Building for Success in Calculus

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)

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

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%

Career goals of students in Mainstream Calculus I

Gender differences of career goals of students in Mainstream Calculus I

Source: HERI

Final Grades as Reported by Instructors

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