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