Precalculus Active Learning Labs Focus on Functions Linda

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

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

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 Pre. Calculus Active Learning Labs: Focus on Functions

Context Pre. Calculus 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 Pre. Calculus Active Learning Labs: Focus on Functions

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) Pre. Calculus Active Learning Labs: Focus on Functions • Labs revised to focus on small group contextual

Pre Calculus Active Learning Lab Content Week 1 Table Dimensional Analysis and Conversions Example Week 2 Linear and Piecewise Linear Functions Week 3 Quadratic Functions Week 4 Exponential Functions Week 5 Function Match and Modeling Week 6 Circles and Ellipses (Desmos) Week 7 Modeling Different Situations with the Same Function Week 8 Logarithms Week 9 Unit Circle Week 10 Sine and Cosine Graphs (Desmos)

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 Pre. Calculus Active Learning Labs: Focus on Functions

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. Pre. Calculus Active Learning Labs: Focus on Functions

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

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 Pre. Calculus Active Learning Labs: Focus on Functions

Function Match and Modelling Lab Population Cards by Brigitte Lahme

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. Pre. Calculus above in first Active Learning Labs: Focus on Functions quarter Business Calc

Statement MATH 9 L The activities in MATH 9 L helped me better learn Precalculus concepts and procedures. In general, participating in MATH 9 L has helped me become a better problem solver. My ability to talk about mathematics has improved as a result of participating in MATH 9 L. I am now more comfortable discussing concepts with other students as a result of participating in MATH 9 L. Participating in MATH 9 L had a positive effect on my MATH 9 grade. SA A N D SD 7 22 6 7 7 9 14 13 5 8 8 18 11 5 7 7 21 8 5 8 7 18 20 3 1 27 22 4 1 3 3 I am confident in my ability to learn math. 18 I am confident I can pass my math class at the end of the term. 26 I am confident I can get a grade better than a B in my math 10 18 8 11 5 Pre. Calculus Active Learning Labs: Focus on Functions class at the end of this term.

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) Pre. Calculus Active Learning Labs: Focus on Functions

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

References • Bielaczyc, K; Pirolli, P. & Brown, A. (1995). Training in selfexplanation 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. , Mc. Donough, 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 Pre. Calculus Active Learning Labs: Focus on Functions Academy of Sciences, 111(23), 8410 -8415.

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. Mc. Guire, S. , Cook, E. Pre. Calculus (2014)Active Metacognition: An Learning Labs: Focus on Functions effective tool to promote success in