The Models and Modeling Working Group at PME-NA has provided a forum for discussing and collaborating on projects fundamental to research on mathematical modeling since the first PME-NA conference in 1978. We propose to convene this Working Group at PME-NA 41 with a dual purpose: (1) to build on a theme begun in Greenville, holding a focused…

Previous studies revealed that many students cannot perform well when it comes to word problem-solving questions. There are various problem-solving strategies that can be applied to help students to overcome the problem. Visualisation techniques in learning have been used to help students enhance their conceptual understanding of the mathematical…

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs,…

For students working on realistic complex modelling problems as autonomously as possible the support by a tutor is indispensable for the students. However, how this support can be realised is still a question that has not been sufficiently answered. Based on prior research, it turned out that teacher interventions based on heuristic strategies…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…

This study examined the criteria used by prospective mathematics teachers in determining whether a problem was a mathematical modeling problem. Two data collection tools were used in this case study. The first was a written evaluation form which consists of four problems developed by 27 prospective teachers individually that enrolled in a…

A mathematics framework was developed to integrate problem-solving that incorporated simulation of real-life problems in the classrooms. The framework coined as the "RECCE-MODEL" emphasised understanding and thinking with a view on mathematics embedded in real-life. The "RECCE" which stands for Realistic, Educational,…

The purpose of this study is to reveal factors considered by mathematics student teachers while posing modelling problems. The participants were twenty-seven mathematics student teachers and posed their modelling problems within their groups. The data were obtained from the modelling problems posed by the participants, their solutions on these…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

Attention to mathematical modeling has grown, but most practicing and future teachers have limited experience with mathematical modeling and how to integrate it into their practice. However, documents such as the Common Core and GAIME Report emphasize the importance of mathematical modeling in mathematics education. Engaging students in…

The purpose of this systematic review is to reveal the research findings that suggest instructional practices to foster the creativity of students in mathematics. Although several studies have investigated the effects of various instructional practices influencing the mathematical creativity of students, little is known about how the findings of…

This study investigated pre-service secondary mathematics teachers' (PSMTs') anticipation and identification of students' thinking as they engaged in examining and analyzing student work on four modelling problems. The study comprised four two-week-long cycles. The data were collected through individual reflection papers and written group reports…

The International Mathematical Modeling Challenge takes place towards the end of Term 1 each year in Australia. Students use their research, mathematical and creative abilities to develop a mathematical model to address a real world problem. Ross Turner describes some aspects of the competition.

Integrating the disciplines of mathematics and science is one way to place the calculations of volume and surface area into a real life context. The authors present an activity for middle-school students that aims to promote their learning of these key concepts in a personally meaningful way, whilst also developing inquiry and problem solving…

In order to support physics students in their future careers, there is a need to understand the relationship between undergraduate education and professional practice in physics-related fields. This study investigated high-level goal driven mathematical problem-solving activities that are found within two disciplinary cultures: physical science…