What Does Research Suggest About the Teaching and Learning of Introductory Statistics at the College Level? A Review of the Literature

References

• American Educational Research Association. (2006), AERA Draft Standards for Reporting on Research Methods, http://www.aera.net/uploadedFiles/Publications/AERA_Standards/AERAStandardsforReview.pdf
   Google Scholar
• American Statistical Association. (2005), GAISE College Report, http://ww2.amstat.org/education/gaise/GAISECollege.htm
   Google Scholar
• Aberson, C. L., Berger, D. E., Healy, M. R., Kyle, D. J., and Romero, V. L. (2000), “Evaluation of an Interactive Tutorial for Teaching the Central Limit Theorem,” Teaching in Psychology, 27(4), 289–291.
   Web of Science ®Google Scholar
• Alldredge, J. R., and Brown, G. R. (2006), “Association of Course Performance with Student Beliefs: An Analysis by Gender and Instructional Software Environment,” Statistics Education Research Journal [Online], 5(1), 64–77. http://www.stat.auckland.ac.nz/∼iase/serj/SERJ_5(1)_Alldredge_Brown.pdf
   Google Scholar
• Becker, B. J. (1996). “A Look at the Literature (and Other Resources) on Teaching Statistics,” Journal of Educational and Behavioral Statistics, 21(1), 71–90.
   Web of Science ®Google Scholar
• Biggs, J. B., and Collis, K. F. (1982), Evaluating the Quality of Learning: The SOLO Taxonomy (Structure of Observed Learning Outcomes), New York: Academic Press.
   Google Scholar
• Birenbaum, M., and Eylath, S. (1994), “Who is Afraid of Statistics? Correlates of Statistics Anxiety Among Students of Educational Sciences,” Educational Research, 36(1), 93–98.
   Web of Science ®Google Scholar
• Budé, L., Van De Wiel, M. W. J., Imbos, T., Candel, M. J. J. M., Broers, N. J., and Berger, M. P. F. (2007), “Students' Achievements in a Statistics Course in Relation to Motivational Aspects and Study Behaviour,” Statistics Education Research Journal [Online], 6(1), 5–21. http://www.stat.auckland.ac.nz/∼iase/serj/SERJ6(1)_Bude.pdf
   Google Scholar
• Cashin, S.E., and Elmore, P.B. (2005), “The Survey of Attitudes Toward Statistics Scale: A Construct Validity Study,” Educational and Psychological Measurement, 65(3), 509–524.
   Web of Science ®Google Scholar
• Chance, B., dleMas, R., and Garfield, J. (2004), “Reasoning About Sampling Distributions,” in The Challenge of Developing Statistical Literacy, Reasoning and Thinking, eds. D. Ben-Zvi and J. Garfield, Dordrecht, The Netherlands: Kluwer Academic Publishers, pp. 295–323.
   Google Scholar
• Chance, B. L., and Garfield, J. B. (2002), “New Approaches to Gathering Data on Student Learning for Research in Statistics Education,” Statistics Education Research Journal [Online], 1(2), 38–41. http://www.stat.auckland.ac.nz/∼iase/publications/4/751.pdf
   Google Scholar
• Clark, J., Mathews, D., Kraut, G., and Wimbish, J. (1997), “The Fundamental Theorem of Statistics: Classifying Student Understanding of Basic Statistical Concepts,” unpublished manuscript. http://www1.hollins.edu/faculty/clarkjm/papers.htm
   Google Scholar
• Cobb, G. (2005), “Forword,” in Innovations in Teaching Statistics, MAA Notes, vol. 65, ed. J. B. Garfield, Washington DC: Mathematical Association of America, pp. vii–viii.
   Google Scholar
• Collins, L., and Mittag, K. (2005), “Effect of Calculator Technology on Student Achievement in an Introductory Statistics Course,” Statistics Education Research Journal [Online], 4(1), 7–15. http://www.stat.auckland.ac.nz/∼iase/serj/SERJ4(1)_Collins_Mittag.pdf
   Google Scholar
• delMas, R. C., Garfield, J., and Chance, B. L. (1999), “A Model of Classroom Research in Action: Developing Simulation Activities to Improve Students' Statistical Reasoning,” Journal of Statistics Education [Online], 7(3). http://ww2.amstat.org/publications/jse/secure/v7n3/delMas.cfm
   Google Scholar
• delMas, R., Garfield, J., Ooms, A., and Chance, B. (in press), “Assessing Students' Conceptual Understanding After a First Course in Statistics,” Statistics Education Research Journal [Online].
   Google Scholar
• delMas, R.C., and Liu, Y. (2005), “Exploring Students' Conceptions of the Standard Deviation,” Statistics Education Research Journal [Online], 4(1), 55–82. http://www.stat.auckland.ac.nz/∼iase/serj/SERJ4(1)_delMas_Liu.pdf
   Google Scholar
• Derry, S. J., Levin, J. R., Osana, H. P., Jones, M. S., and Peterson, M. (2000), “Fostering Students' Statistical and Scientific Thinking: Lessons Learned From an Innovative College Course,” American Educational Research Journal, 37(3), 747–773.
   Web of Science ®Google Scholar
• Dubinsky, E., and McDonald, M. (2001), “A Constructivist Theory of Learning in Undergraduate Mathematics Education Research,” in The Teaching and Learning of Mathematics at University Level: An ICMI Study, ed. D. Holton, Dordrecht, The Netherlands: Kluwer Academic Publishers, pp. 275–282.
   Google Scholar
• Fernandez, C. (2002), “Learning from Japanese Approaches to Professional Development: The Case of Lesson Study,” Journal of Teacher Education, 53(5), 390–405.
   Web of Science ®Google Scholar
• Finney, S.J., and Schraw, G. (2003), “Self-Efficacy Beliefs in College Statistics Courses,” Contemporary Educational Psychology, 28, 161–186.
   Web of Science ®Google Scholar
• Fong, G. T., Krantz, D. H., and Nisbett, R. E. (1986), “The Effects of Statistical Training on Thinking About Everyday Problems,” Cognitive Psychology, 18, 253–292.
   Web of Science ®Google Scholar
• Gal, I., and Ginsburg, L. (1994), “The Role of Beliefs and Attitudes in Learning Statistics: Towards an Assessment Framework,” Journal of Statistics Education [Online], 2(2). http://ww2.amstat.org/publications/jse/v2n2/gal.html
   Google Scholar
• Gal, I., Ginsburg, L., and Schau, C. (1997), “Monitoring Attitudes and Beliefs in Statistics Education,” in The Assessment Challenge in Statistics Education, eds. I. Gal and J. B. Garfield, Amsterdam, The Netherlands: The International Statistical Institute, pp. 37–51. http://www.stat.auckland.ac.nz/∼iase/publications/assessbk/chapter04.pdf
   Google Scholar
• Gall M.D., Borg W. R., and Gall J.P. (1996), Educational Research: An Introduction, New York: Longman Publishers.
   Google Scholar
• Garfield, J. B. (1995), “How Students Learn Statistics,” International Statistical Review, 63, 25–34.
   Web of Science ®Google Scholar
• Garfield, J. B. (1998a), “Challenges in Assessing Statistical Reasoning,” Paper presented at the meeting of the American Educational Research Association. San Diego, CA.
