Creating a Geometry Classroom

“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
I have
a question about a problem I ask the question, why?”
from my
“I like how it is focused on yourself
out the problem
– though
“I think
that presenting
my solution
is that
was hard for me to adjust to – most
made meI am
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
Sunshine Greene and Carmel Schettino
Mathematics Department, Emma Willard School
Comparison of Traditional and
Relational Classroom
Lecture, direct-instruction
Student-centered instruction
Separate Knowing*
Connected Knowing*
Dualistic view of truth
Appreciation of multiple views of
Authority in meaning-making lies
in teacher
Perception that meaning-making
is constructed by learning
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
 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
 Relational Authority
Solar, 1995, Anderson, 2005, Bingham, 2004, Boaler, 2008
Teacher Behaviors
Schettino, 2009
The Curriculum
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
Problem Purposes
reviewing material from past courses
triggering prior knowledge for an upcoming
inspiring construction of new knowledge
introducing new terminology
practicing a new skill
challenging the more able students (differentiated
seeing the same new idea from a different
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
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.
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),
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.
Solar, C. (1995). An inclusive pedagogy in mathematics education. Educational Studies in Mathematics, 28(4),
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 or directly by using
this url

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