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The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University
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The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Mar 29, 2015

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Page 1: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

The Mindset Revolution:Teaching mathematics for a growth mindset

Jo BoalerProfessor of Mathematics EducationStanford University

Page 2: 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

Page 3: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

The myth of mathematics Being good at math is a “gift” –

some people are naturally good at math, some are not

Page 4: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Shake It Up Chicago

Page 5: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Hollywood

Page 6: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Hollywood

Page 7: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Hollywood

Page 8: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Brain Plasticity

Page 9: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

When learning happens …

A synapse fires

Page 10: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Synapses are like footprints in the sand – the brain follows the footprints and makes them deeper the more they are followed

Page 11: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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”

Page 12: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Brain growth

Page 13: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

London ‘Black Cab’ Drivers

Page 14: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

“The Knowledge” – 25,000 streets and 20,000 landmarks

Page 15: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Brain Growth

London taxi drivers have a larger hippocampus than London bus drivers

Page 16: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 17: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Neuroplasticity refers to the life long capacity of the brain to change and rewire itself in response to learning and experience.

Page 18: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 19: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Brain research tells us: Every child can excel in

mathematics in school, from elementary to high school

Page 20: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Ability?

Each new learning experiences changes your “ability”.

We use fixed ability language all the time – high and low kids etc

Page 21: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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.

Page 22: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

How important are the ideas that students hold about ability?

Page 23: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 24: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

7th grade students with a growth mindset outperform those with a fixed mindset in math

Page 25: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

The impact of a mindset intervention (same math teacher, same curriculum)

Page 26: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 27: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 28: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 29: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 30: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 31: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

MessagesMindset

+ Math

Messages

Messages

Messagesmistakes

grading

&

feedback

grouping

tasksquestions asked

norm se

tting

What has mindset got to do with my math teaching?

Page 32: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Today - mindset

Grouping Classroom Math Tasks Assessment & Grading Mistakes Messages

Page 33: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Ability Grouping

Burris, C., Heubert, J., & Levin, H. (2006).

Accelerating Mathematics Achievement Using Heterogeneous Grouping.

American Educational Research Journal, 43(1), 103-134.

Page 34: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 35: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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?

Page 36: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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.

Page 37: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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.

Page 38: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 39: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

How many blocks are in case 100? \

Page 40: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Sarah Kate Selling

Page 41: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Luke Jorge Carlos

Page 42: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Case n has (n+1)2 blocks

Recursive pattern: +5, +7…

Jorge

Carlos

Luke

Case 1 Case 2 Case 3

Page 43: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Recognizing different ways of seeing

Page 44: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Explaining different ways of seeing

Page 45: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Resolving through connecting

Page 46: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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?

Page 47: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

3 boys video

Page 48: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 49: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 50: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Assessment &Grading

Grades Diagnostic

Feedback

Diagnostic Feedback significantly higher

Grades Diagnostic

Feedback Diagnostic

Feedback& Grades

Diagnostic Feedback significantly higher

(Butler)

Page 51: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Timed Tests?

Page 52: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

From 1st to 5th grade

A Timed Test of 50 questions to finish in 3 minutes

Page 53: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

From neuroscience ..

Math should never be associated with speed

Page 54: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

From Sian Beilock:

Page 55: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

no relation between stress and prior achievement

Math stress cuts across the achievement spectrum –particularly affecting girls

Page 56: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

From Sian Beilock:

Page 57: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

4th grade:

Page 58: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.
Page 59: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.
Page 60: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.
Page 61: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.
Page 62: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.
Page 63: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

2nd grade:

Page 64: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.
Page 65: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.
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www.joboaler.com

Page 70: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

“Every time a student makes a mistake in math they grow a new synapse” (Carol Dweck)

Mistakes

Page 71: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 72: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Reposition mistakes

In classroom norms In 1:1 interactions

Page 73: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 74: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

What is the big messages or message(s) that the students took away?

Page 75: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Stanford freshmen

Page 76: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

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

Page 77: The Mindset Revolution: Teaching mathematics for a growth mindset Jo Boaler Professor of Mathematics Education Stanford University.

Udacity & Stanford ‘MOOC’

Teaching Mathematics for the Common Core

https://www.udacity.com

Talk no longer than 90 seconds before engaging the learner