Correlation and Regression in the Training of Teachers

  • Joachim Engel
  • Peter Sedlmeier
Part of the New ICMI Study Series book series (NISS, volume 14)


Although the notion of functional dependence of two variables is fundamental to school mathematics, teachers often are not trained to analyse statistical dependencies. Many teachers’ thinking about bivariate data is shaped by the deterministic concept of a mathematical function. Statistical data, however, usually do not perfectly fit a deterministic model but are characterised by variation around a possible trend. Therefore, understanding regression and correlation requires, apart from basic knowledge about functions, an appreciation of the role of variation. In this chapter, common errors and fallacies related to the concepts of correlation and regression are revisited and suggestions on how teachers may overcome some of these difficulties are provided.


Mathematics Teacher Statistical Concept Local Conception Previous Belief Bivariate Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Anscombe, F. J. (1973). Graphs in statistical analysis. American Statistician, 27, 17–21.Google Scholar
  2. Batanero, C., Estepa, A., & Godino, J. (1997). Evolution of students’ understanding of statistical association in a computer-based teaching environment. In J. Garfield & G. Burrill (Eds.), Research on teaching statistics and new technologies (pp. 191–206). Voorburg, The Netherlands: International Statistical Institute.Google Scholar
  3. Blum, W., Galbraith, P., Henn, H., & Niss, M. (2002). Modelling and applications in mathematics education: The 14th ICMI Study. New York: Springer.Google Scholar
  4. Castro-Sotos, A. E., Van Hoof, S., Van den Noortgate, W., & Onghena, P. (2009). The transitivity misconception of Pearson’s correlation coefficient. Statistics Education Research Journal, 8(2), 33–55.Google Scholar
  5. Chapman, L. J., & Chapman, J. P. (1969). Illusory correlation as an obstacle to the use of valid psychodiagnostic signs. Journal of Abnormal Psychology, 74, 271–280.CrossRefGoogle Scholar
  6. Engel, J. (2009). Anwendungsorientierte Mathematik: Von Daten zur Funktion (Application oriented mathematics: From data to functions). Heidelberg: Springer.Google Scholar
  7. Engel, J., & Sedlmeier, P. (2005). On middle-school students’ comprehension of randomness and chance variability in data. Zentralblatt für Didaktik der Mathematik, 37(3), 168–179.CrossRefGoogle Scholar
  8. Engel, J., Sedlmeier, P., & Wörn, C. (2008). Modeling scatterplot data and the signal-noise metaphor: Towards statistical literacy for pre-service teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey, Mexico: International Commission on Mathematical Instruction and International Association for Statistical Education. Online:
  9. Erlick, D. E., & Mills, R. G. (1967). Perceptual quantification of conditional dependency. Journal of Experimental Psychology, 73(1), 9–14.CrossRefGoogle Scholar
  10. Estepa, A., & Batanero, C. (1996). Judgments of correlation in scatter plots: An empirical study of students’ intuitive strategies and preconceptions. Hiroshima Journal of Mathematics Education, 4, 25–41.Google Scholar
  11. Estepa, A., & Sanchez Cobo, F. (2001). Empirical research on the understanding of association and implications for the training of researchers. In C. Batanero (Ed.), Training researchers in the use of statistics (pp. 37–51). Granada, Spain: International Association for Statistical Education.Google Scholar
  12. Fiedler, K., Brinkmann, B., Betsch, R., & Wild, B. (2000). A sampling approach to biases in conditional probability judgments: Beyond base-rate neglect and statistical format. Journal of Experimental Psychology: General, 129, 1–20.CrossRefGoogle Scholar
  13. Fiedler, K., Walther, E., Freytag, P., & Plessner, H. (2002). Judgment biases in a simulated classroom: A cognitive-environmental approach. Organizational Behavior and Human Decision Processes, 88, 527–561.CrossRefGoogle Scholar
  14. Freedman, D., Pisani, R., & Purves, R. (1998). Statistics (3rd ed.). New York: Norton.Google Scholar
  15. Inhetveen, H. (1976). Die Reform des gymnasialen Mathematikunterrichts zwischen 1890 und 1914 (The reform of mathematics instruction for upper level schools between 1980 and 1914). Bad Heilbrunn: Klinkhardt.Google Scholar
  16. Jennings, D. L., Amabile, T. M., & Ross, L. (1982). Informal covariation assessment: Data-based versus theory-based judgments. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 211–230). New York: Cambridge University Press.Google Scholar
  17. Kharsikar, A. V., & Kunte, S. (2002). Understanding correlation. Teaching Statistics, 24(2), 66–67.CrossRefGoogle Scholar
  18. 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
  19. Lane, D. M., Anderson, C. A., & Kellam, K. L. (1985). Judging the relatedness of variables: The psychophysics of covariation detection. Journal of Experimental Psychology, 11(5), 640–649.Google Scholar
  20. Levin, J. (1993). An improved modification of a regression-towards-the-mean demonstration. American Statistician, 47, 24–26.Google Scholar
  21. Nisbett, R., & Ross, L. (1980). Human inference: Strategies and shortcomings of social judgment. New Jersey: Prentice Hall.Google Scholar
  22. Sedlmeier, P. (2006). Intuitive judgments about sample size. In K. Fiedler & P. Juslin (Eds.), Information sampling and adaptive cognition (pp. 53–71). Cambridge: Cambridge University Press.Google Scholar
  23. Smedslund, J. (1963). The concept of correlation in adults. Scandinavian Journal of Psychology, 4, 165–173.CrossRefGoogle Scholar
  24. Stelzl, I. (1982). Fehler und Fallen der Statistik (Errors and fallacies in statistics). Bern: Huber.Google Scholar
  25. Vallee-Tourangeau, F., Hollingsworth, L., & Murphy, R. (1998). Attentional bias in correlation judgements? Smedslund (1963) revisited. Scandinavian Journal of Psychology, 39, 221–233.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.University of EducationLudwigsburgGermany
  2. 2.University of TechnologyChemnitzGermany

Personalised recommendations