Change the classroom: Equity with PBL

Carmel Schettino, Ph.D.
NCTM, April 2014

Change the classroom
Not the students: Attaining
Equity Using PBL
©carmelschettino.org

What is PBL?
Boaler, How to Learn Math, 2013

What is RPBL?
an approach to curriculum and pedagogy
where student learning and content material
are (co)-constructed by students and
teachers through mostly contextually-based
problems in a discussion-based classroom
where student voice, experience, and prior
knowledge are valued in a non-hierarchical
environment utilizing a relational pedagogy.

Relationships in Learning
Hawkins, 1974

1. Learning in the mathematics
classroom is social, not individual
2. Coming to know mathematics
depends upon active participation
in the enterprises so valued in
that community of mathematics
practice that they are accepted
within that community
Burton, 2002

What are the practices accepted
in your learning community?
What are the enterprises valued
in your learning community?
What does active participation
look like in your learning
community?

Learning
https://www.teachingchannel.org/videos/geometry-lesson-quadrilaterals creative commons open license

What do you observe?
• What appeared to be the practices that
were accepted in this learning community?
• What appeared to be the enterprises
valued in this learning community?
• What did active participation look like in
this learning community?

Change the classroom
How does teaching with PBL
help attain a sense of equity?
Empowermen
t
Inclusion
Active
Participation
Student
Voice

Research Questions
How do we encourage young women to
enjoy learning mathematics?
What parts of the teaching of high school
mathematics are not working for girls?
When a mathematics teacher uses RPBL
what are the experiences of young women?

Study Participants
Name Leona Isabelle Kacey Sarah Alanna
Grade 10 9 10 (repeat) 9 9
Race White Mixed White White African-American
SES Upper Middle Middle
Upper
Middle
Lower
Ability Low Middle Low Middle High
Interest Low Medium High Low Low
Boarder/Day Boarder Boarder Boarder Day Day

An airplane is flying at 36,000
feet directly above
Lincoln, Nebraska. A little later
the plane is flying at 28,000 feet
directly above Des
Moines, Iowa, which is 160 miles
from Lincoln. Assuming a
constant rate of descent, predict
how far from Des Moines the
airplane will be when it lands.

Leona‟s Solution

I feel accomplished that I get to…not influence, but
in a way influence others and at the same time
receive influence from others, because…then I feel
accomplished like I‟ve done something [that] not
only affects myself as a learner, but others as well.
And…it‟s just a good feeling that I could hope to
make others understand, if I‟m correct with what
I‟m saying. And even if I‟m not, I mean, everyone
learns from mistakes so to present myself and kind
of put myself out there, too, in front of people, it‟s
nice to have them accept what I‟m saying, or
choose not to. And so, I feel accomplished.
Leona, Grade 10

In triangle ABC, it is given that
angle A is 59 degrees and angle
B is 53 degrees. The altitude
from B to line AC is extended
until it intersects the line through
A that is parallel to segment BC;
they meet at K. Calculate the size
of angle AKB.

I must first identify that the point at which the altitude of B
intersects side AC forms a 90 degree angle. I know [sic]
have one side of my triangle figured out. Notice how I am
using a smaller triangle to prove the angle of AKB. Next I
look at angle C which I found from subtracting the sum of
angles B and A from 180. Angle C corresponds with (and
she drew an arrow to KAC in her diagram) so they are
congruent because the lines are parallel.
(from Kacey’s journal)

Multiple Perspectives
Dynamic Objectivity (Keller)
Duty of Interpretation (Maher)
Dance of Agency (Boaler)
Main theoretical tenets of
RPBL©carmelschettino.org

Two circles intersect and the
distance between the centers
is 14 cm. The radius of one of
the circles is 13 cm and the
length of the common chord is
24 cm. How large is the other
circle?
Sample Problem

Attitudes of the students from the
beginning of the problem to the end
Openness and Risk-taking in ideas
Perseverance
Critiquing others‟ ideas
Observations to make:

RPBL Classroom

On traditional methods…
“my old teacher, kind of said „here‟s what it is‟, but there was never
that why, there was the how, there was the what, but that was it.”
“questions were always a possibility. Teachers never denied us of
that, like, privilege; I guess you could call it. I could ask
questions, but I couldn‟t go and …just understand it more and it kind
of goes with that „why”‟ thing. Like I couldn‟t go and ask…I could go
ask what, but I couldn‟t ask why, which really affected me too.”
“I really wouldn‟t say anything. I would know the answer, I just
wouldn‟t say anything. [opportunities that you had to ask like
extension questions…] They were like non-existent.”
“You‟re not talking, you‟re listening. You‟re not contributing, you‟re
having someone talk to you and lecture you.”

