Report on the MAA National Study of College Calculus

Report on the MAA National Study of College Calculus David Bressoud St. Paul, MN Chicago Symposium Series Chicago, IL February 5, 2016 PDF file of these slides available at www.macalester.edu/~bressoud/talks

Characteristics of Successful Programs in College Calculus PI: David Bressoud co-pi s: Chris Rasmussen San Diego State Marilyn Carlson Arizona State 2009 2016 Vilma Mesa U Michigan Michael Pearson MAA DRL REESE #0910240 Linda Braddy MAA Statistical Consultants: Phil Sadler & Gerhard Sonnert, Harvard

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)

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

AP exam 3 34% 30% 18% 18% HS calc/no AP exam 25% 34% 18% 23% AP exam < 3 13% 26% 30% 31% no HS calc 14% 26% 26% 34% 0% 20% 40% 60% 80% 100% A B C DFW Source: MAA CSPCC

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

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

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) 0.46 4.42 (1.18) 4.40 (1.19) 4.63 (1.27) 4.69 (1.24) 0.27 4.28 (1.37) 4.28 (1.35) 2.93 (1.02) 2.97 (1.00) 0.09 2.84 (1.08) 2.83 (1.07) 0.47 0.33 0.14 lowest = strongly disagree, highest = strongly agree

Good Teaching (in order of significance) My Calculus Instructor: 1. provided explanarons that were understandable 2. helped me become a beser problem solver 3. allowed Rme for me to understand difficult ideas 4. made me feel comfortable in asking quesrons during class 5. presented more than one method for solving problems 6. made class interesrng 7. asked quesrons to determine if I understood what was being discussed

AmbiRous Pedagogy (in order of significance) 1. Instructor had students work with one another 2. Assignments were submised as group projects 3. Exam quesrons included word problems 4. Assignments included word problems 5. Assignments required explanaron of thinking 6. Assignments included problems unlike those done in class or in the book 7. Instructor held whole-class discussion

InteracRon on student confidence 5 Post-Survey Confidence 4 3 2 1 high "good teaching" low "good teaching" 0 Low AmbiRous Pedagogy High AmbiRous Pedagogy

Ellis & Rasmussen model of switchers Variables: gender, SAT/ACT math, previous calculus, intended major, institution type, good teaching, ambitious teaching, instructor type. Strongest predictors of switching: 1. Female (1.68 times male) 2. Low good teaching (1.54 times high) 3. Taught by graduate student (1.43 times other) 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.

Switchers by grade in Calculus I. Women: A: 10% B: 13% C: 24% Men A: 6% B: 6% C: 12% Women in Engineering: A or B: 4% C: 19% Men in Engineering A or B: 2% C: 7%

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 Rme 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.

8 Common Features of Calculus Programs at Selected PhD Granting Institutions 1- Rigorous courses 2- Attention to local data 3- Solid GTA professional development 4- Support for active learning 5- Coordination of courses 6- Strong student support services 7- Attention to placement issues 8- Regular meetings of course instructors

insights andrecommendations fromthe maa nationalstudyof college calculus Bressoud, Mesa, & Rasmussen (eds.). 2015. Insights and Recommendations from the MAA National Study of College Calculus. EDITORS DAVID BRESSOUD VILMA MESA CHRIS RASMUSSEN Chapters describing best practices in Placement Student support PDF available at Pedagogy maa.org/cspcc Departmental dynamics Preparation for teaching for graduate students

Progress through Calculus 2015 2019 DUE I-USE #1430540 PI: David Bressoud co-pi s and senior personnel: Chris Rasmussen San Diego State Linda Braddy MAA Jess Ellis Colorado State Estrella Johnson Virginia Tech Sean Larsen Portland State

Progress through Calculus Restrict to departments with graduate programs in Mathematics (Masters and/or PhD) Pre-Calculus through Calculus II sequence Multiple outcome measures (including pre- and post-testing of student knowledge, tracking persistence, success in subsequent courses) Focus on networking and observing departments that are reforming one or more courses in this sequence

Spring 2015, surveys on the precalculus through single variable calculus sequence sent to all 330 US math departments offering a graduate degree in mathematics. Response rates: PhD departments: 134/178 = 75% MA departments: 89/152 = 59% Overall: 223/330 = 68%

Successful 0.70 0.60 0.50 0.40 0.30 CC UCC GTAT SSP 0.20 UoD 0.10 AL RIM 0.00 0.00 0.20 0.40 0.60 0.80 1.00 Important Weighted average of responses: very important or successful, +1 somewhat, 0 not important or successful, 1 SP UCC = uniform course components CC = challenging courses GTAT = graduate teaching assistant training SSP = student support programs SP = student placement RIM = regular instructor meerngs UoD = use of data AL = acrve learning

90% 80% 70% 60% 50% 40% 30% 20% 10% 0% What is important vs where they are successful PhD programs very important very successful

90% 80% 70% 60% 50% 40% 30% 20% 10% 0% What is important vs where they are successful Masters programs very important very successful

Percentage of respondents using placement tool (could select multiple placement tools) 70% 60% 50% 40% 30% 20% 10% 0% PhD Masters

From 2010 to 2015, use of ALEKS for placement at universities with PhD programs has jumped from 10% to 28%. Adaptive questioning Includes focused instructional modules Opportunities for retesting Does not use multiple choice questions

120 Number (out of 223) using each placement tool With degree of overall satisfaction with placement 100 80 60 40 20 0 SaRsfied Adequate, could be improved DissaRsfied

Across all placement instruments 9% are not satisfied 39% consider them adequate, but could be improved 30% are currently replacing or have recently replaced their placement instrument(s) 29% are considering changing their placement instruments

Interesting approaches (in place or planned):" " Illinois-Urbana/Champaign. Separate 5-credit Calculus I for those who have not had calculus Arizona & Michigan. Diversion to special precalculus class that starts after first exam OK State. Diagnostic quiz after Calc I starts with easy switch to precalculus. Florida, George Mason, Colorado-Boulder. Easy late switch to precalculus

Primary style of instrucron for Mainstream Calculus Lecture + CBI 3% Other 13% Mainly acrve learning 3% Some acrve learning 18% Lecture 63% 35% of surveyed universities are using active learning in at least some sections Some acrve learning (e.g. clickers), mostly lecture Mainly acrve learning (e.g. flipped classes), minimal lecture CBI = Computer based instrucron Other includes too much variaron to specify one style

Next Stages: Building networks of universities sharing common concerns. Conference on Precalculus to Calculus: Insights and Innovation, Saint Paul, MN, June 16 19, 2016 www.maa.org/cspcc Identification of twelve universities for detailed study over three years. A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks