Teaching Calculus Now: Current Trends &

Best Practices

Western Michigan University Kalamazoo, MI November 3, 2016

PDFfileoftheseslidesavailableatwww.macalester.edu/~bressoud/talks

David Bressoud St. Paul, MN

MATHEMATICAL ASSOCIATION OF AMERICA

CSPCC#0910240PtC#1430540

The Problems

1.  Economic realities

2.  Demands of the client disciplines

3.  The rush to calculus

Solutions

EconomicRealiHes

Source:AMS

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

PostedDoctoralPosi.ons:Ra.ooftenuretracktonon-tenure-track

Career goals of students in mainstream* Calculus I

DemandsoftheClientDisciplines

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”impliesitcanbeusedaspartofthepre-requisitestreamformoreadvancedmathemaHcscourses.

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%

comp2%

geo3%

bio43%

teacher10%

social2%

business7%

other5% undecided

9%

CareerGoals,allwomen

DemandsoftheClientDisciplines

Source: MAA CSPCC

0

50,000

100,000

150,000

200,000

250,000

IntendedSTEMMajors

Engineering BioSciences PhysicalSciences

MathemaHcalSciences ComputerScience

94% increase from 2007 to 2015

DemandsoftheClientDisciplines

Source:TheAmericanFreshman,HERI

Report to the President: Engage to Excel Feb., 2012

DemandsoftheClientDisciplines

Recommendation 3-1: “This national experiment should fund … college mathematics teaching and curricula developed and taught by faculty from mathematics-intensive disciplines other than mathematics, including physics, engineering, and computer science.”

Report to the President: Engage to Excel Feb., 2012

DemandsoftheClientDisciplines

Rationale: “Discipline-based education [research] on effective undergraduate mathematics teaching also appears less developed when compared with other STEM disciplines.” “Many college students … often are left with the impression that [mathematics] is dull and unimaginative, and they can extend this judgment to all STEM disciplines.”

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

APCalculusExams

allexams bystudentsbeforegrade12 bystudentsbeforegrade11

TheRushtoCalculus

Between800,000and900,000highschoolstudentsenrollincalculuseachyear,morethanhalfthe1.5millionwhomatriculateasfull-Hmestudentsinfour-yearundergraduateprograms.

Source:TheCollegeBoard

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

GrowthofAPCalculusExams

Allexams,year1=1981 examstakenbeforegrade12,year1=2001

TheRushtoCalculus

0

100

200

300

400

500

600

700

800

FirstCollegeMathClassforthosewhotookCalculusinHighSchool

(thousands)

CalcIIorhigher

CalcI,earnAorB

CalcI,earnCorlower

BusinessCalc,Stat,ornomath

Precalc,CollegeAlgebra,orlower

TheRushtoCalculus

EsHmatesbasedonmulHplesources

Today we teach greater numbers of students, who are less prepared, using fewer resources, and with increased expectations for student success.

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

maa.org/cspcc

8 Features of Successful Calculus Programs

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

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

Chris Rasmussen San Diego

State

DUE I-USE #1430540

Jess Ellis

Colorado State

Estrella Johnson Virginia

Tech

Sean Larsen

Portland State

Linda Braddy Tarrant County College

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%

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NSF Award #1430540

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Gotomaa.org/cspcc UnderProgress through Calculus

clickonPublications and Reports

Varia.on PhD(133) MA(89)Precalc over 2 semesters as option 33 29

Precalc contemporaneous with calculus 2 1 Stretched out Calculus I 13 7 Stretched out Calculus 1 & 2 6 1 Calculus infused with precalculus 7 4 Mainstream Calculus for biology 11 4 Mainstream Calculus for engineering 14 0 Mainstream Calc for another subject 3 0 Calculus for first-timers 1 0 Accelerated/AP Calculus 12 2 Transition to mainstream 2 1

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=regularinstructormeeHngs

UoD=useofdata

AL=acHvelearning

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%

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

SaHsfied Adequate,couldbeimproved DissaHsfied

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

60

65

70

75

80

85

90

-1.5 -1 -0.5 0 0.5 1Pred

ictedGrade

inCollegeCalculus

CutoffPrepara.onScoreforAssignmenttoPrecalculus

PrecalcboundaryNoPrecalcboundary

Source:Sonnert,G.,&Sadler,P.M.(2014).Theimpactoftakingacollegeprecalculuscourseonstudents’collegecalculusperformance.Interna0onalJournalofMathema0calEduca0oninScienceandTechnology,45(8),1188-1207

Lecture63%SomeacHve

learning18%

MainlyacHvelearning

3%

Lecture+CBI3% Other

13%

PrimarystyleofinstrucHonforMainstreamCalculus

SomeacHvelearning(e.g.clickers),mostlylectureMainlyacHvelearning(e.g.flippedclasses),minimallectureCBI=ComputerbasedinstrucHon“Other”includestoomuchvariaHontospecifyonestyle

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

ApplyingtheScienceofLearningtotheUniversityandBeyond

“ItwouldbedifficulttodesignaneducaHonalmodelthatismoreatoddswiththefindingsofcurrentresearchabouthumancogniHonthantheonebeingusedtodayatmostcollegesanduniversiHes.”

Halpern&Hakel,Change,July/August2003

Donovan & Bransford (eds.). 2005. How Students Learn: Mathematics in the classroom. National Research Council Search for How Students Learn at nap.edu

Freeman et al. 2014. Active learning increases student performance in science, engineering, and mathematics. Proc. National Academy of Sciences. 111(23)

Kober, N. 2015. Reaching Students: What research says about effective instruction in undergraduate science and engineering. National Research Council

TPSEMath.org

Mission:TPSEMathwillfacilitateaninclusivemovementtostrengthenpost-secondaryeducaHoninmathemaHcs…TPSEMathwillidenHfyinnovaHvepracHceswheretheyexist,advocateforinnovaHonwheretheydonot,andworkwithandthroughpartnerstoimplementandscaleeffecHvepracHces.

Governors:PhillipGriffiths(IAS)EricFriedlander(USC)S.JamesGates,Jr.(UMD)MarkGreen(UCLA)

TaraHolm(Cornell)KarenSaxe(Macalester)UriTreisman(UT-AusHn)Execu.veDirector:BritKirwan

Saxe, K., & Braddy, L. 2016. A Common Vision for Undergraduate Mathematical Science Programs in 2025. Joint report of AMATYC, AMS, ASA, MAA, SIAM. Search for Common Vision at maa.org

Active Learning in Post-Secondary Mathematics Education 15 July 2016

“We call on institutions of higher education, mathematics departments and the mathematics faculty, public policy-makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms.”FullstatementatCBMSWEB.org.SignedbypresidentsofAMATYC,AMS,ASA,MAA,SIAMand10othersocieHes

SEMINAL A new 5-year, $3,000,000 collaborative NSF grant: Student Engagement through an Institutional Network for Active Learning. Faculty will collaborate with APLU to better understand both how to sustain success in implementing active learning in undergraduate mathematics classes and how to influence similar success at other institutions.

PDFfileoftheseslidesavailableatwww.macalester.edu/~bressoud/talks