This interview features insights from the JTE article, An Examination of Preservice Teachers’ Capacity to Create Mathematical Modeling Problems for Children, by Catherine Paolucci and Helena Wessels. The article was published in the May/June issue of the Journal of Teacher Education. You can read the full text by visiting this link.
Q1. What motivated you to pursue this particular research topic?
While many teacher education programs are structured to provide a strong foundation in mathematics content, this doesn’t necessarily translate into proficiency and confidence with important teaching tasks such as posing mathematics problems. As researchers, we had seen this to be a particular challenge with mathematical modeling, which involves more open, complex and cyclical problem solving. We were also conscious of the fact that research and resources exploring and supporting mathematical modeling with young children are more limited than those focused on upper elementary, secondary, and higher education.
We had the opportunity to work with pre-service teachers who were preparing to teach Foundation Phase (up to grade 3). They were in a four-year program with a strong focus on mathematical modeling. That meant that they had gained experience with completing, analyzing and evaluating mathematical modeling problems. We felt that this would be an excellent population with which to examine whether extensive work with mathematical modeling translated into confidence and competence with posing their own mathematical modeling problems using specific criteria as a guide. We felt that this would not only have implications for their ability to pose such problems, but also their ability to choose or adapt effective problems based on criteria offered by researchers in the field.
Given that these teachers were at the very end of their program and about enter the classroom as qualified teachers, we wanted to examine how well prepared they were to pose effective modeling tasks for their students. But beyond this, we were also generally curious about the suitability of modeling criteria and frameworks, that currently appear in the literature, for evaluating modeling problems for young children. Pretty much everything that we had seen and could find was designed for higher grade levels and more advanced mathematics. We wondered whether any of these would actually be suitable for evaluating the types of modeling tasks that were age and developmentally appropriate for children in the earliest years of their mathematics education.
Q2. What were some difficulties you encountered with the research?
One of the first difficulties that we immediately encountered with our research was with the task that we gave to the participating pre-service teachers. It initially asked them to pose a mathematical modeling problem that could be used to help their students explore and apply learning in the curriculum area of patterns and early algebra. After several questions, and listening in on their conversations, we realized that they were very uncomfortable with creating a modeling problem for this area of the curriculum.
Because we were limited in our time with them, we decided to open it up to all areas of the curriculum, with the stipulation that they had to identify the areas of the curriculum that were involved in their problem. While this was a difficulty, it also became our first finding. It was later reinforced when we were able to see how many participants stuck with patterns and early algebra and how many of them abandoned it for other areas of the curriculum. It also introduced an unexpected component to our research, from which other interesting findings emerged relating to familiarity with the mathematics in the curriculum and the content areas within which they felt most comfortable integrating mathematical modeling.
Q3. Writing, by necessity, requires leaving certain things on the cutting room floor. What didn’t make it into the article that you want to talk about?
Because we ended up with several unexpected findings, we ultimately abandoned one of our original research aims. Initially, when designing our study, we wanted the study to have a more substantial focus on what we could learn about pre-service teachers’ mathematical knowledge for teaching, as presented in Ball, Thames, and Phelps (2008), by examining their choices in creating their modeling problems. We felt that this could help to inform continued development of coursework and programmatic experiences focused both specifically on mathematical modeling, and more comprehensively on development of mathematical knowledge for teaching. Understanding the strengths and gaps in prospective teachers’ knowledge and their understanding of how to teach it, can inform the scaffolding of their problem posing ability.
Q4. What current areas of research are you pursuing?
Findings from our research presented in this article have inspired us to conduct follow-up research aimed at scaffolding the process of problem posing. This research has engaged final-year preservice teachers in converting traditional textbook word problems into mathematical modeling problems. In addition, the pre-service teachers in this study have also had the opportunity to evaluate each other’s work. We felt like this was a significant next step that we wish we could have done with the students in our problem posing study featured in the article. On one hand, the fact that the participants were at the very end of their program was valuable for highlighting gaps in their preparation for teaching. On the other hand, it really highlighted for us the need to look further into what we can do about these gaps. We would have loved to be able to follow up with those students and have them look at each other’s problems, offer feedback, and then look back at their own problems to evaluate their own work. Analysis of data collected through this follow-up project is currently underway.
Q5. What advice would you give to new scholars in teacher education?
One of the most important outcomes from our research is the clear need for further research in this area – both the posing of mathematical modeling problems, and the integration of mathematical modeling into children’s earliest experiences with mathematics. We would encourage new scholars to explore practical research with concrete implications that can strengthen both pre-service and practicing teachers’ ability to pose mathematical modeling problems and other types of complex problems across subject areas. We would also encourage them to explore this at all levels of education and consider differences in how we need to develop and use criteria or frameworks across these levels. Complex, open-ended tasks, such as modeling problems or other interdisciplinary problems, allow students of all ages to develop and celebrate their creativity as they explore ways to integrate their learning and address real and relevant issues.
Ball, D., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 387-407.
If you would like to connect with the corresponding author, she can be reached at the information below:
Catherine Paolucci, State University of New York at New Paltz, New Paltz, NY 12561, USA. Email: firstname.lastname@example.org
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