Building for
Success in
Calculus
David Bressoud
St. Paul, MN
NSF #0910240
The First Two Years of College Math:
Building Student Success
Reston, VA
October 5–7, 2014
A pdf file of this PowerPoint is available at
www.macalester.edu/~bressoud/talks
For more information see www.maa.cspcc
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 Bressoud
co-PI’s:
Marilyn
Carlson
ASU
Vilma
Mesa
U Michigan
DRL REESE
#0910240
Michael
Pearson
MAA
Linda
Braddy
MAA
Chris
Rasmussen
SDSU
Statistical Consultants: Phil Sadler & Gerhard Sonnert
Progress through Calculus
DUE IUSE
#1420839
PI: David Bressoud
co-PI’s:
Chris
Rasmussen
SDSU
Linda
Braddy
MAA
Jess Ellise
Colorado State
Sean Larsen
Portland State
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
research master undergrad 2 year
s
Average high
school math GPA
Took calculus in
high school
≥ 3 on AP Calc
Took Precalculus
in college
Agree that to
succeed in
Calculus I, must
have taken it
before.
3.77
3.58
3.64
3.37
70%
43%
53%
24%
26%
9%
14%
5%
13%
31%
17%
60%
49%
36%
40%
37%
Age, year in college, enrollment status
PhD
BA
MA
2Y Coll
AVG
Mean age
18.3 (2.4) 18.8 (2.9) 20.5 (5.3) 22.0 (7.4) 19.7 (3.5)
(SD)
Freshman
83%
73%
50%
25%
63%
Soph10%
16%
27%
40%
21%
omore
Junior/Se
6%
10%
17%
18%
11%
nior
Enrolled
99%
98%
91%
76%
92%
full time
Socio-economic status
Father completed
college
Mother completed
college
Some concern
about paying for
college
Major concern
about paying for
college
PhD
BA
MA
2Y Coll
AVG
65%
58%
49%
44%
56%
62%
56%
47%
40%
53%
54%
40%
57%
55%
51%
13%
10%
13%
23%
14%
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.
Graphing calculator usage in high school
Comfortable
with
graphing
calculator
Graphing
calc
allowed on
exams
TI-89 or -92
allowed
on exams
PhD
BA
MA
TYC
Somewhat
14%
14%
18%
18%
Yes
81%
82%
77%
74%
Sometimes
60%
55%
53%
48%
Always
31%
39%
32%
29%
Sometimes
25%
22%
25%
25%
Always
31%
37%
30%
28%
28%
29%
30%
27%
59%
58%
57%
57%
Prepared for Somewhat
calculation
without calc Yesc
Gender differences of career goals of
students in Mainstream Calculus I
math
2%
Career Goals, all men
undecided
7%
other
3%
social
1%
teacher
4%
Career Goals, all women
undecided
9%
other
5%
phys sci
5%
business
9%
eng
38%
math
1%
eng
14%
business
7%
social
2%
comp
geo 2%
3%
teacher
10%
bio
19%
comp
10%
geo
2%
phys sci
4%
bio
43%
Intended STEM Majors
250,000
200,000
150,000
100,000
50,000
0
Engineering
Bio Sciences
Physical Sciences
Mathematical Sciences
Computer Science
Source: HERI
3-Level HLM Model Structure
Main Effects
Institutional
Selectivity
Course
# of students
Pedagogy
Professor
Characteristics
Student
Initial Career
Goal
HS Pedagogy
HS Math
grades
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
All Institutions
Variable
Mean
I am confident in my 4.89
mathematical abilities
(1–6)
4.42
I enjoy doing
mathematics
(1–6)
(SD)
Effect Size
Research Universities
Mean
(SD)
4.93
(1.01)
(1.18)
4.40
(1.19)
4.63
(1.27)
4.69
(1.24)
4.28
(1.37)
4.28
(1.35)
(1.02)
2.97
(1.00)
2.83
(1.07)
If I had a choice, I
2.93
would continue to take
mathematics (1–4)
2.84
(1.01)
(1.08)
–0.46
–0.27
–0.09
lowest = strongly disagree, highest = strongly agree
Effect Size
–0.47
–0.33
–0.14
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 Interactions
Instructor
Good teaching
0.246 ***
Pedagogy
Technology use
Ambitious
pedagogy
0.041 *
Interactions
-0.147 ***
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
Post-Survey Confidence
5
4
high "good
teaching"
3
low "good
teaching"
2
1
0
Low Ambitious
Pedagogy
High Ambitious
Pedagogy
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
Effect of Pedagogy on Switcher Rates
Low Good
Teaching
High Good
Teaching
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