Teaching mathematics for a growth mindset

The Mindset Revolution:
Teaching mathematics for a
growth mindset
Jo Boaler
Professor of Mathematics Education
Stanford University
Carol Dweck, 2006, Mindset:
The New Psychology of Success
The myth of mathematics
Being good at math is a “gift” – some
people are naturally good at math, some
are not
Shake It Up Chicago
Brain Plasticity
When learning happens …
A synapse fires
Synapses are like footprints in the sand – the
brain follows the footprints and makes them
deeper the more they are followed
Learning creates and strengthens synapses
 The plasticity of the brain means that these
connections grow into adult-hood
 If Pathways aren’t followed they may be discarded
 “use it or lose it”
Brain growth
London ‘Black Cab’ Drivers
“The Knowledge”
– 25,000 streets and 20,000 landmarks
Brain Growth
London taxi drivers have a larger
hippocampus than London bus drivers
A 6-year old girl
Had half of her brain removed
 Amazed doctors and scientists - within
months she had recovered functions from
the “missing” side of the brain
Neuroplasticity refers to the lifelong
capacity of the brain to change and rewire
itself in response to learning and
From a local, public high
school math dept in 2012
We know taking advanced math classes is the best predictor for success in college.
Nothing would make us happier than being able to produce only graduates that
have calculus on their transcripts! However, brain theory supports the reality that
confounding student situations interfere with their ability to focus and succeed as
they move through advanced mathematics in high school.
We live in an affluent community. Most of our students are fortunate to come
from families where education matters and parents have the means to support
and guide their children in tandem with us their teachers. Not all of them.
We are concerned about the others who for reasons that are often objective (poor
math background, lack of support at home, low retention rate, lack of maturity
etc) cannot pass our Algebra II regular lane course.
Many of them are VTP students or under-represented minorities. Others are
serious, committed special ed students (etc)
Brain research tells us:
Every child can excel in mathematics in
school, from elementary to high school
Each new learning experiences changes
your “ability”.
 We use fixed ability language all the time –
high and low kids etc
Laurent Schwartz ‘A Mathematician
Grappling with his Century’
..I was always deeply uncertain about my own intellectual capacity; I thought I was
unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things
because I always need to understand them fully. Even when I was the first to answer the
teacher's questions, I knew it was because they happened to be questions to which I already
knew the answer. But if a new question arose, usually students who weren't as good as I was
answered before me. Towards the end of the eleventh grade, I secretly thought of myself as
stupid. I worried about this for a long time.
I never talked about this to anyone, but I always felt convinced that my imposture would
someday be revealed: the whole world and myself would finally see that what looked like
intelligence was really just an illusion. If this ever happened, apparently no one noticed it,
and I’m still just as slow. (...)At the end of the eleventh grade, I took the measure of the
situation, and came to the conclusion that rapidity doesn't have a precise relation to
intelligence. What is important is to deeply understand things and their relations to each
other. This is where intelligence lies. The fact of being quick or slow isn't really
relevant. Naturally, it's helpful to be quick, like it is to have a good memory. But it's neither
necessary nor sufficient for intellectual success.
How important are the ideas
that students hold about
Carol Dweck: Mindset
Mindset: The New Psychology of Success. (2007)
 Fixed - math ability is a “gift”
 Growth – math ability or “smartness” grows
with experience
Growth mindset behaviors – persistence, learn
from mistakes, determination to keep going,
encouraged by other’s success
Affects students from across the achievement
 Role of parents in encouraging fixed mindset
7th grade students with a growth mindset
outperform those with a fixed mindset in
The impact of a mindset
intervention (same math
teacher, same curriculum)
Research on Mindset and
African American students show sharpest
increase in grades and valuing school
 A growth mindset eliminates any gender
gaps eg in highest SAT levels
Mindset and gender
High achieving 5th grade girls did not cope
well with challenge
 The higher their IQ the more difficulty
they had, in boys the reverse was true
 At the end of 8th grade there was a gender
gap but only among fixed mindset students
Mindset and gender
Calculus at Columbia
 Stereotyping is alive and well
 Stereotyping only affected those with a
fixed mindset, their confidence eroded
over the semester and they abandoned
plans to pursue STEM subjects
Seeing math as a gift not only makes
students vulnerable to lack of confidence
but vulnerable to stereotypes too
 Having a growth mindset is what we want
all teachers and all students to have
The big message
Intelligence is malleable, but …
 Students, teachers, schools, parents treat
math learners as though it is relatively
 Brainstorm with others around you - which
aspects of schools / math teaching
encourage a FIXED mindset? Choose your
top 3
What has mindset got to do
with my math teaching?