   Google Scholar
• Garfield, J. B. (1998b), “The Statistical Reasoning Assessment: Development and Validation of a Research Tool,” in Proceedings of the Fifth International Conference on Teaching Statistics, eds. L. Pereira-Mendoza, L. Seu Kea, T. Wee Kee, and W. K. Wong, Singapore: International Statistical Institute, pp. 781–786. http://www.stat.auckland.ac.nz/∼iase/publications/2/Topic6u.pdf
   Google Scholar
• Garfield, J. B. (2003), “Assessing Statistical Reasoning,” Statistics Education Research Journal [Online], 2(1), 22–38. http://www.stat.auckland.ac.nz/∼iase/serj/SERJ2(1).pdf
   Google Scholar
• Garfield, J. B. (2006), “Collaboration in Statistics Education Research: Stories, Reflections, and Lessons Learned,” in Proceedings of the Seventh International Conference on Teaching Statistics, eds. A. Rossman and B. Chance, Salvador, Bahia, Brazil: International Statistical Institute, pp. 1–11. http://www.stat.auckland.ac.nz/∼iase/publications/17/PL2_GARF.pdf
   Google Scholar
• Garfield, J. B., and Ahlgren, A. (1988), “Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research,” Journal for Research in Mathematics Education, 19(1), 44–63.
   Web of Science ®Google Scholar
• Garfield, J., and Ben-Zvi, D. (in press), Developing Students' Statistical Reasoning: Connecting Research and Teaching Practice, Dordrecht, The Netherlands: Springer Publishing.
   Google Scholar
• Garfield, J., and Chance, B. (2000), “Assessment in Statistics Education: Issues and Challenges,” Mathematics Thinking and Learning, 2, 99–125.
   Google Scholar
• Garfield, J., and delMas, R. (1994), “Students' Informal and Formal Understanding of Statistical Power,” Paper presented at the Fourth International Conference on Teaching Statistics, Marrakech, Morocco.
   Google Scholar
• Garfield, J., delMas, R. C., and Chance, B. (2007), “Using Students' Informal Notions of Variability to Develop an Understanding of Formal Measures of Variability,” in Thinking with Data, eds. M. Lovett and P. Shah, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 117–148.
   Google Scholar
• Garfield, J., delMas, R. C., and Chance, B. (n.d.), Assessment Resource Tools for Improving Statistical Thinking. https://app.gen.umn.edu/artist/index.html.
   Google Scholar
• Gigerenzer, G. (1996), “On Narrow Norms and Vague Heuristics: A Reply to Kahneman and Tversky,” Psychological Review, 103(3), 592–596.
   Web of Science ®Google Scholar
• Giraud, G. (1997), “Cooperative Learning and Statistics Instruction,” Journal of Statistics Education [Online], 5(3). http://ww2.amstat.org/publications/jse/v5n3/giraud.html
   Google Scholar
• Gordon, S. (1995), “A Theoretical Approach to Understanding Learners of Statistics,” Journal of Statistics Education [Online], 3(3). http://ww2.amstat.org/publications/jse/v3n3/gordon.html
   Google Scholar
• Groth, R., and Bergner, J. (2005), “Pre-Service Elementary School Teachers' Metaphors for the Concept of Statistical Sample,” Statistics Education Research Journal [Online], 4(2), 27–42. http://www.stat.auckland.ac.nz/∼iase/serj/SERJ4(2)_groth_bergner.pdf
   Google Scholar
• Groth, R., and Bergner, J. (2006), “Preservice Elementary Teachers' Conceptual and Procedural Knowledge of Mean, Median, and Mode,” Mathematical Thinking and Learning, 8(1), 37–63.
   Google Scholar
• Gullickson, A. R., and Ellwein, M. C. (1985), “Teacher-Made Tests: The Goodness-of-Fit Between Prescription and Practice,” Educational Measurement: Issues and Practice, 4(1), 15–18.
   Google Scholar
• Hembree, R. (1988), “Correlates, Causes, Effects, and Treatment of Test Anxiety,” Review of Educational Research, 58(1), 47–77.
   Web of Science ®Google Scholar
• Hirsch, L. S., and O'Donnell, A. M. (2001), “Representativeness in Statistical Reasoning: Identifying and Assessing Misconceptions,” Journal of Statistics Education [Online], 9(2). http://ww2.amstat.org/publications/jse/v9n2/hirsch.html
   Google Scholar
• Kahneman, D., Slovic, P., and Tversky, A. (1982). Judgment Under Uncertainty: Heuristics and Biases, Cambridge: Cambridge University Press.
