Transcript Taking up opportunities to learn: Examining the

Creating Mathematical Futures Through an Equitable
Teaching Approach: The case of Railside School
Studying Teaching & Learning:
3 schools
700 students
4 years of high school
Traditional
Traditional
Teacher Lectures
Short practice
questions
Tracking
Individual work
No Teacher collaboration
Railside
Long, conceptual
problems
Teacher questions
Heterogeneous Groups
Group work
Teacher collaboration
Demographic Comparison
Traditional
Railside
white
71%
19%
Latino
23%
39%
African American
1%
22%
Asian
2%
9%
Filipino
1%
7%
other Groups
2%
4%
Year 1 Pre-Assessment
50
Test Score
40
30
20
10
0
Traditional
Railside
Year 1 Post-Assessment
50
Test Score
40
30
20
10
0
Traditional
Railside
Year 2 Post-Assessment
50
Test Score
40
30
20
10
0
Traditional
Railside
In year 4:
41% of Railside seniors
23% of traditional seniors
were in advanced classes
(pre-calc and calc)
Traditional
I enjoy math in
school - all or most
of the time
47%
Railside
70%
Methods
Over
600 hours of classroom
observations over 4 years
Video coding
Questionnaires
Student and teacher
interviews
Assessments
Railside School
Equitable teaching practices
Conceptual curriculum

Designed by the teachers

Longer problems

Algebra-geometry links

Multiple representations

Algebra Lab gear
1
x
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.
Complex Instruction
Roles
Multidimensionality
Student-toTeacher
Student
Accountability Equalizing
Complex Instruction
Roles
Multidimensional
Classes
Student-toTeacher
Student
Accountability Equalizing
Multidimensionality
Asking good questions
 Rephrasing problems
 Explaining
 Using logic
 Justifying methods
 Using manipulatives
 Helping others

Many more students
were successful because
there were many more
ways to be successful
Multidimensionality
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)
Multidimensionality
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)
Multidimensionality
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)
Multidimensionality
Justification
Equity
Multidimensionality
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)
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)
Multidimensionality
Complex Instruction
Roles
Multidimensionality
Assigning
Competence
Teacher
Equalizing
Complex Instruction
Roles
Multidimensionality
Assigning
Student
Competence
Responsibility

Student
Int: Is learning math an individual
Responsibility
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)
1
x
1
10x + 10
Where’s the 10?
Complex Instruction
Roles
Multidimensionality
Assigning
Student
Competence
Responsibility
Railside Equitable Practices
Roles
Multidimensionality
High
demand Effort
over
Clear
‘ability’
expectations
Assigning
Competence
Student
Responsibility
 To
Effort not
‘Ability’
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%
Padded wall
30 feet
Skateboarder’s path
q
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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