Insights from. The MAA National Study of College Calculus. David Bressoud St. Paul, MN. CMS-SMC Summer Meeting Charlottetown, PEI June 6, 2015

Transcription

1 Insights from DRL REESE # The MAA National Study of College Calculus David Bressoud St. Paul, MN CMS-SMC Summer Meeting Charlottetown, PEI June 6, 2015 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 Arizona State Michael Pearson MAA DRL REESE # Vilma Mesa U Michigan Linda Braddy MAA Chris Rasmussen San Diego State Statistical Consultants: Phil Sadler & Gerhard Sonnert, Harvard

3 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 18 institutions with successful Calculus I programs (Fall, 2012)

4 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

5 Course taking in High School By students taking Calculus I at Research Universities Algebra II* 10 th grade 77% Precalculus* 11 th grade Calculus 12 th grade Statistics 12 th grade 67% 67% 9% * Does not count students who took an integrated curriculum

6 Characteristics of Calculus I Students at Research Universities Average high school math GPA 3.77 SAT scores: 3rd Quartile Median 1st Quartile Took Precalculus in college 13% Agree that to succeed in Calculus I, must have taken it before. 49%

7 Final Grades as Reported by Instructors two year college 21.1% 22.0% 19.5% 37.5% masters university 21.1% 21.8% 20.1% 37.1% undergrad college 24.4% 29.6% 23.7% 22.3% research university 22.7% 29.7% 22.9% 24.7% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% A B C DFW

8 Career goals of students in mainstream* Calculus I Social sciences 1% Mathematical sciences 2% Business 7% Teaching 5% Undecided Other 8% 5% Physical sciences 4% Engineering 31% Bio sciences (includes pre-med) 30% Computer & IT Geo sciences 5% 2% * Mainstream implies it can be used as part of the prerequisite stream for more advanced mathematics courses. Source: MAA CSPCC

9 Gender differences of career goals of students in Mainstream Calculus I social 1% teacher 4% undecided 7% other 3% business 9% bio 19% Career Goals, all men geo 2% math 2% comp 10% phys sci 5% eng 38% business 7% social 2% Career Goals, all women undecided 9% other 5% teacher 10% math 1% phys sci 4% bio 43% eng 14% comp 2% geo 3%

10 Switchers: students who started certain that they would go on to take Calculus II, but by the end of the term were no longer sure or had definitely decided not to continue. Of those who started intending to take Calculus II: 11% of men were switchers 20% of women

11 Switchers by grade in Calculus I. Women: A: 10% B: 13% C: 24% Men A: 6% B: 6% C: 12%

12 Switchers by intended major Women in Bio Science: A or B: 19% C: 29% Men in Bio Science A or B: 13% C: 26% Women in Engineering: A or B: 4% C: 19% Men in Engineering A or B: 2% C: 7%

13 Reason for switching Gender Students earning A or B Too many other courses I need to take Students earning C Women 43% 33% Men 42% 16% Have changed major Women 40% 43% Takes too much Sme and effort Bad experience in Calculus I Don t understand calculus well enough Grade was not good enough Men 33% 39% Women 33% 25% Men 29% 26% Women 18% 53% Men 19% 35% Women 18% 38% Men 4% 26% Women 7% 15% Men 0% 13% Students could select more than one response.

14 Reason for switching Gender Students earning A or B Too many other courses I need to take Students earning C Women 43% 33% Men 42% 16% Have changed major Women 40% 43% Takes too much Sme and effort Bad experience in Calculus I Don t understand calculus well enough Grade was not good enough Men 33% 39% Women 33% 25% Men 29% 26% Women 18% 53% Men 19% 35% Women 18% 38% Men 4% 26% Women 7% 15% Men 0% 13% Students could select more than one response.

15 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)

16 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

17 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

18 AmbiSous 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

19 InteracSon on student confidence 5 Post- Survey Confidence high "good teaching" low "good teaching" 0 Low AmbiSous Pedagogy High AmbiSous Pedagogy

20 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)

21 7 Common Features of Calculus Programs at Selected PhD GranSng InsStuSons 1- Rigorous courses 2- A_enSon to local data 3- GTA professional development 4- SupporSng teaching and acsve learning 5- CoordinaSon 6- Learning resources 7- Placement

22 4- SupporSng Teaching and AcSve Learning Calculus instructors were encouraged to use and try out acsve learning strategies. In some cases faculty received regular s with links to arscles or other informason about teaching. One insstuson even had biweekly teaching seminars led by the math faculty or invited experts. ParScular instrucsonal approaches were not, however, prescribed or required for faculty at any of the insstusons. Faculty had choices.

23 5 - CoordinaSon Calculus I course Coordinator not a rotasng posison or commi_ee assignment Regular meesngs take place where calculus instructors discuss issues of teaching and learning Instructors have pedagogical autonomy CoordinaSon helps establish the teaching of calculus as a joint enterprise where calculus is community property

24 insights andrecommendations fromthe maa nationalstudyof college calculus EDITORS DAVID BRESSOUD VILMA MESA CHRIS RASMUSSEN Bressoud, Mesa, & Rasmussen (eds.) Insights and Recommendations from the MAA National Study of College Calculus. MAA Notes. Available August, 2015 Links to publications and further information at A pdf file of this PowerPoint is available at