   Google Scholar
• Keeler, C. M., and Steinhorst, R. K. (1995), “Using Small Groups to Promote Active Learning in the Introductory Statistics Course: A Report from the Field,” Journal of Statistics Education [Online], 3(2). http://ww2.amstat.org/publications/jse/v3n2/keeler.html
   Google Scholar
• Konold, C. (1989), “Informal Conceptions of Probability,” Cognition and Instruction, 6(1), 59–98.
   Web of Science ®Google Scholar
• Konold, C. (1995), “Issues in Assessing Conceptual Understanding in Probability and Statistics,” Journal of Statistics Education [Online], 3(1). http://ww2.amstat.org/publications/jse/v3n1/konold.html
   Google Scholar
• Konold, C., Pollatsek, A., Well, A. D., Lohmeier, J., and Lipson, A. (1993), “Inconsistencies in Students' Reasoning about Probability,” Journal for Research in Mathematics Education, 24, 392–414.
   Web of Science ®Google Scholar
• Lane, D. M., and Tang, Z. (2000), “Effectiveness of Simulation Training on Transfer of Statistical Concepts,” Journal of Educational Computing Research, 22(4), 383–396.
   Web of Science ®Google Scholar
• Leont'ev (Leontyev) A. N. (1981). Problems of the development of the mind. Moscow: Progress Publishers.
   Google Scholar
• Lissitz, R. W., and Schafer, W. D. (2002), Assessment in Educational Reform: Both Means and Ends, Boston, MA: Allyn and Bacon.
   Google Scholar
• Liu, H. J. (1998), A Cross-Cultural Study of Sex Differences in Statistical Reasoning for College Students in Taiwan and the United States, unpublished Ph.D. dissertation.
   Google Scholar
• Lovett, M. (2001), “A Collaborative Convergence on Studying Reasoning Processes: A Case Study in Statistics,” in Cognition and Instruction: 25 Years of Progress, eds. S. Carver, and D. Klahr, Mahwah, NJ: Erlbaum.
   Google Scholar
• Lunsford, M. L., Rowell, G. H., and Goodson-Espy, T. J. (2006), “Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Courses,” Journal of Statistics Education [Online], 14(3). http://ww2.amstat.org/publications/jse/v14n3/lunsford.html
   Google Scholar
• Lutzer, D. J., Maxwell, J. W., and Rodi, S. B. (2000), Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States: Fall 2000 CBMS Survey, Washington DC: American Mathematical Society.
   Google Scholar
• Magel, R. C. (1998), “Using Cooperative Learning in a Large Introductory Statistics Class,” Journal of Statistics Education [Online], 6(3). http://ww2.amstat.org/publications/jse/v6n3/magel.html
   Google Scholar
• Van Manen, M. (1990), Researching Lived Experience: Human Science for an Action Sensitive Pedagogy, New York: State University of New York Press.
   Google Scholar
• Mathews, D., and Clark, J. (2003), “Successful Students' Conceptions of Mean, Standard Deviation and the Central Limit Theorem,” unpublished manuscript. http://www1.hollins.edu/faculty/clarkjm/papers.htm
   Google Scholar
• Meletiou, M., and Lee, C. (2003), “Studying the Evolution of Students' Conceptions Of Variation Using the Transformative and Conjecture-Driven Research Design,” in Reasoning About Variability: A Collection of Current Research Studies, ed. C. Lee, Mt. Pleasant, MI: Central Michigan University. http://www.cst.cmich.edu/users/lee1c/SRTL3/SRLT_3_papers/SRTL-Meletiou and Lee-10-2003.pdf
   Google Scholar
• Metz, K. E. (1998), “Emergent Understanding and Attribution of Randomness: Comparative Analysis of the Reasoning of Primary Grade Children and Undergraduates,” Cognition and Instruction, 16(3), 285–365.
