Creating Mathematical Futures: An Equitable Teaching Approach at Railside School

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

2. 700 students Studying Teaching & Learning: 3 schools 4 years of high school

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

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

5. Railside Traditional Year 1 Pre-Assessment Test Score 50 40 30 20 10 0

6. Railside Traditional Year 1 Post-Assessment Test Score 50 40 30 20 10 0

7. Railside Traditional Year 2 Post-Assessment Test Score 50 40 30 20 10 0

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

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

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

11. Railside School Equitable teaching practices

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

13. 1 x 1 What is the perimeter of this shape?

14. Complex Instruction Elizabeth Cohen (1986) Status Differences

15. 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.

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

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

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

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

20. Multi- dimensionality 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)

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

22. 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. That’s like a math person I think. (R, m, y1) Multi- dimensionality

23. Multi- dimensionality Justification Equity

24. Multi- dimensionality Int: What happens when someone says an answer.. A: We’ll ask how they got it L: Yeah because we do that a lot in class. (…) Some of the students – it’ll be the students that don’t do their work, that’d be the ones, they’ll 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)

25. Most of them, they just like know what to do and everything. First you’re like “why 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 I’d be like: “I don’t get it why you got that.” And then like, sometimes the answer’s just like, they be like “yeah, he’s right and you’re wrong” But like – why?” (R, m, y2) Multi- dimensionality

26. Complex Instruction Roles Multi-dimensionality Assigning Competence Teacher Equalizing

27. Complex Instruction Roles Multi-dimensionality Assigning Competence Student Responsibility

28. Int: Is learning math an individual or a social thing? G: It’s 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 she’s going to pick. And it depends on that one person that she picks to get the right answer. (R, f, y2) Student Responsibility

29. 1 x 1 10x + 10

30. Where’s the 10?

32. Complex Instruction Roles Multi-dimensionality Assigning Competence Student Responsibility

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

34. 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. It’s kind of a hard subject because it involves many things. (…) but as long as you keep on trying and don’t give up then you know that you can do it. (R, m, y1) Effort not ‘Ability’

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

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

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

39. Math is really beautiful and has these patterns in it that are amazing. Most art is just made up of patterns anyway. And so I’ve 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 me—because it’s like patterns that take multiple measures to repeat because they don’t fit evenly over four bars, and it’s exactly like a fraction because if you take a fraction high enough there’s 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)

41. jo.boaler@sussex.ac.uk