Developing a Growth Mindset for Math
Supporting Productive Failure
David Dockterman, Ed.D.Harvard Graduation School of EducationScholastic Education
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Make it “relevant”Make it “fun”
Historical tendency: “You know how kids love...”
• video games
• computers
• television
• radio
• movies
• magic lanterns
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What motivates humans, including students?
Center on Education Policy
1. Competence (progress)
2. Control/Autonomy (agency)
3. Interest/Value (purpose)
4. Relatedness (community/status)
http://www.cep-dc.org
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1. Competence AND Confidence
• Perceived ability matters more than actual ability
• Girls often do better in math/science than boys but feel less capable
• Fixed vs Growth Mindset
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– Carol Dweck, Ph. D. Author of MindSet
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considered artifacts of high prior ability or achieve-ment (cf. Pomerantz & Saxon, 2001). However, asstudents made the transition to junior high school,their theory of intelligence became a significantpredictor of their mathematics achievement (rs ran-ged from .12 in the fall term of seventh grade, po.05,to .20 in the spring term of eighth grade, po.05).Moreover, an incremental theory of intelligence atthe beginning of junior high school predicted highermathematics grades earned at the end of the secondyear of junior high school (b5 .17, t5 3.40, po.05),controlling for the effect of math achievement testscores before entering junior high school (b5 .43,t5 8.48, po.05). This result held (b5 .10, t5 2.50,po.05) using math grades earned in the first term ofjunior high school (b5 .70, t5 17.50, po.05) insteadof end of sixth-grade test scores.
Relation of Theory of Intelligence to Mathematics GradeGrowth Trajectories
To assess the contribution of theory of intelligenceto the trajectory of achievement over the junior highschool transition, we looked at the growth curves inmathematics grades for students with different im-plicit theories. Growth curves were computed usingBryk and Raudenbush’s (1987, 1992) HierarchicalLinear Modeling (HLM) program. The Level 1equation was
Yit ! b0i " b1i#time$ " eit;
where b0 represents the intercept, or the averagemath grades at Time 1 (i.e., time was coded as 0, 1, 2,3), and b1 is the slope, or average change per unit oftime. The trajectory of math grades was computedacross the four assessments (fall seventh grade,spring seventh grade, fall eighth grade, and springeighth grade).
Implicit theory of intelligence was entered at Lev-el 2. Before computing the growth curves, wewanted to control for potential differences betweenthe four cohorts. Although all students within eachcohort had the same teacher and curriculum, not allcohorts had the same teacher; thus, there could bedifferences in the grading practices or efficacy ofteachers between cohorts. Therefore, dummy vari-ables were created for each cohort and entered intothe equation at Level 2. The Level 2 equation for thegrowth curves was
b0i ! g00 " b01#theory$ " g02#Cohort 1$" g03#Cohort 2$ " g04#Cohort 3$
b1i ! g10 " g11#theory$ " g12#Cohort 1$" g13#Cohort 2$ " g14#Cohort 3$:
By entering the cohort dummies into the Level 2equations, we are estimating the mean-level growthadjusted for possible cohort differences. The averagegrade at Time 1 for the sample was 72.05, about aC% . There was no main effect of theory of intelli-gence on Time 1 grades (b5 .98, t5 1.47, ns) and nochange in average grade across the 2 years (b5 .39,t5 .90, ns). However, there was a significant effect oftheory of intelligence on change in grades (b5 .53,t5 2.93, po.05). The significant effect of theory ofintelligence at Level 2 represents an interaction be-tween theory of intelligence and time. This inter-action suggests that the math achievement growthpatterns differ based on one’s theory of intelligence.To understand this interaction, we followed theguidelines suggested by Aiken and West (1991)and graphed the interaction using scores of 1 SDabove and below the theory of intelligence mean (seeFigure 1).
Although students with the entity and incremen-tal theories did not differ significantly in their mathachievement test scores as they entered junior highschool, as these results show, they began to pull apartover the 2 years of junior high school. We found thattheory of intelligence is related to a set of motiv-ational constructs; thus, we need to take the motiv-ational constructs into account when discussing theeffect of theory of intelligence. In the next section, weaddress the role of these motivational constructs.
Mediational Pathways
One goal of the present study was to go beyonddocumenting the relation between theory of intelli-gence and academic achievement to explain why thisrelation exists. However, we had four mediators thatmight, individually or in combination, explain this
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Fall 7th Grade Spring 7th Grade Fall 8th Grade Spring 8th Grade
Mat
h G
rade
s
Incremental
Entity
Figure 1. Graph of interaction effect of theory of intelligence andtime on math achievement: Growth curves of predicted mathe-matics grades over 2 years of junior high school for students withincremental (11 SD above the mean) and entity (% 1 SD below themean) theories of intelligence.
Implicit Theories and Achievement 251
Growth Mindset ResultsBlackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit
Theories of Intelligence Predict Achievement Across an Adolescent Transition : A Longitudinal Study and an Intervention. Child Development, 78(1), 246–263. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8624.2007.00995.x/full
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What’s Your Fixed Mindset? Are you a video game player?
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Fixed vs Growth Mindset
Fixed Mindset
• “I’m not...”
• avoid failure
• mistake = can’t do (I’m not)
Growth Mindset
• “I can if...”
• look for challenges
• mistake = learning opportunity
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Shift relationship with failure
• “struggle” and “mistakes” are not typically rewarded in school
• In games, failure is the norm. Success is the exception.
• In school, for struggling students, mistakes = “I’m stupid.”
