Moving Toward a More Effective Learning Environment in First Year Calculus

1. Moving Toward a More Effective Learning Environment in First Year Calculus Javier Garza, Tarleton State University March 30, 2012

2. At the end of the semester I would be happy if

3. Beginning of Semester Survey • 17 questions • Responses: CRD Group (N=65)* and Calculus I Group (N=15) * 78 in CRD logged in to survey though only 65 provided consistent responses. • 1 = Strongly Agree 2 = Agree 3 = Neutral 4 = Disagree 5 = Strongly Disagree • Of 78 in CRD group, 63 (84%) were enrolled in RDG 301 (Intro. to Children’s Lit) • A/D Gap is the difference between % reporting 1 or 2 and % reporting 4 or 5

8. What’s eating yoU? Arum, R., & Roksa, J. (2011). Academically adrift: Limited learning on college campuses. Chicago, IL: The University of Chicago Press. 45 percent of students "did not demonstrate any significant improvement in learning" during the first two years of college. 36 percent of students "did not demonstrate any significant improvement in learning" over four years of college. Deslauriers, L., Schelew, E., & Wieman, C. (2011). Improved learning in a large-enrollment physics class. Science 332(6031), 862-864. Abbr. Abstract: We measured the learning of a specific set of topics and objectives when taught by 3 hours of traditional lecture given by an experienced highly rated instructor and 3 hours of instruction given by a trained but inexperienced instructor using instruction based on research in cognitive psychology and physics education. The comparison was made between two large sections (N = 267 and N = 271) of an introductory undergraduate physics course. We found increased student attendance, higher engagement, and more than twice the learning in the section taught using research-based instruction. Merrow, J. (2005). Declining by degrees: Higher education at risk [Motion picture]. United States: Learning Matters, Inc.

9. “The lecture method is a process whereby the lecture notes of the instructor get transferred to the notes of the students without passing through the brains of either”. Eric Mazur: Confessions of a Converted Lecturer

10. Some References Schneps, M. H., & Sadler, P. M. (1988). A private universe: misconceptions that block learning [ Motion picture]. United States: Corporation for Public Broadcasting. Available at http://www.learner.org/vod/vod_window.html?pid=9.  Carlson, M. P., & Rasmussen, C. (Eds.). (2008). Making the connection: research and teaching in undergraduate mathematics education (MAA Notes #73). Washington, DC: Mathematical Association of America. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values and goals. Annual Review Psychology, 53, 109-132.

11. Some More References Finkel, D. L. (2000). Teaching with your mouth shut. Portsmouth, NH: Boynton/Cook. Newcombe, N. S., Ambady, N., Eccles, J., Gomez, L., Klahr, D., Linn, M., Miller, K., & Mix, K. (2009). Psychology’s role in mathematics and science education. American Psychologist, 64(6), 538-550. Nilson, L. B. (2010). Teaching at its best (3rd ed.). San Francisco, CA: Jossey-Bass. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370). New York: MacMillan.

12. This is not about “change” for the sake of change My goal is to provide students a transformationalexperience subsequent to which they believe themselves to be independently equipped and empowered to “do” mathematics and to engage in meaningful mathematical dialogue with others, and are intrinsically inclined to engage in the struggles of problem solving. Indicators of success: Students attend class (based upon intrinsic interest); Students complete the homework with a high level of mastery Students constructively engage in cooperative/collaborative learning activities Students perform well on exams Students take more mathematics coursework Students are successful in “subsequent coursework” Students are interested in independent study

13. Classroom – Justify their attendance; encourage, empower, equip Office – Inviting Home – Learning and evolution toward independence

14. Some strategies implemented • Utilized Enhanced WebAssign for online homework (10% of grade; objective questions), integrating dynamic content and support features • Required written homework assignments (10% of grade; problems requiring justification) • Provided daily course calendar (comfort through explicit demonstration of course design) • Provided grader with rubric for grading written homework (intentional, constructive feedback) • Tailored solutions (Stewart) provided for exam practice problems • Replaced curves with extra credit serving as final exam review

15. More strategies • Administered beginning of semester and end-course (after grades assigned) survey online; compared results to those of other classes • Developed and administered Calculus Concept Inventory (mention Goldstein) at beginning and end of course • Reviewed math education research (Carlson) to bone up on common misconceptions among calculus students and develop activities (example, bottle problem) • Spent over a week to shore up prerequisite knowledge (in particular, notion of function) • Rigidly enforced no-late homework policy

16. More strategies • Recorded item-by-item results for each student on each test to inform opportunities for emphasis next semester. • Sent email to every individual student several times a semester to notify of progress and express support/concerns as needed • Scheduled office hours based upon student availability rather than my convenience. • Recommitted to use of CAS (Mathematica) to facilitate dialogue and enhancement of conceptual understanding

17. More strategies Provide more in-class opportunities for students to make connections between multiple representations of calculus concepts and discuss (Teach with my mouth shut) • Example: Provide function graphs on grids and ask them to sketch derivatives by estimating derivative values • Provide simple (constant, linear) function graphs on grids and ask them to complete a table providing area under the graph on interval [0,t]. Make connection between definite integral and antiderivative. • Directed learning activity connecting prior knowledge of relationship between graphs of f(x) and f(x)+k, and the family of antiderivatives of a function • Provide direction fields for y’=f(x) and ask them to sketch y; make connection to antiderivatives. • Provide table that facilitates their understanding of inherent structure of chain rule application

19. Next steps • Assist Supplemental Instruction leader in developing activities • Change daily MO so that students are expected to complete problems requiring lower level thinking skills independently, outside of class, without benefit of prior coverage (evolution) • “Uncover material”: More effectively utilize class time to enrich conceptual understanding, make connections, facilitate dialogue • Learn while listening more and “telling” less • Integrate in-class presentations at board

20. Thank you!! garza@tarleton.edu