Building forSuccess inCalculus
David BressoudSt. Paul, MN
The First Two Years of College Math: Building Student Success
Reston, VAOctober 5–7, 2014
A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks
For more information see www.maa.cspcc
A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks
For more information see www.maa.cspcc
NSF #0910240
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)
Characteristics of Successful Programs in College Calculus
PI: David Bressoudco-PI’s:
Vilma Mesa
U Michigan
Marilyn Carlson
ASU
Michael PearsonMAA
Chris Rasmussen
SDSU
Linda BraddyMAA
Statistical Consultants: Phil Sadler & Gerhard Sonnert
DRL REESE#0910240
Progress through Calculus
PI: David Bressoudco-PI’s:
Sean LarsenPortland State
Linda BraddyMAA
Jess ElliseColorado State
DUE IUSE#1420839
Chris Rasmussen
SDSU
Fall 2010Phase I: Survey
Responses from
213 colleges and universities
502 instructors representing 663 Calculus I classes and 26,257 students
14,184 students
research masters
undergrad 2 year
Average high school math GPA
3.77 3.58 3.64 3.37
Took calculus in high school
70% 43% 53% 24%
≥ 3 on AP Calc 26% 9% 14% 5%
Took Precalculus in college
13% 31% 17% 60%
Agree that to succeed in Calculus I, must have taken it before.
49% 36% 40% 37%
PhD BA MA 2Y Coll AVGMean age (SD)
18.3 (2.4) 18.8 (2.9) 20.5 (5.3) 22.0 (7.4) 19.7 (3.5)
Freshman 83% 73% 50% 25% 63%Soph-omore
10% 16% 27% 40% 21%
Junior/Senior
6% 10% 17% 18% 11%
Enrolled full time
99% 98% 91% 76% 92%
Age, year in college, enrollment status
PhD BA MA 2Y Coll AVG
Father completed college
65% 58% 49% 44% 56%
Mother completed college
62% 56% 47% 40% 53%
Some concern about paying for college
54% 40% 57% 55% 51%
Major concern about paying for college
13% 10% 13% 23% 14%
Socio-economic status
From The American Freshman, 55% of all incoming full-time students at 4-year institutions have some concern, 11% have major concern, about paying for college.
PhD BA MA TYC
Comfortable with graphing calculator
Somewhat 14% 14% 18% 18%
Yes 81% 82% 77% 74%
Graphing calcallowed on exams
Sometimes 60% 55% 53% 48%
Always 31% 39% 32% 29%
TI-89 or -92allowed on exams
Sometimes 25% 22% 25% 25%
Always 31% 37% 30% 28%
Prepared for calculation without calc
Somewhat 28% 29% 30% 27%
Yesc59% 58% 57% 57%
Graphing calculator usage in high school
Gender differences of career goals of students in Mainstream Calculus I
Source: HERI
3-Level HLM Model StructureMain Effects
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?
Statistically significant drops in confidence, enjoyment, and desire to continue
VariableAll Institutions Research Universities
Mean (SD) Effect Size Mean (SD) Effect Size
I am confident in my mathematical abilities (1–6)
4.89 (1.01)–0.46
4.93 (1.01)–0.47
4.42 (1.18) 4.40 (1.19)
I enjoy doing mathematics(1–6)
4.63 (1.27)–0.27
4.69 (1.24)–0.33
4.28 (1.37) 4.28 (1.35)
If I had a choice, I would continue to take mathematics (1–4)
2.93 (1.02)–0.09
2.97 (1.00)–0.14
2.84 (1.08) 2.83 (1.07)
lowest = strongly disagree, highest = strongly agree
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
– Ambitious pedagogy, 14
– 8 did not load onto factors
“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
“Ambitious 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
Main effects and InteractionsInstructor Good teaching 0.246***Pedagogy Technology
use0.041*
Ambitious pedagogy -0.147***
Interactions Class size × ambitious pedagogy
0.002*** larger classes benefit from ambitious pedagogy
Initial state × good teaching
-0.047** students with poorer initial attitudes benefit more from good teaching
Initial state × ambitious pedagogy
0.037** students with higher initial attitudes benefit more from ambitious pedagogy
Graduate instructor × technology use
-0.206** Graduate student instructors who use technology impact attitude negatively
Interaction on student confidence
Low Ambitious Pedagogy
High Ambitious Pedagogy
Switching percentages. p < 0.001
Low good teaching High good teaching
Low ambitious teaching 16.2% 10.4%
High ambitious teaching 11.9% 7.0%
Conclusions:
1.Calculus I is very effective at lowering student confidence and is a significant factor in discouraging students from continuing in STEM.
2.“Good teaching,” characterized as interacting with students in class and establishing the belief that you are there to support them, is essential.
3.Benefits of ambitious pedagogies are highly dependent on how they interact with other factors, but active learning strategies are generally beneficial.
A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks
For more information see www.maa.cspcc
A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks
For more information see www.maa.cspcc