Teaching Calculus Now: Current Trends &

Best Practices PM Session

St. Michael’s College Colchester, VT October 1, 2016

PDFfileoftheseslidesavailableatwww.macalester.edu/~bressoud/talks.ThankstoDaveKungand

CatherineGoodfromwhomItookmanyoftheseslides

David Bressoud St. Paul, MN

CSPCC#0910240PtC#1430540

MATHEMATICAL ASSOCIATION OF AMERICA

0%

1%

2%

3%

4%

5%

6%

7%

HispanicStudents%ofBachelorsDegreesearnedinmath-intensivemajors

Eng PhysSci Math

10.2%ofallBachelor’sdegrees

10.8%ofallBachelor’sdegrees

0.0%0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%

African-Americans%ofBachelorsDegreesearnedinmath-intensivemajors

Eng PhysSci Math

0%5%

10%15%20%25%30%35%40%45%50%

Women%ofBachelor'sdegreesearnedinmath-intensivemajors

Engineering MathemaTcs PhysicalScience

57.1%ofallBachelor’sdegrees

Guessthepercentages:??%:“Turnedoffto”science ??%:Non-STEMmajorseemsmoreinteresTng??%:LifestyleofSTEMcareerunappealing??%:Inadequateadvising/help??%:PoorteachingbySTEMfaculty??%:ConceptualdifficulTeswithSTEMsubjects (Seymour&Hewid,1997)

Guessthepercentages:??%:“Turnedoffto”science ??%:Non-STEMmajorseemsmoreinteresTng??%:LifestyleofSTEMcareerunappealing??%:Inadequateadvising/help??%:PoorteachingbySTEMfaculty??%:ConceptualdifficulTeswithSTEMsubjects

(Seymour&Hewid,1997)(updatedsoon!)

60%57%43%75%90%27%

SenseofBelonging

FeelinglikeanacceptedmemberofthedomainwhosepresenceandparTcipaTonisvaluedbypeers.

Unpleasant apprehension arising from the awareness of a

negative ability stereotype in a situation where the stereotype is relevant, and thus confirmable.

Stereotype Threat

Steele&Aronson,1995

StereotypeThreatUnderminesLearning

Good,Mangels,&Evelo,2015

*2-way ANOVA: F(1, 121) = 6.45, p = .01, η2 = .05 Non-threat: F(1, 122) = 2.06, p = .15, η2 = .02 *Stereotype Threat: F(1, 122) = 4.62, p = .03, η2 = .04

Additional Studies Finding Performance Effects

•  Women taking math tests (Good, Aronson & Harder, 2008; Spencer, Steele, & Quinn 1999).

•  Latinos taking verbal tests (Aronson & Salinas, 1997).

•  Low SES students taking verbal tests (Croizet & Claire, 1998).

•  Blacks and miniature golf (Stone, 2002).

•  White males taking math tests when compared to Asians (Aronson, Lustina, Good, Keough, Steele, & Brown, 1999).

NegaTveStereotype

QuesTonsability

QuesTonsbelonging

Underperformance Under-representaTon

WhoBelongs?•  WhatstudentcharacterisTcsdoyouvaluemostinyourclassroom?

•  WhatarethefoundaTonsuponwhichstudentsbasetheirsenseofbelonging?– Highachievement?– Quick,elegantsoluTons?–  Perseverance?–  Engagement?– Grit?

•  Caneffort-basedbelongingprotectagainststereotypethreat?

Teachers’MindsetsAffectPedagogicalPracTces

•  Teacherswhoholdanincrementaltheoryofmathintelligence,endorseteachingpracTcesthat–  Conveyamalleableviewof

intelligence,suchasfocusingonstrategiesforoutcomes

–  Emphasizetheroleofeffortinoutcomes

–  IncreaseopportuniTestoworkonchallengingproblems

Ra?an,Good,&Dweck,2012

Teachers’TheoriesofIntelligenceImpactPedagogicalPracTces

•  WhengivenanenTtytheoryofmathintelligence,parTcipantsendorseteachingpracTcesthat–  Conveyafixedviewof

intelligence,suchasimplicaTngunderlyingintelligence,comfortforlackofability

–  ReduceopportuniTestoworkonchallengingproblems

–  De-emphasizetheroleofeffortinoutcomes

Ra?an,Good,&Dweck,2012

GrowthMindsetsDweck,1999

•  Intelligenceisfixed–  Traitlargelydeterminedbynature

•  Intelligenceismalleable–  Qualitythatcanbeincreasedthrough

nurture

Entity Theorists Incremental Theorists

•  Learninggoals–  seekingtodevelopability

•  Performancegoals–  seekingtovalidateability

Desire similar outcome •  achieving good scores, doing “well”

Different motivation for pursuing this outcome

“The main thing I want when I do my school work is to show how good I am at it.”

“In school I am always seeking opportunities to develop new skills and acquire new knowledge.”

Research-basedStrategiesforReducingStereotypeThreat

•  Encouragingstudentsandteacherstoadoptagrowthmindset.–  hdp://www.turnaroundusa.org/7-things-growth-mindset-is-not/

•  Encouragestudentstobasetheirfeelingsofbelongingontheireffortsandengagement.

•  Createaclassroomlearningenvironmentthatvalueseffortandengagementasapathtobelonging.

•  EncouragestudentstoadributetheirdifficulTestocausesotherthantheirownlimitaTons.

•  Normalizeeffortasthepathtosuccess.

WiththankstoDaveKungfromwhomI’vetakenthissequenceofslides.

Lecture63%SomeacTve

learning18%

MainlyacTvelearning

3%

Lecture+CBI3% Other

13%

PrimarystyleofinstrucTonforMainstreamCalculus

SomeacTvelearning(e.g.clickers),mostlylectureMainlyacTvelearning(e.g.flippedclasses),minimallectureCBI=ComputerbasedinstrucTon“Other”includestoomuchvariaTontospecifyonestyle

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

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

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

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,SIAMand10othersocieTes

“ThemathemaTcsprofessionasawholehasseriouslyunderesTmatedthedifficultyofteachingmathemaTcs.”

RameshGangolliMERWorkshopMay31,1991*

*With thanks to Susanna Epp for preserving this quote.

Itismysincerehopethat,almostaquarterofacenturylater,thisisnolongertrue.

DiscussionQuesJons:1.  What are the pedagogical goals for your precalculus/calculus courses and

what active learning strategies may support these goals? 2.  What active learning approaches are being tried? How are you assessing

their effectiveness, and how well are they working? What external resources have you found to be useful?

3.  In what ways does your departmental and/or institutional leadership recognize the importance of and support active learning approaches in the classroom?

4.  What constraints from within and outside your department, are you encountering for implementing active learning approaches? What could your department do to enhance the use of active learning approaches and increase faculty buy-in?

5.  What strategies can we use for nudging our institutions and instructors towards more active learning or student-centered approaches? Consider… Instructors, Coordination, Curriculum, Room Layouts, Teaching Evaluations/Observations, Retention/Teaching/Promotion

PDFfileoftheseslidesavailableatwww.macalester.edu/~bressoud/talks