Jo Boaler Professor Mathematics Education Stanford University The Many Colors of Algebra – Engaging Disaffected Students Through Collaboration and Agency. Jo Boaler Professor Mathematics Education Stanford University while I was a prof at Stanford, where I was for the last 9 years, I studied an unusual approach, not known in the UK, that resulted in very high achievement in mathematics as well as exceptionally good behaviour and respect among students, in an urban school. When I took visitors to this school who were used to inner city schools, we would walk through the deprivation but then they would be open mouthed when they saw the way the students were working together, with impeccable behaviour, respect among students, for each other and ideas. So today I am hoping to sketch the approach for you, briefly, and to show you some video clips from the school, as they give you a very clear sense of how it worked, but perhaps also to spend some time considering what this could mean for British schools.

When students are engaged in .. Mixed ability, heterogeneous, rather than tracked groups Problem solving, rather than rehearsing methods Discussing ideas and reasoning

A case of teaching Jack Dieckmann, Stanford University Tesha Sengupta-Irving, UCLA Nick Fiori – Yale University

Exploratory Algebra Class

Exploratory Algebra Class Algebra as a problem solving tool Integrating mathematical practices with algebraic content

The Students - ethnicity: 39% Latino 34% White 11% African-American 10% Asian 5% Filipino 1% Native American

The students - achievement (prior math class) 40% A or B 20% C 40% D or F Disaffected?

Reasons for attending summer school? 10% involved in choice 90% ‘made’ to come by parents / teachers

4 Teaching principles Engage students as active and capable learners Teach mathematical practices – reasoning, organizing, representing, generalizing Develop a collaborative, mathematical community Give opportunities for student voice

Active and Capable Learners Heterogeneous groups Agency Andrew Pickering The ‘dance of agency’

Mathematical Practices exploring, orienting, representing, generalizing, questioning, organizing mathematical thinking

Develop a collaborative, mathematical community Groups Pairs Student presentations and discussions eg four 4’s

Student Voice

Research Data Summer school applications Lesson observations Student surveys & reflections Student interviews – 35 during the summer, 15 in the fall Class materials – posters, work MARS assessments Grades in fall and winter

Results Achievement Engagement & Enjoyment Future Success

A 24% increase.

Engagement: How much have you enjoyed this math class?

Has this class been more / less useful than regular math class

Kit

Rochelle

An example of the teaching. Week 4. Menu Activities.

An example of the teaching, Week 4, Menu Activities An example of the teaching, Week 4, Menu Activities. Things to watch out for…. Reluctant students Encouragement of collaborative community Teacher attempts to involve all students – even quiet ones, Charles Alonzo (army jacket)

Alonzo

What do you see students learning in this 5 minute clip of teaching?

Collaboration & Agency

The silent math class “For the past year, math year was the hardest because you’re not supposed to talk, you’re not supposed to communicate.” “In other classes it used to like be hard doing my work cause it used to be so boring…and I used to get frustrated and stuff and like right here we get to do group work and we get to talk and stuff and that like helps it not be so boring.”

Increased access to understanding “in normal school you don’t get to do this, but it helped me understand things more” “it helps me see how they see it and to see if I could understand it”   “I kind of build on other people’s ideas, I really do respect what other people say.”

Multiple Methods “I used to use only one way the teacher taught me and not really understand it. Now I use different ways until I get it.” “When I don’t know how to solve a problem the way the teacher does it, I have other ways to solve it.”

Mathematical Seeing “When we would see the problem in different ways we would understand it better.” “ It’s like the way – the way our schools did it is like very black and white, and the way people do it here, it’s like very colorful, very bright. You have very different varieties you’re looking at. You can look at it one way, turn your head, and all of a sudden you see a whole different picture.

Mathematical tinkering “I have learned that after finding a pattern you can stretch it in many ways instead of just staring at it. I have learned to think beyond the answer to the problem ” “Generalizing helped me to look beyond the problems and make challenges for myself” ‘When I’m done, I think of something harder to do”

Common Core Standards: Mathematical Practices. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning Long, complex, challenging Open-ness Need to elicit different ideas and perspectives – in support of these? …Organisation, small cases, representations

Supporting Practices Organisation Taking a smaller case Representation

How many squares are on a chessboard?

Organizing “I have learned to organize my work – write it all down” “I learned to organize my work by making T-tables, making charts, also I learned that I should label important information in directions etc” Organizing

Trying a smaller case “Patterns were very helpful because sometimes the question was asking about a huge number, so then I would just start with some smaller numbers, find a pattern and predict the answer without just taking a lot of time and effort to do the one big problem”

Beans and Bowls. How many ways are there to arrange 3 beans into two bowls?

Representing Answers to ‘What have you learned’: “I learned to say what I’m thinking (in words).” “taking notes, to remember info and drawing pictures to see what’s going on” “I learned to see patterns a lot better and how to understand how it gets bigger (or smaller).”  

Common Core Standards: Mathematical Practices. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

A case: mathematical practices & heterogeneity Gauss

How many blocks are in case 100?

Common Core Standards: Mathematical Practices. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

Heterogeneity This class has been more useful because we take the time to make sure everybody understands everything and we use different methods of learning.

Observations of Fall Classes: Students sitting in rows, teacher presents, students work through worksheets. In silence.

The good news… significant improvement in math grades

The bad news… it didn’t last.

The students wanted: To be given hard challenges To gain understanding through discussions To be able to ‘stretch’ problems and determine mathematical pathways To add some color to their mathematical landscapes

Back in their math classes: I would say…the only way to describe summer school is very colorful and then this class is just still, ugghhh, black and white. And you just wanna ask ‘Can I have a little bit of yellow?’

Common Core Standards: Mathematical Practices. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

2 student cases Alonzo Jorge

A book for teachers and parents..

Panel Discussion After listening to the speakers, what additional or clarifying questions do you have regarding: The Common Core State Standards for Mathematics (CCSS-M) Implementing the 8 Standards for Mathematical Practice in the classroom The changes in formative and summative assessment in your district/classroom Plant a question about how to start implementing the CCSS-M in their districts or classrooms (focus on classroom practice and the 8 Standards for Mathematical Practice and formative assessment such as MARS or other performance assessments.