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

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

Studying Teaching & Learning:

700 students

4 years of high school4 years of high school

3 schools3 schools

Traditional Traditional Railside

Short practicequestions

Teacher Lectures

Tracking

Individual work

Long, conceptualproblems

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-AssessmentT

est

Score

0

10

20

30

40

50

Traditional

Railside

Year 1 Post-Assessment

Test

Score

0

10

20

30

40

50

Traditional

Railside

Year 2 Post-Assessment

Test

Score

0

10

20

30

40

50

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 codingQuestionnairesStudent and teacher interviews

Assessments

Equitable teaching practices

Railside SchoolRailside 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 InstructionComplex Instruction

Roles Multidimensional

Classes

Student-to-Student Accountability

Teacher Equalizing


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)


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)


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)


Justification


Equity

Int: What happens when someone says an answer..A: We’ll ask how they got itL: 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)


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)



Teacher Equalizing

Assigning

Competence



Student

Responsibility

Assigning

Competence


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)

StudentResponsibility

x

1

1

10x + 10

Where’s the 10?


Student

Responsibility

Assigning

Competence


Student

Responsibility

RolesMulti-dimensionality

High demandEffort

over ‘ability’Clear

expectations

Railside Equitable Practices

AssigningCompetence

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’

Anyone can be really good at math if they try

Railside Traditional

83% 50%

Effort not‘Ability’

Padded wall

7 feet

30 feet

Skateboarder’s path

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?

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 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)

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Documents

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