Transcript Postgraduate Research Methods

Some On-Line Applets and How
They Can Be Used
Dr. Bruce Dunham
Department of Statistics
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.
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).
On-line Tools Available
include:
 Rice
Virtual Lab
 Tom Rogers’ intuitor.com
 Statistics On-line Computational
Resources (SOCR)
Rice Applet Lab
 Students
work in small groups. Prereading 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.
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.
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.
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.

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
 For F distribution, a nice tool is
http://socr.ucla.edu/htmls/SOCR_Distri
butions.html
 See also Charts in SOCR.
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.
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.
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.
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.

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, 733739.

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 secondhand knowledge. In Cognition, Education and
Communication Technology (edit. Gardenfors, P. and
Johansson, P.), Lawrence Erlbaum Assoc.

References

Wood, M. (2005): The role of simulation approaches
in Statistics. Journal of Statistics Education Vol.13,
Number 3.