Study Suggests Early Childhood Teacher Candidates Need More Support to Create Mathematical Modeling Problems
Have you seen the JTE Insider blog managed by the Journal of Teacher Education (JTE) editorial team? Check out the following interview with the authors of a recent article. This blog is available to the public, and AACTE members have free access to the articles themselves in the full JTE archives online – justlog in with your AACTE profile here.
This interview features insights from the article “An Examination of Preservice Teachers’ Capacity to Create Mathematical Modeling Problems for Children,” by Catherine Paolucci of the State University of New York at New Paltz and Helena Wessels of Stellenbosch University (South Africa). The article, which appears in the May/June issue of JTE, is summarized in the following abstract:
This study examined preservice teachers’ (PSTs) capacity to create mathematical modeling problems (MMPs) for grades 1 to 3. PSTs created MMPs for their choice of grade level and aligned the mathematical content of their MMPs with the relevant mathematics curriculum. PSTs were given criteria adapted from Galbraith’s MMP design principles to guide their work. These criteria were then used to evaluate the resulting MMPs, leading to findings and implications relevant to two areas – mathematics teacher education, and the design and evaluation of MMPs for young children. Results highlight an inclination toward creating problems for higher grade levels as well as concerns regarding both the PSTs’ proficiency with the curriculum content and their capacity to create MMPs for particular content areas. Findings contribute to an important international conversation about the need for further research and development of resources aimed at supporting the integration of mathematical modeling in early childhood mathematics education.
Q: What motivated you to pursue this particular research topic?
A: 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 preservice teachers who were preparing to teach Foundation Phase (up to grade 3). They were in a 4-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 have implications for not only 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.
Q: What were some difficulties you encountered with the research?
A: One of the first difficulties that we immediately encountered with our research was with the task that we gave to the participating preservice 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.
Q: 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?
A: 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 preservice 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.
Q: What current areas of research are you pursuing?
A: 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 preservice 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 under way.
Q: What advice would you give to new scholars in teacher education?
A: 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 preservice 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.