   Web of Science ®Google Scholar
• Meyer, O., and Lovett, M. (2002), “Implementing a Computerized Tutor in a Statistical Reasoning Course: Getting the Big Picture,” in Proceedings of the Sixth International Conference on Teaching of Statistics, ed. B. Phillips, Voorburg, The Netherlands: International Statistical Institute. http://www.psy.cmu.edu/LAPS/pubs/Meyer02.pdf
   Google Scholar
• Moore, D. (1998). “Statistics Among the Liberal Arts,” Journal of the American Statistical Association, 93, 1253–1259.
   Web of Science ®Google Scholar
• Mosteller, F., and Boruch, R. (2002), Evidence Matters: Randomized Trials in Education Research, Harrisonburg, VA: R. R. Donnelley and Sons.
   Google Scholar
• National Research Council. (2001), Knowing What Students Know: The Science and Design of Educational Assessment, Washington, DC: National Academy of Sciences.
   Google Scholar
• Nisbett, R. E., Fong, G. T., Lehman, D. R., and Cheng, P. W. (1987), “Teaching Reasoning,” Science, 238, 625–631.
   PubMed Web of Science ®Google Scholar
• Noss, R., Pozzi, S., and Hoyles, C. (1999), “Touching Epistemologies: Meanings of Average and Variation in Nursing Practice,” Educational Studies in Mathematics, 40, 25–51.
   Google Scholar
• Onwuegbuzie, A., and Wilson, V. (2003), “Statistics Anxiety: Nature, Etiology, Antecedents, Effects, and Treatments—A Comprehensive Review of the Literature,” Teaching in Higher Education, 8(2), 195–209.
   Google Scholar
• Pedhazur, E. J., and Schmelkin, L. P. (1991), Measurement, Design, and Analysis: An Integrated Approach, Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.
   Google Scholar
• Perney, J., and Ravid, R. (1991), The Relationship Between Attitudes Towards Statistics, Math Self-Concept, Test Anxiety and Graduate Students' Achievement in an Introductory Statistics Course, unpublished manuscript. http://www.eric.ed.gov/ERICWebPortal/contentdelivery/servlet/ERICServlet?accno=ED318607
   Google Scholar
• Pollatsek, A., Lima, S., and Well, A. (1981), “Concept or Computation: Students' Misconceptions of the Mean,” Educational Studies in Mathematics, 12, 191–204.
   Google Scholar
• Quilici, J. L., and Mayer, R. E. (2002), Teaching Students to Recognize Structural Similarities Between Statistics Word Problems,” Applied Cognitive Psychology, 16, 325–342.
   Web of Science ®Google Scholar
• Raudenbush, S. W. (2005), “Learning from Attempts to Improve Schooling: The Contribution of Methodological Diversity,” Educational Researcher, 34(5), 25–31.
   Google Scholar
• Reid, A., and Petocz, P. (2002), “Students' Conceptions of Statistics: A Phenomenographic Study,” Journal of Statistics Education [Online], 10(2). http://ww2.amstat.org/publications/jse/v10n2/reid.html
   Google Scholar
• Reys, R.E., Lindquist, M. N., Lambdin, D. V., and Smith, N. L.  (2006), Helping Children Learn Mathematics (8th ed.), Hoboken, NJ: John Wiley and Sons.
   Google Scholar
• Roberts, D. M., and Bilderback, E. W. (1980), Reliability and Validity of a Statistics Attitude Survey, Educational and Psychological Measurement, 40, 235–238.
   Web of Science ®Google Scholar
• Roseth, C. J., Johnson, D. W., and Johnson, R. T. (in press), “Promoting Early Adolescents' Achievement and Peer Relationships: The Effects of Cooperative, Competitive, and Individualistic Goal Structures,” Psychological Bulletin.
