Surveying Mathematics Departments to Identify Characteristics of Successful Programs in College Calculus Jessica Ellis San Diego State University Marilyn Carlson Arizona State University David Bressoud Macalester University Chris Rasmussen San Diego State University Sally Jacobs Scottsdale Community College Michael Pearson The Mathematical Association of America Eric Weber Arizona State University

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

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

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 after completion of Calculus 1

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)

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

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

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

ContactedResponded% Chairs Coordinators Instructors Pre term1, Post term (of 715) 43 (1,225) Students Pre termAbout 31,54512,22239 Post term12,2226,59854 (of 12,222) 21 (of estimated total) Survey Dissemination and Response Rates

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

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

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

The main issues: English as a second language concisely addressing diverse institution types general lexical issues Constrained by: Survey Monkey Survey consistency Phase 1: Instrument Refinement 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 s with suggested amendments

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?”

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

Preliminary Results: Student pre-term

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?

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

Phase 2: Logic Model

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) Phase 2: Case Study Teams

Phase 2: Logic Model

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)

Phase 2: Logic Model

The end. Thank you for listening. Marilyn Carlson Chris Rasmussen David Bressoud Michael Pearson This research is supported by the NSF under grant REC The views expressed do not necessarily reflect official positions of the NSF. For more information on the project, please contact: Special “thanks” to: Megan WawroGeorge SweeneyMichael Tallman