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Graves, Suurtamm, & Benton
LEARNING AND TEACHING MATHEMATICS IN COMMUNITIES OF
INQUIRY: IS IT ENOUGH TO TRANSFORM PRACTICE?
Barbara Graves, University of Ottawa, bgraves@uottawa.ca
Christine Suurtamm, University of Ottawa, suurtamm@uottawa.ca
Nicola Benton, University of Ottawa, nbenton@uottawa.ca
Abstract
This research examines a professional development initiative designed to assist
beginning elementary and secondary teachers deepen their understanding of
mathematics and mathematics teaching. The research addresses the challenge of
teacher change in mathematics education, and the central question is whether
learning and teaching mathematics in communities of inquiry are enough to
transform beginning teachers knowledge of mathematics to enable them to create
learning environments which support mathematical inquiry. In this qualitative
longitudinal study, we adopt a sociocultural theoretical framework to investigate
how 75 prospective elementary teachers participating in a mathematics learning
community with 6 beginning secondary mathematics teachers as their instructors,
construct themselves as learners and teachers in mathematical inquiry through their
discourse in joint problem-solving activities. Specifically we are exploring what
experiences help beginning teachers develop a deeper understanding of
mathematics and mathematics teaching so that they can facilitate effective
mathematics inquiry in their classrooms. Our initial findings suggest that even
when beginning teachers have experienced learning about mathematics in reformoriented learning environments and acknowledge this approach as supporting
mathematical learning, when they are presented with an opportunity to teach in
inquiry contexts, there remains a visible tension between the reform-oriented and
traditional approaches.
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2
LEARNING AND TEACHING MATHEMATICS IN COMMUNITIES OF
INQUIRY: IS IT ENOUGH TO TRANSFORM PRACTICE?
Barbara Graves, University of Ottawa, bgraves@uottawa.ca
Christine Suurtamm, University of Ottawa, suurtamm@uottawa.ca
Nicola Benton, University of Ottawa, nbenton@uottawa.ca
Introduction. This research examines a professional development initiative
designed to assist beginning elementary and secondary teachers deepen their
understanding of mathematics and mathematics teaching. The research addresses
the challenge of teacher change in mathematics education, and the central question
is whether learning and teaching mathematics in communities of inquiry are
enough to transform beginning teachers knowledge of mathematics to enable them
to create learning environments which support mathematical inquiry. In this
qualitative longitudinal study, we adopt a sociocultural theoretical framework to
investigate how 75 prospective elementary teachers participating in a mathematics
learning community with 6 beginning secondary mathematics teachers as their
instructors, construct themselves as learners and teachers in mathematical inquiry
through their discourse in joint problem-solving activities. Specifically we are
exploring what experiences help beginning teachers develop a deeper
understanding of mathematics and mathematics teaching so that they can facilitate
effective mathematics inquiry in their classrooms. The topic of this research fits
within the first strand of the ICMI-Study 15, as it addresses Pre-Service and Early
Years of Teaching.
The problem. Developing teacher expertise in mathematics and in mathematics
teaching remains a substantial challenge, however, as it requires not only the
ability to reason mathematically, and to interpret and solve mathematical problems
(Artelt, Baumert, Julius-McElvany & Peschar, 2003), but also the ability to
develop pedagogical content knowledge (Shulman, 1987). Pedagogical content
knowledge in mathematics teaching includes the ability to use multiple
representations for mathematical concepts, respond appropriately to learners'
varied understandings and misunderstandings, and to plan and develop lessons and
activities that focus on and develop meaningful mathematics (Ball, 1990; Ball &
Bass, 2002; Shulman, 1987).
Facilitating effective mathematics inquiry poses substantial, albeit different,
challenges for beginning teachers at both the elementary and secondary levels. For
elementary teachers, the research suggests that they lack sufficient knowledge of
mathematics to effectively implement inquiry-oriented mathematics programs
(Ball, 1988, 1990; Ball, Lubienski & Mewborn, 2001). For secondary teachers,
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3
while some of the same concerns exist about the procedural nature of their
mathematics knowledge, the real challenge is to help them shift their teaching
practices from traditional delivery models to more inquiry-oriented approaches
(Stigler & Hiebert, 1999).
