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Surveying Mathematics Departments to Identify Characteristics of Successful Programs in College Calculus. Outline. Goals and Background of Study Research Questions Project Phases Phase 1: National Survey Survey Design Data Collection Preliminary Results Phase 2: Explanatory Case Studies

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  1. Surveying Mathematics Departments to Identify Characteristics of Successful Programs in College Calculus

  2. Outline • Goals and Background of Study • Research Questions • Project Phases • Phase 1: National Survey • Survey Design • Data Collection • Preliminary Results • Phase 2: Explanatory Case Studies • Survey Design • Data Collection

  3. Goals of Study • Identify factors that contribute to success in college calculus • Understand why and how these factors are leveraged in highly successful programs

  4. Success Defined “The most serious problem with current college calculus is not that students are inadequately prepared for the subsequent courses, but rather that they never take the subsequent courses” (Thompson et al., 2007). Success in Calculus I is determined by: • completion of the course with an expected grade of C or higher • and the intention to persist in the study of calculus at least into Calculus II aftercompletion of Calculus 1

  5. Background • College students enrolling calculus or above has decreased steadily from 8.93% in 1990 to 6.39% in 1996 (Lutzer et al., 2007) • Calculus I is a primary filter of students in undergraduate STEM programs across the nation (e.g., Steen, 1997; Thompson et al., 2006) • The pattern of losing students in calculus and STEM majors is a great cost to our nation’s intellectual power and financial well being (Business Higher Education Forum, 2007)

  6. Research Questions • What are the primary variables that affect student success in calculus? • To be addressed primarily in Phase 1 • What institutional, course, and instructor attributes contribute to student success in calculus? • To be addressed primarily in Phase 2

  7. Phases of Analyses Phase 1 Large National Survey Community Colleges Four Year Colleges Masters Granting Institutions PhD Granting Institutions

  8. Phase 1: Data Collection • Five surveys were developed and disseminated: • one course coordinator • student pre-term • student post-term • instructor pre-term • instructor post-term

  9. Survey Dissemination and Response Rates

  10. Phase 1: Major Taxonomy Dimensions Independent Variables A. Student Beliefs and Affect (with 5 subcategories) B. Perceived Behaviors and Values of the Calculus Instructor (with 4 subcategories) C. The Role of Homework and Exams (with 4 subcategories) D. The Role and Behavior of the Student in Learning (with 6 subcategories) E. Supports for Students (with 2 subcategories) F. Readiness for Calculus (Post-survey) Dependent Variables A. Course grade and intention to take Calculus II (with 4 subcategories) B. Impact of Calculus I course on student (with 4 subcategories) C. Student self-perception of knowledge/skills in calculus

  11. Select Independent Variables: Perceived Behaviors and Values of the Calculus Instructor • Wants students to understand the ideas of calculus • Engages students in completing meaningful tasks • Seeks input to assess student understanding • Listens to students when they speak • Encourages students to make logical conjectures • Makes ideas of calculus relevant • Presses students for quality explanations • Holds students accountable for staying on task • Allows time for understanding difficult ideas • Makes class interesting • Makes sure there is closure after working on challenging problems • Supports students in becoming better problem solvers • Provides explanations that are understandable

  12. Select Dependent Variables: Course grade and intention to take Calculus II • Student anticipated course grade • Intention to take Calculus II • Before term • After term • Assuming a Calculus I course grade of A, B, C, likelihood of continuing to Calculus II

  13. Phase 1: Instrument Refinement • The main issues: • English as a second language • concisely addressing diverse institution types • general lexical issues • Constrained by: • Survey Monkey • Survey consistency • The refinement process for these surveys included: • pilot surveys for students and instructors at two large southwestern universities • documents coordinating the five surveys • weekly team conference calls • emails with suggested amendments

  14. Example: Instrument Refinement • Two English as a second language issues surfaced during instructor pilot: • the double negative when answering never: “I never was unable to make time for students to understand difficult ideas.” • the term “make time.” “How can you make time?”

  15. Preliminary Results: Student pre-term • About 60% of students enrolled in Calculus 1 passed Calculus AB • About 58% of students enrolled in Calculus 1 passed Calculus BC

  16. Preliminary Results: Student pre-term

  17. Preliminary Results: Student pre-term

  18. Research Questions • What are the primary variables that affect student success in calculus? • What institutional, course, and instructor attributes contribute to student success in calculus?

  19. Phase 1 Large National Survey Phase 2 Explanatory Case Studies Informative Investigation of two successful programs Community Colleges Informative Investigation of two successful programs Four Year Colleges Informative Investigation of two successful programs Masters Granting Institutions Informative Investigation of two successful programs PhD Granting Institutions

  20. Phase 2: Logic Model

  21. Phase 2: Case Study Teams • Community college Team • Sean Larsen (math ed researcher), John Caughman (mathematician), Estrella Johnson (graduate student) • Four-year college Team • Eric Hsu (math ed researcher), Arek Goetz (mathematician), graduate student • Masters degree granting institution Team • Chris Rasmussen (math ed researcher), Samuel Shen (mathematician), Jess Ellis (graduate student) • PhD granting institution Team • Marilyn Carlson (math ed researcher), Wayne Raskind (mathematician), Michael Tallman (graduate student)

  22. Phase 2: Logic Model

  23. Phase 2: Data Collection • Documentation data • memoranda and other communiqués • Agendas • announcements and minutes of meetings • administrative documents • formal studies and evaluations • Direct observation • Archival records • past Calculus enrollment history • number of sections offered • passing rates and statistical reports • Interviews • Semi structured group (students) • Semi structured individual (key personnel)

  24. Phase 2: Logic Model

  25. The end. Thank you for listening. For more information on the project, please contact: Marilyn Carlson mcarlson@exchange.asu.edu Chris Rasmussen chrisraz@sciences.sdsu.edu David Bressoud bressoud@macalester.edu Michael Pearson pearson@maa.org Special “thanks” to: Megan Wawro George Sweeney Michael Tallman This research is supported by the NSF under grant REC-0910240. The views expressed do not necessarily reflect official positions of the NSF.

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