1. WEI WEI* KATHERINE JOHNSON MATHEMATICS DEPARTMENT METROPOLITAN STATE UNIVERSITY SAINT PAUL, MN The fair use of graphing calculator in introductory statistics courses

2. Outline The Use of TI calculators in an introductory statistics course Our goal of the research Assessments Results

3. Functions used in an introductory statistics course

4. Our goal Pros  Help students to get accurate results quickly  Reduce math anxiety Cons  Some students are good at technology while some are not  May hinder students’ understanding of certain important concepts if relying on calculators too much

5. Our goal Helped with normal probability calculation?  Normalcdf vs.  Standard Normal Distribution Table Hindered the understanding of normal transformation? Helped with hypothesis testing?  T-test, 2-PropZTest, 2-SampTTest etc. vs.  calculating test statistic and p-value using normalcdf Hindered the understanding of p-value, especially the one-tailed and two-tailed p-value? Reduced short-term retention?

6. Our Assessments Two instructors and four sections  Instructor one->calculator section  Instructor one->non-calculator section  Instructor two->calculator section  Instructor two->non-calculator section Two Quizzes and Three Final Exam questions

7. Our Assessment Quiz one:  Given after introducing normal distribution and the calculation of normal probabilities  One multiple choice question and two calculation questions  The multiple choice question is related to standard normal transformation  The calculation questions are finding Z-score and probabilities under a normal distribution

8. Our Assessments Quiz two  Given after introducing two-sample tests  One multiple choice and one calculation  One multiple choice question related to the understanding of p-value  One calculation question related to two-sample proportion test (null and alternative hypotheses were given)

9. Our Assessments Final exam questions  One multiple choice question related to normal transformation  One multiple choice questions related to p-value  One calculation question on one-sample T-test

10. Results Quiz one-multiple choice question (conceptual understanding of normal transformation) Mantel-Haenszel test No significant difference between the two instructors (p=0.66) The proportion of correctness from the calculator sections was significantly higher than the non-calculator sections (p=0.030)

11. Results Quiz one-calculation questions (finding probabilities under a normal distribution) The mean grade from the calculator sections was significantly higher than the mean grade from the non-calculator sections (p=0.0099) No significant interaction between instructor and pedagogy No instructor effect Average grade ( percentage )

12. Results Quiz two- multiple choice question (conceptual understanding of p-value) Mantel-Haenszel test No significant difference between the two instructors (p=0.31) The proportions of correctness were not significantly different between the calculator and non-calculator sections (p=0.990)

13. Results Quiz two-Calculation question (two-sample Z-test) Two-way ANOVA The mean score from the calculator section was significantly higher than the mean score from the non-calculator section (p=0.0017) A significant interaction between instructor and pedagogy (p=0.0024) Significant difference between two instructors (p=0.0074) Average grade ( percentage )

14. Results For short-term retention (analysis of final exam question)  Multiple choice question-Normal transformation  Mantel-Haenszel test  No significant difference between the two instructors (p=0.15)  No significant difference between calculator and non-calculator sections (p=0.44)

15. Results For short-term retention (analysis of final exam question)  Multiple choice question-p-value  Mantel-Haenszel test  Significant difference between the two instructors (p=0.0067)  For instructor one: proportion of correctness from the calculator section was significantly higher (p=0.025)  For instructor two: proportions of correctness are not significantly different between the calculator and non-calculator sections (p=0.11)

16. Results For short-term retention (analysis of final exam question)  Calculation question-one sample T-test  Two-way ANOVA  No instructor effect (p=0.54)  No pedagogy effect (p=0.99)  No significant interaction (p=0.27) Average grade ( percentage )

17. Conclusion The TI calculator significantly helped students with the calculation of normal probabilities and understanding of normal transformation It did not significantly helped with hypothesis testing or short-term retention, but it did not hinder students’ understanding

18. Questions???