Building for Success in College Calculus: National Survey and Case Studies

1. Building for Success in Calculus David Bressoud St. Paul, MN The First Two Years of College Math: Building Student Success Reston, VA October 57, 2014 A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks For more information see www.maa.cspcc A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks For more information see www.maa.cspcc NSF #0910240

2. Characteristics of Successful Programs in College Calculus Three parts: 1. National survey of students in mainstream Calculus I and their instructors (Fall, 2010) 2. Statistical model of factors influencing changes in student attitudes and intention to persist from start to end of Calculus I 3. Case studies of 17 institutions with successful Calculus I programs (Fall, 2012)

3. Characteristics of Successful Programs in College Calculus PI: David Bressoud co-PI s: Vilma Mesa U Michigan Marilyn Carlson ASU Michael Pearson MAA Chris Rasmussen SDSU Linda Braddy MAA Statistical Consultants: Phil Sadler & Gerhard Sonnert DRL REESE #0910240

4. Progress through Calculus PI: David Bressoud co-PI s: Sean Larsen Portland State Linda Braddy MAA Jess Ellise Colorado State DUE IUSE #1420839 Chris Rasmussen SDSU

5. Fall 2010 Phase I: Survey Responses from 213 colleges and universities 502 instructors representing 663 Calculus I classes and 26,257 students 14,184 students

6. research master s undergrad 2 year Average high school math GPA 3.77 3.58 3.64 3.37 Took calculus in high school 70% 43% 53% 24% 3 on AP Calc 26% 9% 14% 5% Took Precalculus in college 13% 31% 17% 60% Agree that to succeed in Calculus I, must have taken it before. 49% 36% 40% 37%

7. PhD BA MA 2Y Coll AVG Mean age (SD) 18.3 (2.4) 18.8 (2.9) 20.5 (5.3) 22.0 (7.4) 19.7 (3.5) Freshman 83% 73% 50% 25% 63% Soph- omore 10% 16% 27% 40% 21% Junior/Se nior 6% 10% 17% 18% 11% Enrolled full time 99% 98% 91% 76% 92% Age, year in college, enrollment status

8. PhD BA MA 2Y Coll AVG Father completed college 65% 58% 49% 44% 56% Mother completed college 62% 56% 47% 40% 53% Some concern about paying for college 54% 40% 57% 55% 51% Major concern about paying for college 13% 10% 13% 23% 14% Socio-economic status From The American Freshman, 55% of all incoming full-time students at 4-year institutions have some concern, 11% have major concern, about paying for college.

9. PhD BA MA TYC Comfortable with graphing calculator Somewhat 14% 14% 18% 18% Yes 81% 82% 77% 74% Graphing calc allowed on exams Sometimes 60% 55% 53% 48% Always 31% 39% 32% 29% TI-89 or -92 allowed on exams Sometimes 25% 22% 25% 25% Always 31% 37% 30% 28% Prepared for calculation without calc Somewhat 28% 29% 30% 27% Yes c 59% 58% 57% 57% Graphing calculator usage in high school

10. Gender differences of career goals of students in Mainstream Calculus I

11. Source: HERI

12. 3-Level HLM Model Structure Main Effects Student Course Institutional Selectivity # of students Initial Career Goal Pedagogy HS Pedagogy Professor Characteristics HS Math grades

13. Dependent Variables Attitudes Change, pre to post Confidence I am confident in my mathematics abilities Enjoyment I enjoy doing mathematics If I had a choice If I had a choice: I would never take another mathematics course to I would continue to take mathematics Change in Interest, post only This course has increased my interest in taking more mathematics Intention to take Calc II Change, pre to post Do you intend to take Calculus II?

14. Statistically significant drops in confidence, enjoyment, and desire to continue Variable All Institutions Research Universities Mean (SD) Effect Size Mean (SD) Effect Size I am confident in my mathematical abilities (16) 4.89 (1.01) 0.46 4.93 (1.01) 0.47 4.42 (1.18) 4.40 (1.19) I enjoy doing mathematics (16) 4.63 (1.27) 0.27 4.69 (1.24) 0.33 4.28 (1.37) 4.28 (1.35) If I had a choice, I would continue to take mathematics (14) 2.93 (1.02) 0.09 2.97 (1.00) 0.14 2.84 (1.08) 2.83 (1.07) lowest = strongly disagree, highest = strongly agree

15. Instructor Pedagogy Factor Analysis 61 student ratings of what teachers do 53 used 3 factors arose from analysis Variables loading on the same factor 49% of the variance average classroom ratings Factors Good teaching, 22 variables Technology, 17 Ambitious pedagogy, 14 8 did not load onto factors

16. Good Teaching My Calculus Instructor: listened carefully to my questions and comments allowed time for me to understand difficult ideas presented more than one method for solving problems asked questions to determine if I understood what was being discussed discussed applications of calculus encouraged students to seek help during office hours frequently prepared extra material Assignments were challenging but doable My exams were graded fairly My calculus exams were a good assessment of what I learned

17. Ambitious Pedagogy My Calculus Instructor: Required me to explain my thinking on homework and exams Required students to work together Had students give presentations Held class discussions Put word problems in the homework and on the exams Put questions on the exams unlike those done in class Returned assignments with helpful feedback and comments

18. Main effects and Interactions Instructor Good teaching 0.246 *** Pedagogy Technology use 0.041 * Ambitious pedagogy -0.147 *** Interactions Class size ambitious pedagogy 0.002 *** larger classes benefit from ambitious pedagogy Initial state good teaching -0.047 ** students with poorer initial attitudes benefit more from good teaching Initial state ambitious pedagogy 0.037 ** students with higher initial attitudes benefit more from ambitious pedagogy Graduate instructor technology use -0.206 ** Graduate student instructors who use technology impact attitude negatively

19. Interaction on student confidence

20. Low Ambitious Pedagogy High Ambitious Pedagogy Switching percentages. p < 0.001 Low good teaching High good teaching Low ambitious teaching 16.2% 10.4% High ambitious teaching 11.9% 7.0%

21. Conclusions: 1. Calculus I is very effective at lowering student confidence and is a significant factor in discouraging students from continuing in STEM. 2. Good teaching, characterized as interacting with students in class and establishing the belief that you are there to support them, is essential. 3. Benefits of ambitious pedagogies are highly dependent on how they interact with other factors, but active learning strategies are generally beneficial. A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks For more information see www.maa.cspcc A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks For more information see www.maa.cspcc