlation in scatterplots: Students’ intuitive strategies and preconceptions. Hiroshima Journal of Mathematics Education, 4, 25–41.Google Scholar
  9. Estepa, A., & Sanchez-Cobo, F. T. (2003). Evaluacion de la comprension de la correlacion y regression a partir de la resolucion de problemas. Statistics Education Research Journal, 2(1), 54–68.Google Scholar
  10. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). Guidelines for Assessment and Instruction in Statistics Education (GAISE) report: A PreK-12 curriculum framework. Alexandria, VA: American Statistical Association.Google Scholar
  11. Garfield, J. B., & Ben-Zvi, D. (2004). Research on statistical literacy, reasoning, and thinking: Issues, challenges, and implications. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 397–409). Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar
  12. Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory. Chicago, IL: Aldine.Google Scholar
  13. Groth, R. E. (2015). Working at the boundaries of mathematics education and statistics education communities of practice. Journal for Research in Mathematics Education, 46(1), 4–16.CrossRefGoogle Scholar
  14. Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289.CrossRefGoogle Scholar
  15. Moore, D. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). Washington, D.C.: National Academy Press.Google Scholar
  16. Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. (2013). Calculus students’ and instructors conceptualizations of slope: A comparison across academic levels. International Journal of Science and Mathematics Education, 11, 1491–1515.CrossRefGoogle Scholar
  17. Nolan, C., & Herbert, S. (2015). Introducing linear functions: An alternative statistical approach. Mathematics Education Research Journal, 27(4), 401–421.CrossRefGoogle Scholar
  18. Qualifications and Curriculum Authority. (2007). The national curriculum 2007. Earlsdon Park, Coventry: Author.Google Scholar
  19. Roschelle, J. (1995). Learning in interactive environments: Prior knowledge and new experience. In J. H. Falk & L. D. Dierking (Eds.), Public institutions for personal learning: Establishing a research agenda (pp. 37–51). Washington, DC: American Association of Museums.Google Scholar
  20. Zaslavsky, O., Sela, H., & Leron, U. (2002). Being sloppy about slope: The effect of changing the scale. Educational Studies in Mathematics, 49, 119–140.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Eastern Michigan UniversityYpsilantiUSA
  2. 2.Penn State Erie, The Behrend CollegeErieUSA

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