Students' Understanding of Bar Graphs and Histograms: Results From the LOCUS Assessments

References

• Agresti, A. and Franklin, C. A. (2013), Statistics: The Art and Science of Learning From Data (3rd ed), Upper Saddle River, NJ: Pearson.
   Google Scholar
• Bakker, A. and Gravemeijer, K. P. (2004), “Learning to Reason About Distribution,” in The Challenge of Developing Statistical Literacy, Reasoning and Thinking, pp. 147–168. Springer. Available at http://link.springer.com/content/pdf/10.1007/1-4020-2278-6_7.pdf
   Google Scholar
• Bakker, A. and Gravemeijer, K. P. E. (2006), “An Historical Phenomenology of Mean and Median,” Educational Studies in Mathematics, 62, 149–168. Available at: http://doi.org/10.1007/s10649-006-7099-8
   Google Scholar
• Beniger, J. R. and Robyn, D. L. (1978), “Quantitative Graphics in Statistics: A Brief History,” The American Statistician, 32, 1–11. Available at http://doi.org/10.2307/2683467
   Web of Science ®Google Scholar
• Bright, G. W. and Friel, S. N. (1998), “Students' (Grades 6–8) Understanding of Graphs,” in Proceedings of the Fifth International Conference on Teaching Statistics (pp. 656–662). Voorburg, The Netherlands: International Statistical Institute. Available at http://iase-web.org/documents/papers/icots5/Topic6b.pdf
   Google Scholar
• Chance, B. L. (2002), “Components of Statistical Thinking and Implications for Instruction and Assessment,” Journal of Statistics Education, 10.
   Google Scholar
• College Board (2010), AP Statistics Course Description. Available at http://apcentral.collegeboard.com/apc/public/repository/ap-statistics-course-description.pdf
   Google Scholar
• Cooper, L. L. and 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.
   PubMedGoogle Scholar
• Cooper, L. L. and Shore, S. F. (2010), “The Effects of Data and Graph Type on Concepts and Visualizations of Variability,” Journal of Statistics Education, 18, 1–16.
   Google Scholar
• Crocker, L. M. and Algina, J. (1986), Introduction to Classical and Modern Test Theory. New York: Holt, Rinehart, and Winston.
   Google Scholar
• Cryer, J. D. (2001), “Problems with Using Microsoft Excel for Statistics,” in Proceedings of the Annual Meeting of the American Statistical Association. Atlanta, GA.
   Google Scholar
• delMas, R., Garfield, J., and Ooms, A. (2005), “Using Assessment Items to Study Students' Difficulty Reading and Interpreting Graphical Representations of Distributions,” in K. Makar, ed. Proceedings of the Fourth International Research Forum on Statistical Reasoning, Thinking and Literacy. Auckland, New Zealand: University of Auckland. Retrieved from https://www.causeweb.org/artist/articles/SRTL4_ARTIST.pdf
   Google Scholar
• delMas, R., Garfield, J., Ooms, A., and Chance, B. (2007), “Assessing Students' Conceptual Understanding after a First Course in Statistics,” Statistics Education Research Journal, 6, 28–58. Available at https://www.stat.auckland.ac.nz/∼iase/serj/SERJ6(2)_delMas.pdf
   Google Scholar
• delMas, R., and Liu, Y. (2005), “Exploring Students' Conceptions of the Standard Deviation,” Statistics Education Research Journal, 4, 55–82. Available at http://iase-web.org/documents/SERJ/SERJ4(1)_delMas_Liu.pdf
   Google Scholar
• English, L. D. (2013), “Surviving an Avalanche of Data,” Teaching Children Mathematics, 19, 364–372.
   Google Scholar
• Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., and Scheaffer, R. (2007), Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework. American Statistical Association. Available at www.amstat.org/education/gaise
   Google Scholar
• Garfield, J., delMas, R., and Chance, B. (2007), “Using Students' Informal Notions of Variability to Develop an Understanding of Formal Measures of Variability,” in M. Lovett & P. Shah, eds. Thinking with Data (pp. 117–147).
   Google Scholar
• Haberstroh, J., Jacobbe, T., delMas, R., Hartlaub, B., Miller, D., Scheaffer, R., and Watson, J. (2015), “LOCUS Evidence Model,” Available at https://locus.statisticseducation.org/about-locus/evidence-model
   Google Scholar
• histogram, n. (2014), OED Online. Oxford University Press. Available at http://www.oed.com/view/Entry/87286
   Google Scholar
• Jacobbe, T., Case, C., Whitaker, D., and Foti, S. (2014), “Establishing the Validity of the LOCUS Assessments Through an Evidenced-Centered Design Approach,” in K. Makar and R. Gould, eds. Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9, July, 2014), Flagstaff, Arizona, USA. Voorburg, The Netherlands: International Statistical Institute. Available at http://icots.net/9/proceedings/pdfs/ICOTS9_7C2_JACOBBE.pdf
   Google Scholar
• Kaplan, J. J., Fisher, D. G., and Rogness, N. T. (2009), “Lexical Ambiguity in Statistics: What do Students Know About the Words Association, Average, Confidence, Random and Spread,” Journal of Statistics Education, 17, n3.