On RPBL methods…
“you notice things for yourself. That‟s how I like to see it. I
notice things for myself so I have a better grasp and
understanding of it in my own eyes. Whereas, I‟m just learning
from what you‟re teaching me - it‟s like, your opinion not mine.”
“Sometimes in my class, I don‟t know, when one person‟s at
the board the others are really listening to what they have to
say. Because not everybody can solve all the problems on the
homework, So, if one person‟s at the board and they fully
understand it and they explain it to the class I think it means
more than just a teacher telling you how to do a
problem…Yeah the more people that participate, the more you
understand it.”

On RPBL methods…
“To hear other people‟s… um, point of view and see how they
see a problem because then it helps them, um, like if it‟s like a
beneficial way… to find a better way to do the problem or if it‟s
not, to see like why you should not do it that way like explain
more, so like don‟t do this, it‟s not like don‟t do this, it‟s like
don‟t do this because…”
“Sometimes in my class, I don‟t know, when one person‟s at
the board the others are really listening to what they have to
say. Because not everybody can solve all the problems on the
homework, So, if one person‟s at the board and they fully
understand it and they explain it to the class I think it means
more than just a teacher telling you how to do a
problem…Yeah the more people that participate, the more you
understand it.”

On RPBL methods for African American students…
Lim (2008b) said this of the internal conflict that young
African-American students grapple with in a traditional
mathematics classroom:
“Black students‟ communication style (e.g., free verbal
expression and talking aloud) and learning preference
(e.g., holistic, relational, and field-dependent) were
rarely respected in the classroom space; rather they
were considered disruptive behaviors or, at best, an
attitude non-conducive to mathematics learning.”

More Connected and
Expressive
Isabelle: “Like, if more math classes were taught
like this, I… I might like them a lot more. Um,
because it‟s not so uptight and [laughs], like it‟s not
like focused, „memorize all of this stuff‟. ”

High Ability AA
• Alanna: “Well, for me while sitting in the
classroom, I‟ll always be the distraction. I would
always be the one always talking „cause I
understood it. I got it. But I would always
distract students who didn‟t get it. It would
always be me and a couple people who got it.
And it was just like talking, but it was never really
like me paying attention.”

Coed Results n=25
Statement Average
response
I am more independent in math class 3.2
I like learning math 3.2
Math class is very different than I have always learned math 3.3
I am more frustrated now than I was at the beginning of the
year.
1.7
I appreciate other people's perspectives in my learning and
seeing their ways of doing a problem.
3.4
I like listening to the teacher more in math class. 2.7
I feel more comfortable asking questions in class. 3.2
My attitude towards my ability has not changed much. 2.3
I feel more confident in my math ability. 3

You could, kind of, add in your perspective
and it kind of gives this sense like “Ooh, I
helped with this problem” and then another
person comes in and they helped with that
problem, and by the end no one knows who
solved the problem. It was everyone that
solved the problem. Like, everyone
contributed their ideas to this problem and
you can look at this problem on the board and
you can maybe only see one person‟s
handwriting, but behind their handwriting is
everyone‟s ideas. So yeah, it‟s a sense of
“our problem” it‟s not just Karen‟s problem, it‟sKacey, 16

“our
problem”
Shared
Authority
increased
equity

Interested in changing
your classroom?
Sample problems in the handout
Pedagogical resources on my website
carmelschettino.org (website)
Rubrics and discussion of classroom
practice on website
Teacher Training and PD in PBL
methods©carmelschettino.org

Contact Me
Carmel Schettino, Ph.D. (Facebook)
carmel@carmelschettino.org (email)
@SchettinoPBL (Twitter)
carmelschettino.org (website)
Where you can find lots of
resources, papers and curriculum

• Burton, L. (1995). Moving towards a feminist
epistemology of mathematics. In P. Rogers & G. Kaiser
(Eds.), Equity in Mathematics Education: Influences of
feminism and culture (pp. 209-225). Washington, D.C.:
Falmer Press.
• Schettino, C., (2013). Dismantling the Birdcage:
Adolescent girls’ attitudes towards learning mathematics
with a relational pedagogy in a problem-based
environment. Retrieved from ProQuest/UMI.
Submission Number suny.alb11007
• Boaler, J. (2008). Promoting 'relational equity' and high
mathematics achievement through an innovative mixed-
ability approach. British Educational Research Journal,
32(2), 167-194.
• Maher, F. A., & Thompson Tetreault, M. K. (2001). The
Feminist Classroom. New York: Rowman & Littlefield
Publishers, Inc.
• Keller, E.F.(1995). Reflections on gender and science.
New Haven: Yale University Press©carmelschettino.org

Change the classroom: Equity with PBL

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