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Building for Success in Calculus

This presentation explores the characteristics of successful programs in college calculus, including a national survey of students and instructors, statistical models of factors influencing student attitudes, and case studies of institutions with successful calculus programs.

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Building for Success in Calculus

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  1. Building for Success in Calculus NSF #0910240 The First Two Years of College Math: Building Student Success Reston, VA October 5–7, 2014 David Bressoud St. Paul, MN A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks For more information see www.maa.cspcc

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

  3. Percentage of students in Calculus by gender/race/ethnicity Respondents could select more than one racial category. Self-identification as Hispanic was a separate question.

  4. Career goals of students in Mainstream Calculus I

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

  6. Source: HERI

  7. Final Grades as Reported by Instructors

  8. 3-Level HLM Model StructureMain Effects

  9. 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?

  10. Statistically significant drops in confidence, enjoyment, and desire to continue lowest = strongly disagree, highest = strongly agree

  11. 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

  12. “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

  13. “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

  14. Main effects and Interactions

  15. Interaction on student confidence

  16. Low Ambitious Pedagogy High Ambitious Pedagogy Switching percentages. p < 0.001

  17. Conclusions: Calculus I is very effective at lowering student confidence and is a significant factor in discouraging students from continuing in STEM. “Good teaching,” characterized as interacting with students in class and establishing the belief that you are there to support them, is essential. 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

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