Experiences and Third Spaces: A
Model for Pre-Service Elementary
Mathematics Teacher Education
Marcy Wood, Erin Turner, Courtney Koestler
University of Arizona
Marta Civil
University of North Carolina at Chapel Hill
The Beyond Bridging Project is supported by the National Science Foundation (Grant No.
DRL-1019860.) Any opinions, findings, and conclusions are those of the authors and do not
necessarily reflect the views of the National Science Foundation.
Introduction
• Theory-Practice divide between university methods
courses and elementary classrooms (Anderson, 1997;
Bencze, Hewitt, & Pedretti, 2001; Zeichner, 2010).
• Field has explored various ways to bridge this gap,
such as cases and a focus on high leverage
practices (Campbell, 2008; Feiman-Nemser & Beasley,
2007)
• Our project, Beyond Bridging, seeks to build
connections through co-educational learning
spaces, involving mentor teachers (MTs), preservice
teachers (PSTs), teacher educators (TEs) and
mathematicians
Co-Educational Learning Spaces as
Third Spaces
• Building co-educational, “third space” learning
environments (Moje et al., 2004) where the
perspectives and expertise of each group (MTs, PSTs,
TEs, mathematicians) are leveraged to enhance the
understanding of all
• Third spaces have the potential to bridge different
discourses and to work towards shared and
potentially more robust understandings of teaching
and learning mathematics
Elementary Education
Program Context
• Cohort, Field-Based Model
• Groups of 20-30 PSTs are placed at cluster of 2-3 elementary
schools for a three semester sequence
• Two semesters of methods and foundations coursework
• Courses 2.5 days per week at one elementary school in the
cluster
• Field applications 1.5 days per week at the same school or other
cluster school
• One semester of full time student teaching at one of the
cluster schools with one of the cohort mentor teachers
Co-Educational Learning Spaces in
Elementary Math Teacher Preparation
Joint Mathematics
Methods Sessions
PSTs and their MTs attend
selected sessions of a
methods course together
Example: Prepare to conduct
task-based interviews with
students in MTs classroom.
Parallel Professional
Development and
Mathematics
Methods Sessions
Mentor Teachers
Co-Teaching in
Mathematics
Methods
PSTs attend methods course
and MTs attend a professional
development sessions focused
on similar topics
MTs and teacher educator (TE)
co-plan and co-teach a specific
math methods class. MTs
contribute to class sessions in
various ways, e.g., bring
student work, modeling
activities, and discussing
curriculum.
Example Parallel Sessions:
-Cognitively Guided
Instruction
-Status and Complex
Instruction
Joint Math Methods Sessions
Goals of working jointly with PSTs and MTs:
1) Familiarize MTs with key theories of methods
course so that they might continue
conversations in their classrooms with PSTs
2) Leverage MTs unique knowledge and
experiences with students, classrooms, and
curriculum to enhance PST learning
Structure of Joint Methods Sessions
• Two sessions
• Focused on interviewing students
• Sequence of events:
• AM in methods class: introduction to
interviewing and CGI problem
structures/children’s strategies
• PM in MTs’ classrooms: MT/PST pairs interview
several MT students
• Afterschool debrief session with MT/PST/TE
Methods
• Transcription of 7 hours of audio and video
involving whole group and small group talk
• Coding for MT contributions
Research Focus
• In the context of a common mathematics methods
activity, conducting and discussing problem solvingbased interviews for the purpose of learning about
children’s mathematical thinking:
• How do MTs draw on experiences to think about
children’s activity and their teaching?
• In what ways might MTs contributions create
opportunities to expand the learning of PSTs?
• What challenges and tensions arise?
Findings Overview
1. Classroom CONTEXT
2. Some ideas that were DISSONANT with
methods
3. Some ideas that RESONATED with methods
4. LINKING interviews to teaching
1. Bringing in CONTEXT
Problem: There are 20 marbles that 4 friends want to share evenly. Each
friend wants to have the same number. How many marbles can each
friend have?
Ria (PST): One of the girls…wrote 4, 8, 16, 20, and she said, 'oh, each is
going to have 4.' She didn't like click in her head that each person is
going to get 5 marbles…
Zelda (MT): because we have really been doing …floors and rooms, so
what my kids have been doing is doing patterning, they're saying 'for
one, 4 marbles; for two, 8 marbles', so what she was just doing is doing
what she is remembering which was number patterns. So she's not
thinking about dividing them out… I understand her thinking because I
know what we just did. We were just doing number patterns and so
she was doing a number pattern thing, 4, 8, 12, 16, 20. See? That’s why.
2. Some DISSONANCE with Methods
(but not as much as one might think….)
TE: There's some blue blocks and some red blocks, you
know the total and the number of blue, so how many
are red? So you know the parts, you know one part
and you know the whole and you're trying to find the
other part.
Ron (MT): That is a really, I'm finding for the ELL
students, that is a really hard concept for them to
understand because they see the first part of the
number and then they see the end number, and they
want to combine them even though they know it's not
addition, but they still end up doing addition, when
you look at their answers.
TE: And I would add that it's not ELL kids who struggle
with that; that all kids struggle with that
3. RESONANCE with methods
Example Problem: Ana has 8 flowers. How many more flowers
does Ana have to pick to have 12 flowers?
Celine (MT): When I was in first grade, my kids, I remember that
my kids had a lot of trouble with starting with a number and
trying to get to a stopping number. Because they would start to
add them and then they would be counting the ones that they
were putting on and not realize that when they get to twelve.
Or, they would get to twelve and not realize how many they
added on, so then they have to stop, and then separate out
again. And so that made it another step in the problem that
they would get confused on.
4. Linking to Teaching
Evan (MT): I know, like I saw my influence, my imprint, or
whatever you were saying, especially on the second kid…
because he was having a little more trouble actually doing the
problems, and he got stuck at one point, and I asked him to do an
easier way of doing more methods, and then he showed me a
grid multiplication method that I had thought I had taught them,
but he was unclear on that, and it was kind of uncomfortable
because, you know, that was totally me, my responsibility, I
showed him that, because he kept on looking at me
Benefits for PSTs and TEs
• Provide contextualization otherwise not
available
• Get deficit thinking in the open
• Demonstration of linking interviews to teaching
• Present the complexity of teaching and
reflection on learning
• Explore use of institutional labels
Tensions for PSTs and TEs
• Contextualization adds complexity
• supplant methods goal
• lots for PSTs to manage
• Much less control, can’t select MT talk or prepare specific
responses
• Additional teachers = shift in addressing PST ideas
• Different interactions
• Less time for PST talk
• MTs as co-teachers AND co-learners
Implications
These findings mean that we can
• Specifically address/invite certain MT input
• Craft TE responses to best leverage MT input
• For when MT talk might not parallel TE message
• For when MT talk adds complexity
• That recognize and utilize potential of MT talk
• Like asking MTs to elaborate/explain their talk
But we need to know more about
• How PSTs think about the complexity
• Multiple teachers
• Multiple messages
• How CONTEXT (methods vs. field) might matter
Questions?
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Marcy Wood, mbwood@email.arizona.edu
Erin Turner, eturner@email.arizona.edu
Courtney Koestler, ckoestler@email.arizona.edu
Marta Civil, civil@email.unc.edu
• For more information about the Beyond Bridging Project see,
http://www.coe.arizona.edu/bb