In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

The revised Australian curriculum presents a new emphasis in primary schools on the process of Mathematical Modelling. A modelling focus brings close attention to confidence and capability with a potentially new problem-solving process, associated language, and pedagogical processes. This paper presents a Year 4 classroom modelling experience that…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

Although culturally responsive mathematics teaching is important, post-secondary education for preservice teachers (PTs) does not typically lead to learning opportunities for them to use mathematics to recognize the roles of social agents. To address this issue, we created a culturally responsive mathematical modeling task in which we invited PTs…

Across the world, standards and practices for preparing teachers of mathematics emphasize the importance of math modeling (MM) in developing students' mathematical thinking. The aim of this research study was to develop the Mathematical Modeling Knowledge Scale (MAMKS), capable of determining preservice teachers' (PSTs') knowledge of MM. The study…

Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits. These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. In these approaches, a differential equation like dy…

Mathematical modelling emphasizes the connection between mathematics and reality -- still, tasks are often exclusively introduced inside the classroom. The paper examines the potential of different task settings for mathematical modelling with real objects: outdoors at the real object itself, with photographs and with a 3D model representation. It…

This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

In this paper, we share a mentorship model we developed and implemented while collaborating with pre-service teachers (PSTs) on their Model Eliciting Activity projects and the outcomes of the mentorship model in terms of PSTs' growth as teachers as well as researchers. For their projects, PSTs designed and developed their own mathematical modeling…

This Perspectives on Practice manuscript focuses on an innovation associated with "Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task" from Volume 7, Issue 2 of "MTE". The Flint Water Task has shown great promise in achieving the dual goals of exploring mathematical…

In a small rural school district in the southeast, two high schools have both seen a decline in their enrollment, so the two high schools are merging into one facility until a new school is built. Naturally students have concerns about the proposed organization, with students at one school already having concerns about the current lunch schedule,…

To successfully solve the complex challenges facing us in the 21st century, people with expertise in the science, technology, engineering, arts and mathematics (STEAM) fields and other fields are needed, especially for their interdisciplinary way of thinking and working. These competencies should be learned in school, which first implies teacher…

This research contributes to the need to identify and expand learning environments that encourage undergraduate students to develop collaborative work skills and apply their classroom knowledge to solve real-world problems. Using qualitative methods, we examine the effects of the interaction between two teams of students when solving a…

This is the first of four columns by Tim Erikson which introduces us to the Common Online Data Analysis Platform (CODAP). CODAP is a free, web-based software tool that your students can use for many types of tasks. This first column shows how CODAP can be used for mathematical modelling and where it might fit with the "Australian Curriculum:…