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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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Carol Dweck, 2006, Mindset: The New Psychology of Success

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The myth of mathematics Being good at math is a gift – some people are naturally good at math, some are not

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Shake It Up Chicago

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Hollywood

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Brain Plasticity

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When learning happens … A synapse fires

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

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Plasticity Learning creates and strengthens synapses The plasticity of the brain means that these connections grow into adult-hood If Pathways arent followed they may be discarded use it or lose it

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Brain growth

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London Black Cab Drivers

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

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Brain Growth London taxi drivers have a larger hippocampus than London bus drivers

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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

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

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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

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Brain research tells us: Every child can excel in mathematics in school, from elementary to high school

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Ability? Each new learning experiences changes your ability. We use fixed ability language all the time – high and low kids etc

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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 Im 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.

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How important are the ideas that students hold about ability?

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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 others success Affects students from across the achievement spectrum Role of parents in encouraging fixed mindset

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

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

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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

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Mindset and gender High achieving 5 th 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 8 th grade there was a gender gap but only among fixed mindset students

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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

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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

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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

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Messages Mindset + Math Messages mistakes grading & feedback grouping tasks questions asked norm setting What has mindset got to do with my math teaching?

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Today - mindset Grouping Classroom Math Tasks Assessment & Grading Mistakes Messages

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Ability Grouping Burris, C., Heubert, J., & Levin, H. (2006). Accelerating Mathematics Achievement Using Heterogeneous Grouping. American Educational Research Journal, 43 (1),

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Ability Grouping In England researchers followed 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

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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?

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Most math classrooms offer math as a performance subject not a learning subject. Rachel Lamberts 6 year old son: Math is too much answer time and not enough learning time Tasks need to give students the space to learn.

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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.

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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 7 th, 8 th grade students Tasks – Ruth Parker, Mark Driscoll, SMILE, Points of Departure

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How many blocks are in case 100? \

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Sarah Kate Selling

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Luke Jorge Carlos

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Case n has ( n +1) 2 blocks Recursive pattern: +5, +7… Jorge Carlos Luke Case 1 Case 2 Case 3

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Recognizing different ways of seeing

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Explaining different ways of seeing

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Resolving through connecting

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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?

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3 boys video

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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

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1 ÷ 2/3 Cathy Humphreys, 7 th graders Connecting Mathematical Ideas – video cases Mathematics as sense-making which encourages: Different ways of seeing Different methods / pathways Different representations

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Assessment &Grading Grades Diagnostic Feedback Diagnostic Feedback significantly higher Grades Diagnostic Feedback & Grades Diagnostic Feedback significantly higher (Butler)

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Timed Tests?

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From 1 st to 5 th grade A Timed Test of 50 questions to finish in 3 minutes

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From neuroscience.. Math should never be associated with speed

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From Sian Beilock:

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no relation between stress and prior achievement Math stress cuts across the achievement spectrum –particularly affecting girls

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From Sian Beilock:

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4 th grade:

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2 nd grade:

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

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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

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Reposition mistakes In classroom norms In 1:1 interactions

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Messages (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

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

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Stanford freshmen

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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

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Udacity & Stanford MOOC Teaching Mathematics for the Common Core https://www.udacity.com Talk no longer than 90 seconds before engaging the learner

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