building for success in calculus
DESCRIPTION
Building for Success in Calculus. NSF #0910240. The First Two Years of College Math: Building Student Success Reston, VA October 5–7, 2014. David Bressoud St. Paul, MN. A pdf file of this PowerPoint is available at www.macalester.edu/~bressoud/talks - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/1.jpg)
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
![Page 2: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/2.jpg)
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)
![Page 3: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/3.jpg)
Race/Ethnicity
ResearchUniversities
MastersUniv.
Under-graduate
2-yearColleges
Total
Female 46% 47% 47% 34% 42%
White 81% 82% 86% 73% 81%
Black 5% 8% 8% 10% 7%
Asian-American
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.
Percentage of students in Calculus by gender/race/ethnicity
![Page 4: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/4.jpg)
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%
![Page 5: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/5.jpg)
Career goals of students in Mainstream Calculus I
![Page 6: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/6.jpg)
Gender differences of career goals of students in Mainstream Calculus I
![Page 7: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/7.jpg)
Source: HERI
![Page 8: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/8.jpg)
Final Grades as Reported by Instructors
![Page 9: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/9.jpg)
![Page 10: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/10.jpg)
![Page 11: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/11.jpg)
![Page 12: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/12.jpg)
3-Level HLM Model StructureMain Effects
![Page 13: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/13.jpg)
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?
![Page 14: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/14.jpg)
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
![Page 15: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/15.jpg)
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
![Page 16: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/16.jpg)
“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
![Page 17: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/17.jpg)
“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
![Page 18: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/18.jpg)
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
![Page 19: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/19.jpg)
Interaction on student confidence
![Page 20: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/20.jpg)
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%
![Page 21: Building for Success in Calculus](https://reader034.vdocuments.mx/reader034/viewer/2022051516/568131d1550346895d9839bd/html5/thumbnails/21.jpg)
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