Some recent studies suggest that teachers can move towards the use of
investigation and open-ended problem solving when they themselves have
experienced learning new mathematics through these pedagogical approaches
(Makar & Confrey, 2004; Roulet & Suurtamm, 2004; Shifter, 1998). In addition, it
may be possible for teachers to deepen their understanding of mathematics and
mathematics teaching through the activity of teaching itself (Ball & Lampert,
1999; Ma, 1999; Segall, 2001). Further, other researchers suggest that increased
mathematical knowledge and more effective mathematics teaching may be
developed through the engagement of meaningful collaboration with other teaching
colleagues (Ma, 1999; Wilcox, Schram, Lappan, & Lanier, 1991).
The present research study
Our qualitative longitudinal research study builds on these findings to determine
the teaching and learning experiences that are most effective in developing
beginning teachers’ mathematical knowledge and ability to facilitate inquiry-based
learning.
Theoretical framework. In order to investigate how the mathematical and
pedagogical experiences are understood by prospective elementary and beginning
secondary teachers, the research adopts a sociocultural perspective which views
learning as situated activity acquired from meaningful participation in specific
communities in which learners construct knowledge in relational networks that
emerge from the interactions of people and activity contexts (Cole, 1996; Greeno,
1998; Kirshner & Whitson, 1997; Lave, 1996; Vygotsky, 1978, 1986; Wenger,
1998; Wertsch, 1998). Mathematical knowledge and inquiry processes are thus
considered to be social activities which are mediated by cultural artifacts and
resources, and mathematics learning occurs through the process of mathematical
communication in social contexts (Forman, 2003). This shifts the traditional view
of learning from the acquisition of something to a formulation of learning as
participatory (Sfard, 1998) which is important for conceptualizing classrooms as
learning communities for inquiry. Thus, mathematical inquiry becomes a set of
social practices which are understood/learned by participants through participation
in language and multiple activities in specific contexts. This theoretical framing
allows us to focus on issues of knowledge, agency, and identity in order to
understand more fully what it means to participate in mathematical inquiry
practices from the perspectives of learner and teacher.
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The initial site. The study began with a one-week, intensive Summer Mathematics
Program designed for 75 prospective elementary teachers with the goal of
deepening their mathematical understanding and developing a more open-ended
perspective of mathematics before they enter their teacher education program. The
6 mathematics instructors for the summer program were recently graduated
secondary mathematics teachers. For the prospective elementary teachers, the
summer math program served as a learning environment for mathematical inquiry.
For the mathematics instructors, the summer program served as an initial teaching
setting that is closely aligned with the theories of inquiry-based mathematics
learning that they have been introduced to in their teacher education courses but
have not necessarily experienced in practicum settings.
Selecting the participants. When the offers of admission were sent out in Spring
2004 to the successful applicants to the Teacher Education Program, we included a
flyer describing the 5-day Summer Math Program (aka Math Camp) to be held
August 23-27, 2004. We invited prospective elementary teachers who were
interested in developing their understanding of mathematics and/or addressing
some of their math anxieties. We informed the applicants were prepared to
accommodate 75 participants and that selection would be on a first-come-firstserved basis. We received 192 applications.
Selecting the instructors. In the Teacher Education Program 2003-04, there were
65 teacher candidates specializing in secondary mathematics. They were all
informed of the summer math initiative and were invited to apply for positions as
math instructors. Twenty of the 65 applied for the 6 instructor positions. Following
the application and interview process 6 instructors were chosen for their
knowledge of mathematics and for their understanding and excitement about
inquiry-based pedagogy in mathematics. During the summer math program , the
instructors worked with groups of 15 participants and facilitated open-ended
mathematical inquiry group activities.
Planning the program. The researchers (who are also mathematics educators) and
the instructors met on several occasions prior to the summer math program to
begin developing a sense of what we hoped to accomplish during the summer math
program. During the week before the summer math program, the math instructors
and researchers worked collaboratively to develop a series of group activities
incorporating a variety of strategies. These included small group problem-solving,
open-ended investigations, use of manipulatives, focus on sharing solutions,
introduction to use of technology for math investigation, and outdoor activities
including a math trek in Ottawa.
