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

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Creating Mathematical Futures Through an
Equitable Teaching Approach The case of Railside
School
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Studying Teaching Learning
3 schools

• 700 students

4 years of high school
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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
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Demographic Comparison
Traditional
Railside

• 71
• 23
• 1
• 2
• 1
• 2    

19 39 22 9    7 4
white Latino African American  Asian   Filipino o
ther Groups 
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Year 1 Pre-Assessment
Test Score
50
40
30
20
10
0
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Year 1 Post-Assessment
Test Score
50
40
30
20
10
0
7
Year 2 Post-Assessment
Test Score
50
40
30
20
10
0
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In year 4 41 of Railside seniors 23 of
traditional seniors were in advanced classes
(pre-calc and calc)
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Railside
Traditional
I enjoy math in school - all or most of the time
47
70
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Methods

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

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Equitable teaching practices
Railside School
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Conceptual curriculum

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

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1
x
1
What is the perimeter of this shape?
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Complex Instruction

• Elizabeth Cohen (1986)

Status Differences
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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.

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Complex Instruction
Multi-dimensionality
Roles
Student-to-Student Accountability
Teacher Equalizing
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Complex Instruction
Roles
Multidimensional Classes
Student-to-Student Accountability
Teacher Equalizing
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• Asking good questions
• Rephrasing problems
• Explaining
• Using logic
• Justifying methods
• Using manipulatives
• Helping others

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

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• 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)

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• 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)

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Justification

• Equity

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• 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)

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• Most of them, they just like know what to do and
  everything. First youre 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 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)

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Complex Instruction
Roles
Multi-dimensionality
Assigning Competence
Teacher Equalizing
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Complex Instruction
Roles
Multi-dimensionality
Assigning Competence
Student Responsibility
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• 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)

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10x 10
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Wheres the 10?
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(No Transcript)
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Complex Instruction
Roles
Multi-dimensionality
Assigning Competence
Student Responsibility
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Railside Equitable Practices
Multi-dimensionality
Roles
High demand
Effort over ability
Clear expectations

Student Responsibility
Assigning Competence
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• 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)

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Railside
Traditional
Anyone can be really good at math if they try
83
50
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Padded wall
30 feet
Skateboarders 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 oclock position, at which
time s/he is 30 feet from the wall. How long will
it take the skateboarder to hit the wall?
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(No Transcript)
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Question What have students learned in order to
work in these ways?
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• 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)

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(No Transcript)
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jo.boaler_at_sussex.ac.uk