Creating Mathematical Futures Through an Equitable Teaching Approach: The case of Railside School

Studying Teaching & Learning: 700 students 4 years of high school 3 schools

Traditional Railside Short practice questions Teacher Lectures Tracking Individual work Long, conceptual problems Teacher questions Heterogeneous Groups Group work No Teacher collaboration Teacher collaboration

Demographic Comparison 71% 23% 1% 2% 1% 2% 19% 39% 22% 9% 7% 4% white Latino African American Asian Filipino other Groups Traditional Railside

Year 1 Pre-Assessment Test Score Traditional Railside

Year 1 Post-Assessment Test Score Traditional Railside

Year 2 Post-Assessment Test Score Traditional Railside

In year 4: 41% of Railside seniors 23% of traditional seniors were in advanced classes (pre-calc and calc)

I enjoy math in school - all or most of the time Railside Traditional 47% 70%

Methods Over 600 hours of classroom observations over 4 years Video coding Questionnaires Student and teacher interviews Assessments

Equitable teaching practices Railside School

Conceptual curriculum Designed by the teachers Longer problems Algebra-geometry links Multiple representations Algebra Lab gear

x 1 1 What is the perimeter of this shape?

Complex Instruction Elizabeth Cohen (1986) Status Differences

Messages There are many ways to be smart, no-one is good at all of them and everyone is good at some of them You have 2 responsibilities – if anyone asks for help you give it. If you need help you ask for it.

Roles Multi- dimensionality Student-to- Student Accountability Teacher Equalizing Complex Instruction

Roles Multidimensional Classes Student-to- Student Accountability Teacher Equalizing Complex Instruction

Asking good questions Rephrasing problems Explaining Using logic Justifying methods Using manipulatives Helping others Multi- dimensionality

Many more students were successful because there were many more ways to be successful

Back in middle school the only thing you worked on was your math skills. But here you work socially and you also try to learn to help people and get help. Like you improve on your social skills, math skills and logic skills. (R, f, y1) Multi- dimensionality

J: With math you have to interact with everybody and talk to them and answer their questions. You cant be just like oh heres the book, look at the numbers and figure it out Int: Why is that different for math? Its not just one way to do it (…) Its more interpretive. Its not just one answer. Theres more than one way to get it. And then its like: why does it work? (R,f,y2) Multi- dimensionality

A math person is a person who knows like, how to do the work and then explain it. Like explaining everything to everyone so they could get it. Or they could explain it the hard way, the easy way or just, like average – so we could all get it. Thats like a math person I think. (R, m, y1) Multi- dimensionality

Justification Multi- dimensionality Equity

Int: What happens when someone says an answer.. A: Well ask how they got it L: Yeah because we do that a lot in class. (…) Some of the students – itll be the students that dont do their work, thatd be the ones, theyll be the ones to ask step by step. But a lot of people would probably ask how to approach it. And then if they did something else they would show how they did it. And then you just have a little session! (R, m, y3) Multi- dimensionality

Most of them, they just like know what to do and everything. First youre likewhy you put this? and then like if I do my work and compare it to theirs theirs is like super different cos they know, like what to do. I will be like – let me copy, I will be like why you did this? And then Id be like: I dont get it why you got that. And then like, sometimes the answers just like, they be like yeah, hes right and youre wrong But like – why? (R, m, y2) Multi- dimensionality

RolesMulti- dimensionality Teacher Equalizing Assigning Competence Complex Instruction

RolesMulti- dimensionality Student Responsibility Assigning Competence Complex Instruction

Int: Is learning math an individual or a social thing? G: Its like both, because if you get it, then you have to explain it to everyone else. And then sometimes you just might have a group problem and we all have to get it. So I guess both. B: I think both - because individually you have to know the stuff yourself so that you can help others in your group work and stuff like that. You have to know it so you can explain it to them. Because you never know which one of the four people shes going to pick. And it depends on that one person that she picks to get the right answer. (R, f, y2) Student Responsibility

x x + 10

Wheres the 10?

RolesMulti- dimensionality Student Responsibility Assigning Competence Complex Instruction

Student Responsibility Roles Multi- dimensionality High demand Effort over ability Clear expectations Railside Equitable Practices Assigning Competence

To be successful in math you really have to just like, put your mind to it and keep on trying – because math is all about trying. Its kind of a hard subject because it involves many things. (…) but as long as you keep on trying and dont give up then you know that you can do it. (R, m, y1) Effort not Ability

Anyone can be really good at math if they try Railside Traditional 83%50% Effort not Ability

Padded wall 7 feet 30 feet Skateboarders path The platform has a 7-foot radius and makes a complete turn every 6 seconds. The skateboarder is released at the 2 oclock position, at which time s/he is 30 feet from the wall. How long will it take the skateboarder to hit the wall?

Question: What have students learned in order to work in these ways?

Math is really beautiful and has these patterns in it that are amazing. Most art is just made up of patterns anyway. And so Ive written a lot of poems about it, and a lot of songs involving it. Polyrhythms was one thing that kind of interspersed music and math for mebecause its like patterns that take multiple measures to repeat because they dont fit evenly over four bars, and its exactly like a fraction because if you take a fraction high enough theres going to be common denominators. And so seeing how patterns can be interesting and, artistic. And math intersperses a lot for me that way. (Toby, age 16)