   Google Scholar
• Scheaffer, R., Smith, W. B. (2007). Using statistics effectively in mathematics education research: A report from a series of workshops organized by the American Statistical Association with funding from the National Science Foundation. Alexandria, VA: American Statistical Association. http://ww2.amstat.org/research_grants/pdfs/SMERReport.pdf
   Google Scholar
• Schau, C., and Mattern, N. (1997), “Use of Map Techniques in Teaching Statistics Courses,” The American Statistician, 51(2), 171–175.
   Web of Science ®Google Scholar
• Schau, C., Stevens, J., Dauphinee, T. L., and Del Vecchio, A. (1995). “The Development and Validation of the Survey of Attitudes Toward Statistics,” Educational and Psychological Measurement, 55, 868–875.
   Web of Science ®Google Scholar
• Sedlmeier, P., and Gigerenzer, G. (1997), “Intuitions About Sample Size: The Empirical Law of Large Numbers,” Journal of Behavioral Decision Making, 10, 33–51.
   Web of Science ®Google Scholar
• Shaughnessy, J. M. (1992), “Research in Probability and Statistics: Reflections and Directions,” in Handbook of Research on Mathematics Teaching and Learning, ed. D. Grouws, New York: McMillan, pp. 465–494.
   Google Scholar
• Sides, A., Osherson, D., Bonini, N., and Viale, R. (2002), “On the Reality of the Conjunction Fallacy,” Memory and Cognition, 30, 191–198.
   PubMed Web of Science ®Google Scholar
• Snee, R. (1990), “Statistical Thinking and Its Contribution to Quality,” The American Statistician, 44, 116–121.
   Web of Science ®Google Scholar
• Snee, R. (1999), “Discussion: Development and Use of Statistical Thinking: A New Era,” International Statistical Review, 67(3), 255–258.
   Web of Science ®Google Scholar
• Tempelaar, D. T., Gijselaers, W. J., and van der Loeff, Schim S. (2006), “Puzzles in Statistical Reasoning,” Journal of Statistics Education, 14(1), 1–26. http://ww2.amstat.org/publications/jse/v14n1/tempelaar.html
   Google Scholar
• Thorndike, R. M., (2004), Measurement and Evaluation in Psychology and Education (7th Ed.). Upper Saddle River, NJ: Prentice Hall.
   Google Scholar
• Thorndike, R. L., and Hagen, E. (1986), Cognitive Abilities Test: Examiner's Manual Form 4, Chicago, IL: Riverside.
   Google Scholar
• Utts, J., Sommer, B., Acredolo, C., Maher, M. W., and Matthews, H. R. (2003), “A Study Comparing Traditional and Hybrid Internet-Based Instruction in Introductory Statistics Classes,” Journal of Statistics Education [Online], 11(3). http://ww2.amstat.org/publications/jse/v11n3/utts.html
   Google Scholar
• Ward, B. (2004), “The Best of Both Worlds: A Hybrid Statistics Course,” Journal of Statistics Education [Online], 12(3). http://ww2.amstat.org/publications/jse/v12n3/ward.html
   Google Scholar
• Watson, J. M., and Moritz, J. B. (2000), “Development of Understanding of Sampling for Statistical Literacy,” Journal of Mathematical Behavior, 19, 109–136.
   Google Scholar
• Weller, L. D.Jr. (2001), “Building Validity and Reliability into Classroom Tests,” National Association of Secondary School Principals Bulletin, 85, 32–37.
   Google Scholar
• Wild, C.J., and Pfannkuch, M. (1999), “Statistical Thinking in Empirical Enquiry,” International Statistical Review, 67, 221–248.
   Web of Science ®Google Scholar
• Wise, S. L. (1985), “The Development and Validation of a Scale Measuring Attitudes Toward Statistics,” Educational and Psychological Measurement, 45, 401–405.
   Web of Science ®Google Scholar
• Zieffler, A. (2006), A Longitudinal Investigation of the Development of College Students' Reasoning About Bivariate Data During an Introductory Statistics Course, unpublished Ph.D. dissertation, University of Minnesota.
   Google Scholar