“There was one time during class that I put a problem up at the board and got the
entire thing correct. I was actually, in a way, disappointed because I feel like I learn
“Whenever
I have
a question about a problem I ask the question, why?”
better
from my
mistakes.”
“I like how it is focused on yourself
figuring
out the problem
– though
“I think
that presenting
my solution
is that
was hard for me to adjust to – most
however
it’sbecause
made meI am
much
moreto
useful
forced
independent math-wise.”
participate and learn from other people.”
“You can see that everyone here wants to figure out how they got
a certain problem. There’s more of an interest than just getting
something right, instead of just getting an A. It’s something you
know that they want to understand how. “
“My best description is that of a light bulb. I could see where the rest of
“I was presenting a problem that I wasn’t quite sure I had
the problem might lead and the concept that it covered.”
answered right, and with a little push from the class, the concept
suddenly clicked in my mind. I was able to finish the rest of the
problem quickly and felt good about my success.”
Sunshine Greene and Carmel Schettino
Mathematics Department, Emma Willard School
CREATING A GEOMETRY
CLASSROOM BASED ON THE
RELATIONAL LEARNING OF
GIRLS
Sunshine Greene and Carmel Schettino
Mathematics Department, Emma Willard School
Comparison of Traditional and
Relational Classroom
Traditional
Relational
Lecture, direct-instruction
Student-centered instruction
Separate Knowing*
Connected Knowing*
Dualistic view of truth
Appreciation of multiple views of
truth
Authority in meaning-making lies
in teacher
Perception that meaning-making
is constructed by learning
community
Majority of classroom practice is
individual work+
Majority of classroom practice is group
problem solving and presentation+
Group/Pair Work Process-Oriented
Group/Pair Work Construction of
Knowledge Oriented
*Belenky,et al, 1986, +Boaler, 2008
The Theory of Girls’ Learning





Preference for Collaboration
Active Learning
Connected
 Prior Knowledge
 People
 Current Knowledge
Need to feel valued, listened to
Questioning, Curious for real understanding
The Pedagogy

Feminist Mathematics Pedagogy
 Dissolution
of Hierarchy
 Empowerment and Agency
 Inclusion of all Voices
 Ownership in Learning

A Pedagogy of Relation
 Relational
Equity
 Relational Authority
Solar, 1995, Anderson, 2005, Bingham, 2004, Boaler, 2008
Teacher Behaviors
Schettino, 2009
The Curriculum









Problem-Based
Discourse-Driven
Spiraled and Parallel Topics
Built on Prior Knowledge
Student Construction of New Knowledge
Teacher Facilitation and Scaffolding - Key
Multiple Representations
Assessment Variations
Ownership of New Knowledge via Metacognitive
Journaling
Problem Purposes







reviewing material from past courses
triggering prior knowledge for an upcoming
problem
inspiring construction of new knowledge
introducing new terminology
practicing a new skill
challenging the more able students (differentiated
instruction)
seeing the same new idea from a different
representation
Slope – Multiple Perspectives
The vertices A, B and C are
collinear. Find the
dimension n.
Slope – Multiple Perspectives
An airplane is flying at 36000 feet directly
above Lincoln, Nebraska. A little later the plane
is flying at 28000 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.
Slope – Multiple Perspectives
The diagram at right shows the graph of 3x + 4y =
12. The shaded figure is a square, three of whose
vertices are on the coordinate axes. The fourth
vertex is on the line. Find the lengths of the sides
of the square.
Right Angles – Multiple Perspectives
Let A = (3, 2), B = (1, 5), and P = (x, y). Find xand y-values that make ABP a right angle. Describe
the configuration of all such points P.
Right Angles – Multiple Perspectives
Find coordinates for the vertices of a lattice
rectangle that is three times as long as it is wide
with none of the sides horizontal.
References








Anderson, D. L. (2005). A portrait of a feminist mathematics classroom: What adolescent girls say about
mathematics, themselves, and their experiences in a "unique" learning environment. Feminist Teacher, 15(3),
175-193.
Belenky, M., Clinchy, B., Goldberger, N. and Tarule, J. (1986). Women’s Ways of Knowing: The
Development of Self, Voice and Mind. Basic Books:.
Biesta, G. (2004). Mind the gap. In C. Bingham & A. M. Sidorkin (Eds.), No education without relation (pp.
11-22). New York: Peter Lang.
Bingham, C. (2004). Let's treat authority relationally. In C. Bingham & A. M. Sidorkin (Eds.), No education
without relation (pp. 23-38). New York: Peter Lang.
Boaler, J. (2008). Promoting 'relational equity' and high mathematics achievement through an innovative
mixed-ability approach. British Educational Research Journal, 34(2), 167-194.
Fisher, B., M. (2001). No Angel in the Classroom: Teaching Through Feminist Discourse. Lanham, MD: Rowman
& Littlefield Pulishers, Inc.
Hmelo-Silver, C., & Barrows, H. (2006). Goals and strategies of a Problem-Based Learning facilitator. The
Interdisciplinary Journal of Problem-Based Learning, 1(1), 21-39.
Hmelo-Silver, C., & Barrows, H. (2008). Facilitating collaborative knowledge building. Cognition and
Instruction, 26, 48-94.
References

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
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Solar, C. (1995). An inclusive pedagogy in mathematics education. Educational Studies in Mathematics, 28(4),
311-333.
Taylor, C., & Robinson, C. (2009). Student voice: Theorising power and participation. Pedagogy, Culture and
Society, 17(2), 161-175.
Thayer-Bacon, B., J. (2004). Personal and social relations in education. In C. Bingham & A. M. Sidorkin (Eds.),
No education without relation. New York: Peter Lang.
Our Curriculum can be accessed at my website at a geometry course link
http://community.emmawillard.org/Math/Schettino/index.htm or directly by using
this url http://tinyurl.com/2djncvb