• In good games, mistakes = “I need to try again.” “What can I do differently?”
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Give Students a Running Start
• we persevere when we believe we can succeed
• but we need evidence
• shaky confidence + early failure = total shutdown
• games provide a gradual slope
Slice It! -- com2us.com
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But move quickly to the edge
The Math Curriculum
edge of competence
Know & Do
“I’m good!”
Just the Right Frustration Can be Very Satisfying
“I can’t”“I’m bored”
Zone of Proximal Development
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Shift the Reference Point
• Set the expectation for struggle
• When low SES or minority students struggle at college...
• don’t belong, drop out
• but if expect to struggle, then more likely to stay and graduate
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• with words
• by modeling with your own mistakes
• using examples
• by teaching about growth mindset
“Wow, that problem didn’t turn out the way I
wanted. Let me see if I can figure out what I did wrong....Ah, maybe that’s it.
Good. I learned something new. That was a good
Words, Models, & Knowledge vs
“Let’s start with an
easy one.”
“This might take a
few tries.”
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› DAY 1
PROFILE NUMBER
Some people believe that you are born with or without certain skills. Others believe that you can become better at anything through hard work and effort. Let's find out what you think.
Week 1FIRSTTWO WEEKS
› Add up all the profi le numbers and write the total.
Agree Disagree
A No matter how much intelligence you have, you can always change it a good deal. 6 5 4 3 2 1
B I like my work best when it makes me think hard. 6 5 4 3 2 1
C I like work that I'll learn from even if I make a lot of mistakes. 6 5 4 3 2 1
D When something is hard, it just makes me want to work more on it, not less. 6 5 4 3 2 1
E You can learn new things, but you cannot really change your basic level of intelligence. 1 2 3 4 5 6
F I like my work best when I can do it really well without too much trouble. 1 2 3 4 5 6
G I like my work best when I can do it perfectly without any mistakes. 1 2 3 4 5 6
H To tell the truth, when I work hard, it makes me feel as though I'm not very smart. 1 2 3 4 5 6
TOTAL
Mindset Scan
Decide how much you agree or disagree with each statement. Circle and write your answer.
RANKING GUIDEAgreea lot
Agree Agree a little
Disagree a little
Disagree Disagree a lot
6 5 4 3 2 1
THIS IS NOTA TEST!
It is an opinion survey about your beliefs,goals, and
thoughts on intelligence.
5A MATH 180
What’s Your Mindset?
• http://www.mindsetworks.com
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Use Appropriate Feedback
• Can’t learn from failure without feedback
• Reinforce the right
• Correct the wrong
• Imagine practicing putting without seeing if the ball goes in the hole
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Corrective Feedback
• or practicing free throws without seeing if the ball goes in the basket
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Corrective Feedback
• or practicing math procedures without knowing if the answers are correct
• digital games provide immediate feedback and can be incredibly failure tolerant
• so do simulations and visual models
• try...see results...revise...repeat
• provides a sense of control
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Show Progress
• Progress -- Harvard Business Review #1 big idea for 2010
• Marketers motivating us
• Motivating ourselves
• Making long waits a little more tolerable
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Progress through Levels How far to go
Angry Birds -- rovio.com
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Progress through Skills FASTT Math Next Generation
FASTT Math -- scholastic.com/fasttmath
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Student Dashboards MATH 180
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2. Control/Autonomy
• Our brains may not be rational, but they do rationalize
• “If you make me do it, I must not want to do it”
• Intrinsic motivation fueled by choice, undermined by outside control
• But we don’t want to give the choice not to participate
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Choices
• Personalized space
• How to get there
• Strategies
• Choice Architecture
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Manage the Stakes
frontier learning routine performance
failure tolerant goal of error-free
low stakes high stakes
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Learning
frontier learning routine performance
failure tolerant goal of error-free
low stakes high stakes
Instruction
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Practicing
frontier learning routine performance
failure tolerant goal of error-free
low stakes high stakes
Practice
formative assessment
learning tasks
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Performing
frontier learning routine performance
failure tolerant goal of error-free
low stakes high stakes
Performance Assessment
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Give students some control over readiness...
frontier learning routine performance
failure tolerant goal of error-free
low stakes high stakes
Practice
lots of replay
improve speed & accuracy
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3. Interest/Value (Purpose)
• “When will I ever use this?”
• Short-term value: Is this relevant? OR Is it just interesting?
• Long-term value: “I need this for college.” “I need this for...”
• It doesn’t work to TELL students that it’s important for them.
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Which Number Doesn’t Belong?
9 16 25 43
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Purpose Situating math in real stories
Start with Applicationhttp://www.scholastic/math180
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4. Relatedness/Community
• The quest for status may be our most basic evolutionary drive.
• Risky fish get the girls.
• Humans crave social acceptance, and self-efficacy (and grades) are related to peer group support.
• Build a growth mindset classroom culture
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Mastery vs Performance
Mastery
• Personal progress -- where am I vs where I was before
• all about getting better
• best for struggling students who have a history of failure
• choose when and with whom to share growth
Performance
• Competitive -- where am I compared to others
• all about winning
• good for high performers who think they have a chance of winning
• performance always on display
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Who Cares?
• Teacher - Student
• Parent - Student
• Student - Student
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The power of YET (Carol Dweck)
• “You haven’t mastered those skills...yet.”
• “You’re not explaining the connection between the graph and the equation clearly...yet.”
• “We haven’t reached all the students...yet”
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“If you think you can catchthe bus, you will run for it.” - Lee Peng Yee
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