Precalculus Active Learning Labs: Focus on Functions

1. Precalculus Active Learning Labs:Focus on Functions Linda C. Burks MAA MathFest 2019: Encouraging Effective Teaching Innovation Sponsored by the Koret Foundation and Anonymous Donors

2. Background Fall 2017 Three Initiatives to Improve First Year Math Experience based on CSPCC Recommendations • Active Learning Labs • ALEKS Placement Test • Mathematics Learning Center PreCalculus Active Learning Labs: Focus on Functions

3. Background Active Learning (Freeman et. al., 2014; Larsen et. al., 2015 ) Active Student Engagement Improves Student Performance Deepens Conceptual Knowledge Strengthens Problem Solving Skills Develops Sophisticated View of Mathematics Builds Confidence PreCalculus Active Learning Labs: Focus on Functions

4. Context PreCalculus Active Learning Labs 65 minute P/NP corequisite each week Lab Instructor is not necessarily the precalculus instructor Lab instructors have 2 days of training in active learning techniques Lab instructors have independence and flexibility in lab design PreCalculus Active Learning Labs: Focus on Functions

5. Phases • Fall 2016 Pilot with LEAD (First Generation College Students) • No significant performance improvement in precalc or first quarter calc. • Fall 2017 (Required for LEAD students; recommended for students who don’t place into precalc) • Students don’t opt to take if recommended. No significant results. • Fall 2018 (Required for LEAD students; required for students who don’t place into precalc)  • Labs revised to focus on small group contextual problem solving activities related to different functions covered in the precalculus curriculum PreCalculus Active Learning Labs: Focus on Functions

6. Table Example

7. Linear Functions Lab: Warm Up • Coordinate System/Slope Review • Classroom Size Coordinate System • Each student given coordinates of a point • Colored Jump Ropes Represent Lines of Given Slope PreCalculus Active Learning Labs: Focus on Functions

8. Piecewise Linear Functions: Palm Tree Scenario A ten year old palm tree measures 4 feet tall. In twelve more years, the tree grows to be 40 feet. From year 22 to year 50, the growth rate is only 1 inch per year. PreCalculus Active Learning Labs: Focus on Functions

9. Function Match: Warm Up What Do you Notice? PreCalculus Active Learning Labs: Focus on Functions

10. Function Match and Modelling Lab • Function Card Match • Model, Table, Equation, Graph • Identify Type of Function • Create your own model/table/equation/graph for quadratic function PreCalculus Active Learning Labs: Focus on Functions

11. Function Match and Modelling Lab Population Cards by Brigitte Lahme

12. Results • 80% of students in lab earned C- or above in Precalc class • 85% of students of not in lab earned C- or above in Precalc class. • 89% of lab students earned a C or above in first quarter STEM Calc • 84% of precalc (no lab) students earned C or above • 82% of lab students earned a C or above in first quarter Business Calc • 90% of precalc (no lab) earned C or above PreCalculus Active Learning Labs: Focus on Functions

13. PreCalculus Active Learning Labs: Focus on Functions

14. What’s Ahead • Fall 2019 (All precalc students will take lab) • Labs will again use small group problem solving activities related to different functions, but will add 35 minutes of self-regulation work. • Self Regulation Activities (Pintrich, 2002) • Metacognition improves learning in undergraduate science (Zhao et. al., 2014). • Self-regulation improves problem solving (Bielaczyc et. al.,1995) PreCalculus Active Learning Labs: Focus on Functions

15. Thanks for listening! • Questions to ask? • Insights to share? PreCalculus Active Learning Labs: Focus on Functions

16. References • Bielaczyc,K; Pirolli, P.& Brown, A. (1995). Training in self-explanation and self-regulation strategies: Investigating the effects of knowledge acquisition activities on problem solving. Cognition and Instruction, 13(2), 221-252. • Bressoud, D; Mesa, V; and Rasmussen C. Eds. (2015) Insights and Recommendations from the MAA National Study of College Calculus: Mathematics Association of America. • Ellis, J., Kelton, M. L., & Rasmussen, C. (2014). Student perceptions of pedagogy and associated persistence in calculus. ZDM, 46(4), 661-673. • Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410-8415. PreCalculus Active Learning Labs: Focus on Functions

17. References Continued • Hsu, E., & Bressoud, D. (2015). Placement and student performance in Calculus I. Insights and Recommendations from the MAA National Study of College Calculus. MAA Notes, 59-67. • Johnson, E., & Hanson, K. (2015). Academic and social supports. Insights and recommendations from the MAA nationalstudy of college calculus, 69-82. • Larsen, S., Glover, E., & Melhuish, K. (2015). Beyond good teaching. Insights and recommendations from the MAA national study of college calculus, 93. • Pintrich, P. (2002) The role of metacognitive knowledge in learning, teaching, and assessing. Theory into Practice. 41(4), 219-225. • Zhao, N., Wareska, J. McGuire, S., Cook, E. (2014) Metacognition: An effective tool to promote success in PreCalculus Active Learning Labs: Focus on Functions