Post on 29-Mar-2015
The Mindset Revolution:Teaching mathematics for a growth mindset
Jo BoalerProfessor of Mathematics EducationStanford 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
Hollywood
Hollywood
Hollywood
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
Plasticity
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 life long capacity of the brain to change and rewire itself in response to learning and experience.
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)
From a local, public high school math dept in 2012
Brain research tells us: Every child can excel in
mathematics in school, from elementary to high school
Ability?
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 ability?
Carol Dweck: Mindset
Mindset: The New Psychology of Success. (2007) Fixed - math ability is a “gift” Growth – math ability or
“smartness” grows with experienceGrowth mindset behaviors – persistence, learn from mistakes, determination to keep going, encouraged by other’s successAffects students from across the achievement spectrum Role of parents in encouraging fixed
mindset
7th grade students with a growth mindset outperform those with a fixed mindset in math
The impact of a mindset intervention (same math teacher, same curriculum)
Research on Mindset and equity 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
Implications
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 fixed
Brainstorm with others around you - which aspects of schools / math teaching encourage a FIXED mindset? Choose your top 3
MessagesMindset
+ Math
Messages
Messages
Messagesmistakes
grading
&
feedback
grouping
tasksquestions asked
norm se
tting
What has mindset got to do with my math teaching?
Today - mindset
Grouping 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), 103-134.
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 learn.
Growth Mindset Task Framework
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 100? \
Sarah Kate Selling
Luke Jorge Carlos
Case n has (n+1)2 blocks
Recursive pattern: +5, +7…
Jorge
Carlos
Luke
Case 1 Case 2 Case 3
Recognizing different ways of seeing
Explaining different ways of seeing
Resolving through connecting
A case: mathematical practices & heterogeneity Gauss
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 for 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
Grades Diagnostic
Feedback
Diagnostic Feedback significantly higher
Grades Diagnostic
Feedback Diagnostic
Feedback& Grades
Diagnostic Feedback significantly higher
(Butler)
Timed Tests?
From 1st to 5th grade
A Timed Test of 50 questions to finish in 3 minutes
From neuroscience ..
Math should never be associated with speed
From Sian Beilock:
no relation between stress and prior achievement
Math stress cuts across the achievement spectrum –particularly affecting girls
From Sian Beilock:
4th grade:
2nd grade:
www.joboaler.com
“Every time a student makes a mistake in math they grow a new synapse” (Carol Dweck)
Mistakes
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 negatively
Reposition mistakes
In classroom norms In 1:1 interactions
Messages
www.brainology.com (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 Core
https://www.udacity.com
Talk no longer than 90 seconds before engaging the learner