Robin L. Rider East Carolina University

1. DIFFERENCES IN STUDENTS’ USE OF COMPUTER SIMULATION TOOLS AND REASONING ABOUT EMPIRICAL DATA AND THEORETICAL DISTRIBUTIONS Robin L. Rider East Carolina University Hollylynne S. Lee North Carolina State University Presented at the Seventh International Conference on Teaching Statistics Salvador, Brazil, July 3, 2006

2. Gives the students a tangible way to visualize the process of an experiment and the outcomes Gives access to large quantity of outcomes from repeated trials Student Created - Option for user to determine probabilities and set up simulation Researcher/Teacher Created - The purpose of the simulation for our research is for the probability to remain unknown to the user Simulating an Event

3. Used a common context – Six sided dice Premise – The production of the dice may have led to biasness Each group of students must make a decision of whether their dice is biased and what is possible probability distribution for the outcomes on their dice At least two groups explored the same dice After listening to group presentations, the class as a whole must determine which of six companies to purchase dice from, assuming they want fair dice Emphasis on providing compelling evidence for the inferences they were making Tool set for each class was very different The Task

4. Example • icots.pbe • Screenshots

5. Context of 6th Grade Study • End of two week CSM intensive study on probability • Sample size, variability, inferences • Very familiar with PE software • Four function calculators were available

6. Context for AP Stats Study • What is AP Stats? • End of course • Heavy emphasis on Graphing calculators for computation, minimal use of simulations • Well versed in confidence interval and hypothesis testing procedures • Given access to PE and Graphing Calculators

7. Middle School Students Larger Samples n>1000 Used Stability of results to support claims Many were successful in fairness predictions Reasonable estimates for probability distribution Repeated sampling of size 100-500 One very large sample 1000<n<7000 Some used small samples n < 100 but were intensely criticized by their peers AP Stats Students Smaller samples 30<n<500 Typically performed tests for Goodness of Fit Tended to use single sample to estimate probability distribution Only one group used the underlying theory of Central Limit Theorem Groups with incorrect procedures or hypothesis test were intensely criticized by their peers Results

8. Middle school students used the dynamic nature of the graphs as to describe the distribution during data collection The dynamic representation became an analysis tool High school students used the graphical and tabular displays to describe the distribution of the data in its final state after the simulation was complete Dynamic Nature of Graphs

9. Curricular Emphasis Statistical Tools Available Exploratory Tools Asking questions of data that inform more data collection AP Students felt no need to experience random process Variability Randomness Familiarity with Software in curricular experiences AP Stats saw it as a statistics problem Middle School Students saw it as a probabilistic problem Conjectures of Differences Between Groups

10. Would AP Stats students with different curricular experiences approach the problem differently? How do similar age students (high school) with different statistical tool sets approach the problem? Longitudinally with younger students, can we strengthen the foundation of probabilistic understanding that is useful for statistical inference? Questions We Have

11. Where or how do we promote the detective approach to data analysis? Tukey suggested statisticians do more with data …to be “data detectives” to search among data for interesting and informative results. He described this as exploratory data analysis. (Tukey, 1977) “Data analysis is like a give and take conversation between the hunches researchers have about some phenomenon and what the data have to say about those hunches. What researchers find in the data changes their initial understanding which changes how they look at the data, which changes their understanding and so forth.” (Konold & Higgins, 2003, p. 194) Final Thoughts… How can probability simulations help promote EDA and this back and forth conversation?

12. References • Konold, C. & Higgins, T. L. (2003). Reasoning about data. In J. Kilpatrick, W. Martin, & D. Schifter, (Eds.). A research companion to principles and standards for school mathematics (pp. 193-215). Reston , VA : National Council of Teachers of Mathematics. • Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.

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