Today - mindset
 Classroom Math Tasks
 Assessment & Grading
 Mistakes
 Messages
Ability Grouping
Burris, C., Heubert, J., & Levin, H. (2006).
Accelerating Mathematics Achievement
Using Heterogeneous Grouping.
American Educational Research Journal, 43(1),
Ability Grouping
In England researchers followed 14000
children through years 4 and 6 comparing
those taught in sets with those grouped
heterogeneously over the period of a year.
 Nunes, Bryant, Sylva & Barros, 2009
Classroom Math Tasks
How do you maintain a growth mindset
when math class is a series of closed
questions that you get right or wrong?
Most math classrooms offer
math as a performance subject
not a learning subject.
Rachel Lambert’s 6 year old son:
“Math is too much answer time and not
enough learning time”
Tasks need to give students the space to
Growth Mindset Task
Task focuses on learning: opportunities to learn
something rather than demonstrate what you know
 Openness
- Ways of seeing
- Multiple entry points
- Multiple paths / strategies
 Clear learning goals and opportunities for feedback.
An example
Comes from a 5 week algebra class I taught
with graduate students in summer school
 Our goal: to teach algebra as a problem
solving tool
 Underachieving 7th, 8th grade students
 Tasks – Ruth Parker, Mark Driscoll,
SMILE, Points of Departure
How many blocks are in case
Sarah Kate Selling
Case n has (n+1)2 blocks
Recursive pattern: +5, +7…
Case 1
Case 2
Case 3
Recognizing different ways of
Explaining different ways of
Resolving through connecting
A case: mathematical practices
& heterogeneity
What engages the students so strongly and
for so long? And what does it have to do
with growth mindset teaching?
3 boys video
When math tasks are opened
Different ways of seeing
 Different methods / pathways
 Different representations
The opportunities for learning and
developing a growth mindset are increased
1 ÷ 2/3
Cathy Humphreys, 7th graders
 Connecting Mathematical Ideas – video cases
 Mathematics as sense-making which encourages:
Different ways of seeing
 Different methods / pathways
 Different representations
Assessment &Grading
Diagnostic Feedback
 Diagnostic Feedback
 Diagnostic Feedback
Diagnostic Feedback & Grades
significantly higher
Diagnostic Feedback
significantly higher
Timed Tests?
A Timed Test of 50 questions to finish in 3 minutes
From 1st to 5th grade
From neuroscience ..
Math should never be associated with speed
From Sian Beilock:
no relation between stress and prior
Math stress cuts across the achievement
spectrum –particularly affecting girls
From Sian Beilock:
4th grade:
2nd grade:
“Every time a student makes a
mistake in math they grow a
new synapse” (Carol Dweck)
Every mistake grows a synapse
Mistakes are good
 They are the time your brain is growing
 Students should be making mistakes
 Students hate making mistakes – because
they have been brought up in a performance
and not a learning culture
 Students & most teachers view them
Reposition mistakes
In classroom norms
 In 1:1 interactions
 (Geoff Cohen)
 “I am giving you this feedback because I
believe in you”
 Resulted in significant achievement gains,
again especially for minority students.
 My freshmen
What is the big messages or message(s)
that the students took away?
Stanford freshmen
To conclude
It is critically important that teachers and
students are encouraged to develop a
‘growth mindset’
 The ideas I have shared for teaching and
assessing are not new but the reason for
implementing them – to develop growth
mindsets - is an important impetus for
change, and an idea that many teachers
and schools understand
 The ways teachers teach math has huge
implications for students’ mindsets
Udacity & Stanford ‘MOOC’
Teaching Mathematics for the Common
Talk no longer than 90 seconds before
engaging the learner

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