TeachingCalculusNowCurrentTrendsand

BestPractices

PartIII:IssuesofDiversity,Equity,andInclusion

PDFfileoftheseslidesavailableatwww.macalester.edu/~bressoud/talks

0%

2%

4%

6%

8%

10%

12%

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

BlackNon-HispanicStudentsas%ofMajorsinDiscipline

Engineering PhysicalSciences Math&Stat AllBachelor's

0%

2%

4%

6%

8%

10%

12%

14%

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

HispanicStudentsas%ofMajorsinDiscipline

Engineering PhysicalSciences Math&Stat AllBachelor's

0%

2%

4%

6%

8%

10%

12%

14%

16%

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Asian-AmericanStudentsas%ofMajorsinDiscipline

Engineering PhysicalSciences Math&Stat AllBachelor's

0%

2%

4%

6%

8%

10%

12%

14%

16%

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Non-ResidentAlienStudentsas%ofMajorsinDiscipline

Engineering PhysicalSciences Math&Stat AllBachelor's

0%

10%

20%

30%

40%

50%

60%

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

Womenas%ofMajorsinDiscipline

Engineering PhysicalSciences Math&Stat AllBachelor's

STEM leavers:• 48% of those who declare STEM majors

do not graduate with a STEM degree• 49% for men, 47% for women• 65% for Black Non-Hispanic students• 50% for Hispanic students• 52% for those whose highest HS math is

precalculus• 36% for those whose highest HS math is

calculus Source:STEMAttrition:CollegeStudents’PathsIntoandOutofSTEMFields,NCES2014-001

Guessthepercentages:

??%: “Turnedoffto”science??%:Non-STEMmajorseemsmoreinteresting??%:LifestyleofSTEMcareerunappealing??%: Inadequateadvising/help??%:PoorteachingbySTEMfaculty??%:Conceptualdifficultieswith STEMsubjects

(Seymour&Hewitt,1997)

Guessthepercentages:

??%: “Turnedoffto”science??%:Non-STEMmajorseemsmoreinteresting??%:LifestyleofSTEMcareerunappealing??%: Inadequateadvising/help??%:PoorteachingbySTEMfaculty??%:Conceptualdifficultieswith STEMsubjects

(Seymour&Hewitt,1997)(updatedsoon!)

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

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 EngineeringA or B: 2% C: 7%

Reasonforswitching Gender StudentsearningAorB

StudentsearningC

ToomanyothercoursesIneedtotake

Women 43% 33%

Men 42% 16%

Havechangedmajor Women 40% 43%

Men 33% 39%

Takestoomuchtimeandeffort

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.

SenseofBelonging

Feelinglikeanacceptedmemberofthedomainwhosepresenceandparticipationisvaluedbypeers.

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

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).

NegativeStereotype

Questionsability

Underperformance

Questionsbelonging

Under-representation

WhoBelongs?• Whatstudentcharacteristicsdoyouvaluemostinyourclassroom?

• Whatarethefoundationsuponwhichstudentsbasetheirsenseofbelonging?– Highachievement?– Quick,elegantsolutions?– Perseverance?– Engagement?– Grit?

• Caneffort-basedbelongingprotectagainststereotypethreat?

Teachers’TheoriesofIntelligenceImpactPedagogicalPractices

• Whengivenanentity theoryofmathintelligence,participantsendorseteachingpracticesthat– Conveyafixedviewof

intelligence,suchasimplicatingunderlyingintelligence,comfortforlackofability

– Reduceopportunitiestoworkonchallengingproblems

– De-emphasizetheroleofeffortinoutcomes

Rattan,Good,&Dweck,2012

Teachers’MindsetsAffectPedagogicalPractices

• Teacherswhoholdanincremental theoryofmathintelligence,endorseteachingpracticesthat– Conveyamalleableviewof

intelligence,suchasfocusingonstrategiesforoutcomes

– Emphasizetheroleofeffortinoutcomes

– Increaseopportunitiestoworkonchallengingproblems

Rattan,Good,&Dweck,2012

GrowthMindsetsDweck,1999

• Intelligenceisfixed– Trait largelydetermined bynature

• Intelligenceismalleable– Quality thatcanbeincreased through

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.”

GrowthMindsetisnot• … the power of positive thinking• ... only about effort• ... only praising effort• ... about celebrating mistakes• ... a way to blame students• ... only for low-achieving students• ... only about students

www.turnaroundusa.org/7-things-growth-mindset-is-not/

Research-basedStrategiesforReducingStereotypeThreat

• Encouragingstudentsandteacherstoadoptagrowthmindset.

• Encouragestudentstobasetheirfeelingsofbelongingontheireffortsandengagement.

• Createaclassroomlearningenvironmentthatvalueseffortandengagement asapathtobelonging.

• Encouragestudentstoattributetheirdifficultiestocausesotherthantheirownlimitations.

But most students don’t know how to engage in productive effort!

ApplyingtheScienceofLearningtotheUniversityandBeyond

“It would be difficult to design an educational model that is more at odds with the findings of current research about human cognition than the one being used today at most colleges and universities.”

Halpern & Hakel, Change, July/August 2003

Lecture63%

Someactivelearning18%

Mainlyactivelearning

3%

Lecture+CBI3% Other

13%

PrimarystyleofinstructionforMainstreamCalculus

Someactivelearning(e.g.clickers),mostlylectureMainlyactivelearning(e.g.flippedclasses),minimallectureCBI=Computerbasedinstruction“Other”includestoomuchvariationtospecifyonestyle

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

Excerpts from CBMS statement on Active Learning

We use the phrase active learning to refer to classroom practices that engage students in activities, such as reading, writing, discussion, or problem solving, that promote higher-order thinking.

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.

EndorsedbyPresidentsofAMATYC,AMS,MAA,NCSM,NCTM,SIAMand9othersocieties

https://tinyurl.com/cbmsactiveConferenceBoardoftheMathematicalSciences

MATHEMATICAL ASSOCIATION OF AMERICA

Instructional Practices Guide

GuidetoEvidence-BasedInstructionalPracticesinUndergraduate

Mathematics

Search for IP Guide at maa.org

“Themathematicsprofessionasawholehasseriouslyunderestimatedthedifficultyofteachingmathematics.”

RameshGangolliMERWorkshopMay31,1991*

*With thanks to Susanna Epp for preserving this quote.

Itismysincerehopethat,almostaquarterofacenturylater,thisisnolongertrue.

DiscussionQuestions:1. 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?

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

3. 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?

4. 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

5. What could your institution do to improve student success and retention for at risk students?

PDFfileoftheseslidesavailableatwww.macalester.edu/~bressoud/talks