   Google Scholar
• Kaplan, J. J., Gabrosek, J. G., Curtiss, P., and Malone, C. (2014), “Investigating Student Understanding of Histograms,” Journal of Statistics Education, 22.
   Google Scholar
• Kaplan, J. J., Rogness, N. T., and Fisher, D. G. (2012), “Lexical Ambiguity: Making a Case Against Spread: Lexical Ambiguity: Making a Case Against Spread,” Teaching Statistics, 34, 56–60. Available at http://doi.org/10.1111/j.1467-9639.2011.00477.x
   Google Scholar
• Magnello, M. E. (1996), “Karl Pearson's Gresham Lectures: W. F. R. Weldon, Speciation and the Origins of Pearsonian Statistics,” The British Journal for the History of Science, 29, 43–63. Available at https://doi.org/10.1017/S0007087400033859
   PubMed Web of Science ®Google Scholar
• McClain, K., Cobb, P., and Gravemeijer, K. (2000), “Supporting Students' Ways of Reasoning About Data,” in M. J. Burke & R. F. Curcio, eds. Learning Mathematics for a New Century, 2000 Yearbook, Reston, VA: National Council of Teachers of Mathematics. Available at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.471.6638&rep=rep1&type=pdf
   Google Scholar
• Meletiou, M. and Lee, C. (2002), “Student Understanding of Histograms: A Stumbling Stone to the Development of Intuitions About Variation,” in Proceedings of the Sixth International Conference on Teaching Statistics, Cape Town, South Africa. Available at https://www.stat.auckland.ac.nz/∼iase/publications/1/10_19_me.pdf
   Google Scholar
• Mislevy, R. J. and Riconscente, M. M. (2006), “Evidence-Centered Assessment Design,” in S. M. Downing & T. M. Haladyna, eds. Handbook of Test Development (pp. 61–90). Mahwah, N.J.: Lawrence Erlbaum Associates.
   Google Scholar
• National Council of Teachers of Mathematics. (2000), Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010), Common Core State Standards for Mathematics, Washington, D.C.: Authors.
   Google Scholar
• Petty, N. W. (2012, November 12), “Beware of Excel Histograms.” Available at https://learnandteachstatistics.wordpress.com/2012/11/12/beware-of-excel-histograms/
   Google Scholar
• Pfannkuch, M. and Wild, C. (2004), “Towards an Understanding of Statistical Thinking,” in The Challenge of Developing Statistical Literacy, Reasoning and Thinking (pp. 17–46). Springer. Available at http://link.springer.com/chapter/10.1007/1-4020-2278-6_2
   Google Scholar
• Roberts, R., Scheaffer, R., and Watkins, A. (1999), “Advanced Placement Statistics—Past, Present, and Future,” The American Statistician, 53, 307–320. Available at http://doi.org/10.1080/00031305.1999.10474482
   Web of Science ®Google Scholar
• Rumsey, D. J. (2002). “Statistical Literacy as a Goal for Introductory Statistics Courses,” Journal of Statistics Education, 10.
   Google Scholar
• ——— (2009), “Teaching Bits: “Random Thoughts on Teaching,” Journal of Statistics Education, 17. Available at http://www.amstat.org/publications/jse/v17n1/rumsey.html
   PubMedGoogle Scholar
• Spence, I. (2005), “No Humble Pie: The Origins and Usage of a Statistical Chart,” Journal of Educational and Behavioral Statistics, 30, 353–368. Available at http://journals.sagepub.com/doi/pdf/10.3102/10769986030004353
   Web of Science ®Google Scholar
• Tintle, N., VanderStoep, J., Holmes, V., Quisenberry, B., and Swanson, T. (2011), “Development and Assessment of a Preliminary Randomization-Based Introductory Statistics Curriculum,” Journal of Statistics Education, 19, 1–25.
   Google Scholar
• Turegun, M. and Reeder, S. (2011), “Community College Students' Conceptual Understanding of Statistical Measures of Spread,” Community College Journal, 35, 410–426.
   Google Scholar
• Whitaker, D. and Jacobbe, T. (2014), “Lessons from the LOCUS Assessments (Part 1): Comparing Groups,” Statistics Teacher Network, 13–15. Available at https://ww2.amstat.org/education/stn/pdfs/stn83.pdf
   Google Scholar
• Wild, C. J. and Pfannkuch, M. (1999), “Statistical Thinking in Empirical Enquiry,” International Statistical Review, 67, 223–248. Available at http://iase-web.org/documents/intstatreview/99.Wild.Pfannkuch.pdf
   Web of Science ®Google Scholar