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Research re-examines mathematics teaching

By Costa Maragos Posted: August 23, 2016 6:00 a.m.

Dr. Kathleen Nolan, associate professor in mathematics education, is regularly asked to present her research findings. Nolan is the author and co-editor of two books and has authored several peer-reviewed journal articles.
Dr. Kathleen Nolan, associate professor in mathematics education, is regularly asked to present her research findings. Nolan is the author and co-editor of two books and has authored several peer-reviewed journal articles. Photo courtesy of K. Nolan.

Dr. Kathleen Nolan wants our future teachers to critically examine the practices of schools and mathematics teaching and learning.

Nolan is associate professor in mathematics education at the University of Regina. She has recently completed a multi-year research program aimed at reconceptualizing secondary mathematics teacher education. The research is funded by a Social Sciences and Humanities Research Council (SSHRC) Insight Grant, valued at $128,000.

In her research, Nolan predominantly worked with prospective teachers and recent graduates of the University of Regina mathematics teacher education program. We spoke with Kathleen about her research.  

The title of your research is reconceptualizing secondary mathematics teacher education. What do you mean by that?

By reconceptualizing I mean rethinking and reforming aspects of teacher education that appear to be locked in tradition rather than in reflective and critical thought.

In my qualitative research program, I seek to strengthen connections between teacher education, curriculum reform and mathematics education research by studying the interplay of different perspectives, or dimensions, of teacher education. One such perspective includes research into the design and facilitation of a professional learning community for teacher education internship (field experience), which includes researching my role as a faculty advisor and intern supervisor as one of its aims.

This learning community approach has realized benefits on a number of levels, including expanding and transforming my faculty advisor role, creating more collaborative partnerships between the university and schools, and actively engaging the interns in a professional development experience that demands critical reflection on the process of becoming a teacher.

Even though my research program’s primary focus is on reconceptualizing teacher education, its effects move well beyond that context. A critical focus on mathematics teacher education means challenging and disrupting the normative and regulatory discourses of mathematics that exist in schools, and in society at large.

For instance, unacknowledged and unquestioned messages about who can succeed at mathematics—who can do it, who can learn it, and what it means to be a ‘good’ mathematics teacher—need to be challenged.

What do you think makes a good mathematics teacher?
 
Unfortunately, the image of a good mathematics teacher is frequently tied to, among other things, an ability to explain things well.

Part of reconceptualizing mathematics teacher education involves creating opportunities for prospective and new teachers to consider teaching through more inquiry and student centred approaches.

Students in school mathematics classrooms need to have a voice in their learning—they need more ownership, control, and choice in the mathematics that happens in the classroom and this in turn means that mathematics teachers must be willing to relinquish some of those very same things in their teaching.

Teacher education, I think, should be viewed as an opportunity to challenge and rethink (and maybe even unlearn) one’s images of teaching and learning, not as the place where new teachers are ‘trained’ in techniques and strategies.

A critical approach to teacher education encourages new teachers to examine the practices in schools and mathematics classrooms that could be serving to maintain normative and exclusionary aspects of schools and mathematics.

Mathematics Books
Kathleen Nolan reports that teacher education should be viewed as an opportunity to challenge and rethink (and maybe even unlearn) one’s images of teaching and learning.

During the course of your study you’ve spent time with interns and novice teachers. What are some of the areas discussed and their responses to your research ideas in practice?

With interns, the focus has been on exploring and practicing what it looks like to teach mathematics through inquiry and student centred approaches.

Because many students in our secondary mathematics teacher education program have been drawn to pursuing a career in teaching as a result of their own successes with more conventional teacher-directed methods, they are not always willing or able to understand that other pedagogies and dispositions are required in order to address diverse learners and their needs.

I think the internship learning community research helps prospective teachers deconstruct some of the more traditional images of teaching and learning mathematics. With novice teachers, my research has been unpacking what they ‘thought’ they would do and become in their first few years in the classroom.

Several novice teacher research participants shared how, because of their own extensive experience learning through direct teaching methods as a student, they were finding it challenging to disrupt and transform their teaching practices into something different, something that provides their students with more ownership, control, and choice in the mathematics that happens in the classroom.

In that same novice teacher study, I interviewed two novice teachers who were making a solid effort to integrate inquiry teaching and learning into their first few years in the classroom, but they were surprised and frustrated by how much resistance they encountered (from students, parents, school administrators, etc.) when they tried to teach mathematics in more innovative ways.
 
That’s the practical side. On the theory side, what did you come up with?

My research draws extensively on Pierre Bourdieu’s social field theory—a theory that helps me to reveal and unpack the normative and regulatory structures in mathematics education—those that can serve to limit/restrict teachers, students, and classroom pedagogy, while reinforcing dominant perspectives.

Beginning with the most basic definitions of Bourdieu’s key ‘thinking tools’ (habitus, field, social practice, doxa, and social capital), and their intersections with theory-practice transitions in mathematics teacher education, I’ve conceptualized a new theory-methodology framework, which I refer to as a Bourdieu-informed critical discourse analysis (BIDA).

The framework is still in its initial stages of application, but I am encouraged by its potential as I work with my research data to explore the discursive network of relations in the (field of) field experience in teacher education and in my role as a faculty supervisor within that field.

What do you hope will come out of this research?

I am pleased with how the internship professional learning community has developed so I hope to continue that aspect of the project.

However, sustaining the community does require funding for resources and substitution days for teachers so I may look into involving school divisions more closely. My research shows that the professional development model of that learning community benefits both interns and cooperating teachers; that is, it is beneficial in both processes of being and becoming mathematics teachers.

That’s the practice-based side of my research program that I look forward to continuing. On the theoretical side, I hope to further develop and apply my theory-methodology framework, drawing in aspects of social network and graph theory for my research design and analysis. So, even though the SSHRC funding for this research program has come to an end, there is still much work to be done.

Dr. Kathleen Nolan is continuing to analyse the data and further publish her research.
For more information on her work please visit here.
In the fall she will be teaching graduate courses in mathematics curriculum.