Report on the MAA National Study of College Calculus

Chicago Symposium Series Chicago, IL February 5, 2016

PDFfileoftheseslidesavailableatwww.macalester.edu/~bressoud/talks

David Bressoud St. Paul, MN

Characteristics of Successful Programs in College Calculus

2009–2016 PI: David Bressoud co-PI’s:

Marilyn Carlson

Arizona State

Michael Pearson MAA

Vilma Mesa

U Michigan

Chris Rasmussen San Diego

State

Linda Braddy MAA

Statistical Consultants: Phil Sadler & Gerhard Sonnert, Harvard

DRL REESE #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 18 institutions with “successful” Calculus I programs (Fall, 2012)

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

14%

13%

25%

34%

26%

26%

34%

30%

26%

30%

18%

18%

34%

31%

23%

18%

0% 20% 40% 60% 80% 100%

noHScalc

APexam<3

HScalc/noAPexam

APexam≥3

A B C DFW

Source: MAA CSPCC

Career goals of students in mainstream* Calculus I

Source: MAA CSPCC

Mathematical sciences

2%

Physical sciences

4%

Engineering 31%

Computer & IT 5% Geo sciences

2%

Bio sciences (includes pre-med)

30%

Teaching 5%

Social sciences 1%

Business 7%

Other 5%

Undecided 8%

* “Mainstream” implies it can be used as part of the pre-requisite stream for more advanced mathematics courses.

Gender differences of career goals of students in Mainstream Calculus I

math2% physsci

5%

eng38%

comp10%

geo2%

bio19%

teacher4%

social1% business

9%

other3%

undecided7%

CareerGoals,allmenmath1% physsci

4%

eng14% comp

2%

geo3%

bio43%

teacher10%

social2%

business7%

other5%

undecided9%

CareerGoals,allwomen

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 18 institutions with “successful” Calculus I programs (Fall, 2012)

Statistically significant drops in confidence, enjoyment, and desire to continue

Variable All 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

“GoodTeaching” (in order of significance)

My Calculus Instructor: 1.  providedexplanaRonsthatwereunderstandable 2.  helpedmebecomeabeSerproblemsolver 3.  allowedRmeformetounderstanddifficultideas 4.  mademefeelcomfortableinaskingquesRonsduring

class 5.  presentedmorethanonemethodforsolving

problems6.  madeclassinteresRng 7.  askedquesRonstodetermineifIunderstoodwhat

wasbeingdiscussed

“AmbiRousPedagogy”(in order of significance)

1.  Instructorhadstudentsworkwithoneanother2.  AssignmentsweresubmiSedasgroupprojects3.  ExamquesRonsincludedwordproblems4.  Assignmentsincludedwordproblems5.  AssignmentsrequiredexplanaRonofthinking6.  Assignmentsincludedproblemsunlikethosedonein

classorinthebook 7.  Instructorheldwhole-classdiscussion

0

1

2

3

4

5

Post-SurveyCo

nfide

nce high"good

teaching"

low"goodteaching"

LowAmbiRousPedagogy

HighAmbiRousPedagogy

InteracRononstudentconfidence

Switchers: students who started certain that they would go on to take Calculus II, but by the end of the term were no longer sure or had definitely decided not to continue.

Ellis & Rasmussen model of “switchers” Variables: gender, SAT/ACT math, previous calculus, intended major, institution type, good teaching, ambitious teaching, instructor type. Strongest predictors of switching: 1.  Female (1.68 times male) 2.  Low good teaching (1.54 times high) 3.  Taught by graduate student (1.43 times other)

Switchers by grade in Calculus I. Women:

A: 10% B: 13% C: 24% Men

A: 6% B: 6% C: 12%

Women in Engineering: A or B: 4% C: 19%

Men in Engineering A or B: 2% C: 7%

Reasonforswitching Gender StudentsearningAorB

StudentsearningC

ToomanyothercoursesIneedtotake

Women 43% 33%

Men 42% 16%

Havechangedmajor Women 40% 43%

Men 33% 39%

TakestoomuchRmeandeffort

Women 33% 25%

Men 29% 26%

BadexperienceinCalculusI

Women 18% 53%

Men 19% 35%

Don’tunderstandcalculuswellenough

Women 18% 38%

Men 4% 26%

Gradewasnotgoodenough

Women 7% 15%

Men 0% 13%

Students could select more than one response.

