What We Are Learning about Successful Programs In College Calculus

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1 What We Are Learning about Successful Programs In College Calculus David Bressoud St. Paul, MN Knox College Galesburg, IL May 15, 2014 A pdf file of this PowerPoint is available at

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

3 Three parts: 1. National survey of students in College Calculus I and their instructors 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

4 Characteristics of Successful Programs : 1. Faculty culture of concern about student learning and success 2. Departmental attention to local data to monitor program and placement effectiveness 3. Use of active learning approaches 4. Rigorous courses 5. Well-run and heavily utilized tutoring centers At universities with graduate programs: 6. Intensive TA training, monitoring, and support

5 Institution Type* Total Number of Type Sample Size ** Response Rate Two- year Colleges Undergraduate Colleges Master s UniversiPes Research UniversiPes (18%) 54 (26%) (13%) 60 (45%) (33%) 26 (43%) (61%) 73 (61%) * CBMS Classifications ** Used the CBMS sampling frame

6 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

7 Race/ Ethnicity Research Universi1es Masters Univ. Under- graduate 2- year Colleges Total Female 46% 47% 47% 34% 42% White 81% 82% 86% 73% 81% Black 5% 8% 8% 10% 7% Asian- American Percentage of students in Calculus by gender/race/ethnicity 17% 10% 10% 14% 13% Hispanic 9% 7% 11% 18% 11% Respondents could select more than one racial category. Self-identification as Hispanic was a separate question.

8 Career goals of students in Mainstream Calculus I other 4% business 7% soc sci 1% teacher 7% undecided 8% biological science 30% engineer 27% comp sci 7% phys sci 7% math 2%

9 Career goals of students in Mainstream Calculus I Calculus I at Undergrad Colleges soc sci 3% other 9% business 8% teacher 7% undecided 13% bio sci 25% engineer 22% phys sci 6% math 1% comp sci 6%

10 Career goals of women in Mainstream Calculus I Female Students in Calculus I business 7% soc sci 2% other 6% teacher 9% undecided 10% engineer 14% bio science 42% phys sci 6% math 2% comp sci 2%

11 250,000 Intended STEM Majors 200, , ,000 50,000 0 Engineering Bio Sciences Physical Sciences MathemaPcal Sciences Computer Science Source: HERI

12 Percen1le Scores on SAT/ACT Math Exams (as percen1le ranks) Research Masters Undergraduate Two- year Whiskers extend from 5 th to 95 th percentiles.

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

14 Grade for college Calculus I: 23% A 27% B 22% C 28% D, F, or Withdrew

15 40% Grade Distributions 35% 30% 25% 20% 15% 10% 5% 0% A B C DFW research university undergrad college masters university two year college Instructor reported grades

16 Research University Students in Calculus I, Fall 2010 AP exam 3 26% No calc in HS 30% AP exam < 3 15% Calc in HS, no AP exam 29%

17 Distribu1on of students with AP Scores 3 AB 3, BC < 3 2% BC 3 19% AB 3 40% AB %

18 Calculus I Grade (Research Universities) by High School Experience w/ Calculus AP exam 3 HS calc/no AP exam AP exam < 3 no HS calc 0% 20% 40% 60% 80% 100% A B C DFW

19 MAA Dataset Challenges Complex, Fall 2010 cohort 2 student surveys, pre and post (early and end-ofterm) 2 instructor surveys, pre and post 1 institutional coordinator survey Online administration Compliance 13,965 students with at least 1 complete survey 3,459 students with all 5 surveys

20 Strong selection bias at end of term: ~ 40% were getting an A ~ 40% were getting a B ~ 20% were getting a C Essentially none (< 4%) were getting D, F, or W

21 Switcher Analysis: Switcher = student who on initial survey selfidentifies as intending to take Calculus II, but by end of term has decided not to continue to Calculus II Overall rate: 14% Men: 11%, Women: 20%

22 Switcher Rates: 16% at research universities 19% for classes taught by GTAs 6% for engineers 12% science 16% science/math teachers 23% pre-med 27% business

23 Reason for not con1nuing in Calculus I changed my major and now do not need to take Calculus II I have too many other courses I need to complete My experience in Calculus I made me decide not to take Calculus II To do well in Calculus II, I would need to spend more Pme and effort than I can afford I do not believe I understand the ideas of Calculus I well enough to take Calculus II My grade in Calculus I was not good enough for me to conpnue to Calculus II percentage 51% 33% 32% 58% chose at least one of these 31% 23% 11%

24 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?

25 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 (1 6) I enjoy doing mathematics (1 6) If I had a choice, I would continue to take mathematics (1 4) 4.89 (1.01) 4.93 (1.01) (1.18) 4.40 (1.19) 4.63 (1.27) 4.69 (1.24) (1.37) 4.28 (1.35) 2.93 (1.02) 2.97 (1.00) (1.08) 2.83 (1.07) lowest = strongly disagree, highest = strongly agree

26 3- Level HLM Model Structure Main Effects InsPtuPonal SelecPvity Course # of students Pedagogy Professor CharacterisPcs Student IniPal Career Goal HS Pedagogy HS Math grades

27 HLM Where the issues lie? Variance explained Students are very different Instructors are somewhat similar 92% 6% 2% InsPtuPon Professor Student InsPtuPons are very similar

28 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 Progressive pedagogy, 14 8 did not load onto factors

29 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

30 Progressive Teaching 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

31 Main effects and Interactions Instructor Good teaching *** Pedagogy Technology use * Progressive pedagogy *** Interactions Class size progressive pedagogy Initial state good teaching Initial state progressive pedagogy Graduate instructor technology use *** larger classes benefit from progressive pedagogy ** students with poorer initial attitudes benefit more from good teaching ** students with higher initial attitudes benefit more from progressive pedagogy ** Graduate student instructors who use technology impact attitude negatively

32 InteracPon on student confidence 5 Post- Survey Confidence high "good teaching" low "good teaching" 0 Low Progressive Teaching High Progressive Teaching

33 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% Low Progressive Teaching Effect of Teaching on Switcher Rates High Progressive Teaching Low Good Teaching High Good Teaching

34 Conclusions: 1. Calculus I is very effective at lowering student confidence and is a significant factor in discouraging students from continuing in STEM. 2. Students heading into the bio sciences are the largest single group of Calculus I students. Their dominance is growing. 3. Benefits of progressive pedagogies are a complex issue intertwined with many other factors. Good teaching is essential. A pdf file of this PowerPoint is available at

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