1. Some On-Line Applets and How They Can Be Used Dr. Bruce Dunham Department of Statistics

2. On-Line Applets  Most applets attempt to teach as simulation and/or visualization tools.  Can be used in lectures, labs and homework assignments.  Hands-on is best, especially for difficult concepts such as sampling distribution.

3. Simulation-based Tools  There are various tools to assist in promoting understanding... ... yet "Just demonstrating graphical concepts in class via computer simulation was not sufficient …”  “ … needed to have a directed … hands-on experience … with simulations” (Lunsford et al. 2006).

4. On-line Tools Available include:  Rice Virtual Lab Rice Virtual Lab  Tom Rogers’ intuitor.com Tom Rogers’ intuitor.com  Statistics On-line Computational Resources (SOCR) Statistics On-line Computational Resources (SOCR)

5. Rice Applet Lab  Students work in small groups. Pre- reading assigned on-line.  Use applet to simulate 1000 samples of 5 from N(16, 5). Note summary statistics, histograms… questions.  Simulate 1000 samples of 25 from U(0,32). Note summary statistics, histograms … questions.  Repeat for a bimodal distribution.  Histogram matching activity.

6. Comparisons  Two lab versions compared: applet and a similar Excel-based lab.  Responses compared on lab activity, relevant midterm test and final exam questions.  No significant differences on any outcome.

7. Invention Tasks  Studies suggest invention activities can improve student learning and transfer compared to “tell and practice” pedagogy (e.g., Simon et al., 1976, Schwartz and Martin, 2004, Schwartz, Martin and Nasir, 2005).  Students can “invent” sampling distribution theory using applets before meeting the concepts in class.

8. Before instruction on topic students...  … complete a homework assignment using the Rice applet.  … for one part, complete a table entering sample statistics for simulations from N(16, 5) for various values of pair (N,M).  … comment on patterns observed.  … “discover” s.d. of sample mean.  Repeat for median. Compare mean and median as estimators of parent distribution mean.

9. ANOVA etc.  Rice On-line Statsbook http://onlinestatbook.com/stat_sim/in dex.html - several useful apps: One-way ANOVA, Two-way ANOVA, Unequal N http://onlinestatbook.com/stat_sim/in dex.html  For F distribution, a nice tool is http://socr.ucla.edu/htmls/SOCR_Distri butions.html http://socr.ucla.edu/htmls/SOCR_Distri butions.html  See also Charts in SOCR.

10. References  Batanero, C., Godino, J.D., Vallecillos, A., Green, D.R., and Holmes, O. (1994): Errors and difficulties in understanding elementary statistical concepts. International Journal of Mathematics and Education in Science and Technology 25, No. 4, 527-547.  Chance, B., delMas, R. and Garfield, J. (2004): Reasoning about sampling distributions. In The Challenge of Developing Statistical Reasoning and Thinking. Kluwer Academic Press, 295-323.

11. References  delMas, R.C. and Liu, Y. (2005): Exploring students’ misconceptions of the standard deviation. Statistics Education Research Journal 5, No. 2, 23-32.  Lipson, K. (2004): The role of the sampling distribution in understanding statistical inference. In Mathematics Education Research Journal Special Edition on Statistics and Probability. Vol.15, No. 3, 270-287. Mathematics Education Research Group of Australasia.

12. References  Crouch, C.H., Fagen, A.P., Callan, J.P. and Mazur, E. (2004): Classroom demonstrations: Learning tools or entertainment? American Journal of Physics Vol. 72, No. 6, 835-838.

13. References  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, Vol. 14, No. 3.  Pfaff, T.J. and Weinberg, A. (2009): Do hands-on activities increase student understanding: A case study. Journal of Statistics Education Vol. 17, No. 3.

14. References  Rumsey, D.J. (2009): Watching our Language When We Teach Statistics. Journal of Statistics Education, Vol. 17, No. 1.  Simon, J. L., Atkinson, D. T., and Shevokas, C. (1976): Probability and statistics: experimental results of a radically different teaching method. American Mathematical Monthly Vol. 83. No. 9, 733- 739.

15. References  Schwartz, D.L., and Martin, T. (2004): Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction Vol. 22, No. 2, 129-184.  Schwartz, D.L., Martin, T., and Nasir, N. (2005): Designs for knowledge evolution: Towards a prescriptive theory for integrating first- and second- hand knowledge. In Cognition, Education and Communication Technology (edit. Gardenfors, P. and Johansson, P.), Lawrence Erlbaum Assoc.

16. References  Wood, M. (2005): The role of simulation approaches in Statistics. Journal of Statistics Education Vol.13, Number 3.