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The five days of the Summer Math Program were developed around foundational
domains of mathematics: numeracy, measurement, geometry and patterning. Each
day consisted of in-class activities centered on core mathematical problems. Each
day concluded with a one hour meeting of the entire group of 75 teacher candidates
and the 6 instructors. A debriefing session of one hour attended by the researchers
and the instructors followed each day's activities.
Research design. All of the elementary teacher candidates and the mathematics
instructors agreed to participate in the research component of this initiative. The
plan was to collect data during the summer math program and then to follow the
elementary teacher candidates and the mathematics instructors for a period of 3
years through questionnaires and/or focus group interviews. This research design
supports a community of learners as the teacher candidates move through their preservice program and into their first few years of teaching and as the secondary
mathematics instructors in the summer program move through their first two years
of teaching.
 Data sources. There are multiple sources of data from both the prospective
elementary teachers and the mathematics instructors. Data from the instructors
include journals during the two weeks of planning and teaching, video data
from daily briefing sessions, and monthly focus group interviews during their
first year of teaching (videotaped). Data from the prospective elementary
teachers include 2 questionnaires, one at the beginning and one at the end of the
summer math program. Three additional questionnaires are planned during their
regular Teacher Education Program: One just prior to their first practicum in
November 2004, one following it in January 2005, and one following the
second practicum in April, 2005.
 Follow-up focus groups. Beginning in Fall 2005 we plan to have monthly focus
group meetings with a sample of 6-8 of the newly graduated elementary
teachers now in their first year of teaching in the Ottawa region who
participated in the summer math program. They will have volunteered to
continue in the study. [videotaped] We will also continue to have focus group
meetings with the 6 secondary math instructors from the summer math program
who will now be in their second year of teaching. [videotaped]
Findings.
The prospective elementary teachers. The data collected to date suggest that this
week-long intensive immersion in mathematical activity was very beneficial to
both their developing understanding of mathematical concepts and to their sense of
themselves as possible mathematical thinkers. The attrition rate was low as only 4
people left the program before the end. The questionnaire data following the
program suggested that the participants had benefited in many ways from this
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experience. For instance they reported that they learned that there are many ways
to approach a problem and the multiple strategies offered by their co-learners were
both novel and energizing for them. When asked what interfered with their
learning during the week, what they reported most often was that their previous
attitudes and views about mathematics created barriers. The pre-practicum
questionnaire is due to go out in November, 2004 and the findings from this and
the remaining two questionnaires will give us some insight as to how this gets
played out in the context of their elementary classroom placements.
The mathematics instructors. Our findings at this point suggest several things.
Although recently graduated secondary mathematics teachers may feel aligned
with reform-oriented practice in mathematics education, they are substantially
challenged to implement such practices. In the planning sessions preceding the
summer program, the instructors often saw mathematical activity from a very
traditional perspective. For instance, although they were engaged in planning
inquiry-based learning activities, they were concerned with having solution sheets
with multiple right answers to these open-ended problems. As the week
progressed, the video data from the debriefing sessions revealed that instructors
were surprised at the richness of the mathematical knowledge that was generated
by the participants in their groups. Their own confidence in this approach increased
over the five days of the teaching experience, but there was always a tension
between what they were experiencing and what their deeply entrenched notions of
real teaching was. With each day's experience the confidence in understanding
teaching/learning differently was apparent.
The question for us is how can this understanding be further supported so that it
really becomes their own entrenched pedagogical disposition. One possible
unintended outcome of the initiative is now these instructors are contributing to the
professional development of other mathematics educators as they have been
invited to describe their experiences as instructors in the summer math program.
The data from the secondary mathematics instructors who had already bought into
reform oriented approaches as learners, showed us that learning and experiencing
mathematics this way is simply not enough to transform practice. Even in the
context of this summer math initiative, we felt the tensions they experienced. At
this point we are looking forward to the focus group meetings to see how the sense
of community, and collaborative partnerships they have with each other interacts
with the daily norms of their respective teaching positions.
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