Academic journal article Journal of Teacher Education

An Examination of Preservice Teachers' Capacity to Create Mathematical Modeling Problems for Children

Academic journal article Journal of Teacher Education

An Examination of Preservice Teachers' Capacity to Create Mathematical Modeling Problems for Children

Article excerpt

Introduction

Problem solving has long been considered an essential element of mathematical activity and has featured in educational research and reform efforts throughout the world. Amid discussions of the need to promote problem solving in mathematics classrooms, far less focus has been placed on measuring or developing teachers' ability to pose problems that effectively foster students' engagement in problem solving (Cai, Hwang, Jiang, & Silber, 2015; Crespo, 2003). The mathematical tasks that teachers choose to use in their classrooms strongly influence the quality of student learning and perceptions regarding the nature of mathematics (Crespo, 2015; Henningsen & Stein, 1997; National Council of Teachers of Mathematics, 1991). Therefore, teachers need to be able to both select and create effective problems which promote learning in line with the objectives of their curriculum.

A recent increase in research focusing on problem posing has endorsed it as a valuable process for the growth and development of mathematics teachers at all levels (Cai et al., 2015; Grundmeier, 2015; Osana & Pelczer, 2015). In research evaluating the potential for problem posing to support development of primary school teachers' pedagogical content knowledge, Ticha and Hospesova (2010) endorse problem posing as a means to both diagnose and develop future teachers' mathematics-specific didactical competences. They also note that, as a diagnostic tool, problems posed by preservice teachers (PSTs) can offer an opportunity to investigate their understanding of mathematics, including any misconceptions. Teacher educators can gain important insight into PSTs' mathematical knowledge by examining their choices regarding the mathematical content included in their problems.

Pedagogically, problem posing is regarded as integral to teaching and is considered a "high-leverage practice" (Ball & Forzani, 2009). While a high-leverage practice is characterized as a fundamental practice that is essential for helping students to learn, it is typically not a practice that PSTs are likely to learn on their own (Ball & Forzani, 2009). Many teachers are not active problem posers, nor do they have the required skills to pose appropriate problems (Singer & Voica, 2013). Therefore, researchers agree that it is vital for PSTs to be exposed to and supported through problem-posing experiences during their initial training (Ellerton, 2015; Grundmeier, 2015; Hospesova & Ticha. 2015; Lavy & Shriki, 2007; Osana & Pelczer, 2015; Rosli et al., 2015). While the current literature lacks consensus on what a focus on problem posing should look like in teacher education, some studies have offered valuable recommendations. For instance, the research of Crespo (2003) suggests introducing and exploring nontraditional mathematical problems in teacher education classes and encourages collaborative problem posing.

One particular realm of problem posing which offers rich opportunities for analytical thinking, creativity, and problem solving is mathematical modeling. Mathematical modeling is the process of mathematizing a real-world situation and employing multiple cycles of problem solving to make sense of the problem and identify a solution (Lesh & Doerr, 2003). Mathematical modeling problems (MMPs) are open-ended, real-world tasks that require the use of mathematical modeling to reach a solution. When facing an MMP, students typically move through the phases of a modeling cycle which begin with the real-life problem and include identifying relevant mathematics, organizing, and representing the problem mathematically, solving the problem and interpreting the solution (Organisation for Economic Co-Operation and Development [OECD], 2003).

Traditionally, MMPs were only used at secondary and tertiary levels, but recent research has shown that young children can and should engage in the solving of such rich, open-ended tasks in real-world settings (English, 2006; English & Watters, 2004; Fox, 2006; Mousoulides & English, 2011; Usiskin, 2007). …

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