Reasonforswitching Gender StudentsearningAorB

StudentsearningC

ToomanyothercoursesIneedtotake

Women 43% 33%

Men 42% 16%

Havechangedmajor Women 40% 43%

Men 33% 39%

TakestoomuchRmeandeffort

Women 33% 25%

Men 29% 26%

BadexperienceinCalculusI

Women 18% 53%

Men 19% 35%

Don’tunderstandcalculuswellenough

Women 18% 38%

Men 4% 26%

Gradewasnotgoodenough

Women 7% 15%

Men 0% 13%

Students could select more than one response.

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 18 institutions with “successful” Calculus I programs (Fall, 2012)

8 Common Features of Calculus Programs at Selected PhD Granting Institutions

1- Rigorous courses 2- Attention to local data 3- Solid GTA professional development 4- Support for active learning 5- Coordination of courses 6- Strong student support services 7- Attention to placement issues 8- Regular meetings of course instructors

insightsandrecommendations

fromthe

nationalstudyof

collegecalculus

maa

EDITORS DAVID BRESSOUD VILMA MESA CHRIS RASMUSSEN

Bressoud, Mesa, & Rasmussen (eds.). 2015. Insights and Recommendations from the MAA National Study of College Calculus.

Chapters describing best practices in •  Placement •  Student support •  Pedagogy •  Departmental dynamics •  Preparation for teaching for graduate students

PDF available at maa.org/cspcc

Progress through Calculus 2015–2019

PI: David Bressoud co-PI’s and senior personnel:

Estrella Johnson Virginia

Tech

Jess Ellis

Colorado State

Chris Rasmussen San Diego

State

Linda Braddy MAA

DUE I-USE #1430540

Sean Larsen

Portland State

Progress through Calculus •  Restrict to departments with graduate programs in

Mathematics (Masters and/or PhD) •  Pre-Calculus through Calculus II sequence •  Multiple outcome measures (including pre- and

post-testing of student knowledge, tracking persistence, success in subsequent courses)

•  Focus on networking and observing departments that are reforming one or more courses in this sequence

Spring 2015, surveys on the precalculus through single variable calculus sequence sent to all 330 US math departments offering a graduate degree in mathematics. Response rates:

PhD departments: 134/178 = 75% MA departments: 89/152 = 59% Overall: 223/330 = 68%

CC

UCC

RIM

UoD

SP

GTAT

SSP

AL0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.00 0.20 0.40 0.60 0.80 1.00

Succ

essf

ul

Important

UCC=uniformcoursecomponents

CC=challengingcourses

GTAT=graduateteachingassistanttraining

SSP=studentsupportprograms

SP=studentplacement

RIM=regularinstructormeeRngs

UoD=useofdata

AL=acRvelearning

Weighted average of responses: very important or successful, +1 somewhat, 0 not important or successful, – 1

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

WhatisimportantvswheretheyaresuccessfulPhDprograms

veryimportant verysuccessful

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

WhatisimportantvswheretheyaresuccessfulMastersprograms

veryimportant verysuccessful

0%

10%

20%

30%

40%

50%

60%

70%

PhD Masters

Percentage of respondents using placement tool (could select multiple placement tools)

From 2010 to 2015, use of ALEKS for placement at universities with PhD programs has jumped from 10% to 28%. Adaptive questioning Includes focused instructional modules Opportunities for retesting Does not use multiple choice questions

Number (out of 223) using each placement tool With degree of overall satisfaction with placement

0

20

40

60

80

100

120

SaRsfied Adequate,couldbeimproved DissaRsfied

Across all placement instruments 9% are not satisfied

39% consider them adequate, but could be improved

30% are currently replacing or have recently replaced their placement instrument(s)

29% are considering changing their placement instruments

Interesting approaches (in place or planned):""Illinois-Urbana/Champaign. Separate 5-credit

Calculus I for those who have not had calculus

Arizona & Michigan. Diversion to special precalculus class that starts after first exam

OK State. Diagnostic quiz after Calc I starts with easy switch to precalculus.

Florida, George Mason, Colorado-Boulder. Easy late switch to precalculus

Lecture63%SomeacRve

learning18%

MainlyacRvelearning

3%

Lecture+CBI3% Other

13%

PrimarystyleofinstrucRonforMainstreamCalculus

SomeacRvelearning(e.g.clickers),mostlylectureMainlyacRvelearning(e.g.flippedclasses),minimallectureCBI=ComputerbasedinstrucRon“Other”includestoomuchvariaRontospecifyonestyle

35% of surveyed universities are using active learning in at least some sections

Next Stages: Building networks of universities sharing common concerns.

•  Conference on Precalculus to Calculus: Insights and Innovation, Saint Paul, MN, June 16–19, 2016 www.maa.org/cspcc

Identification of twelve universities for detailed study over three years.

ApdffileofthisPowerPointisavailableatwww.macalester.edu/~bressoud/talks