The purpose of this study is to gain understanding of how secondary teachers conceptualize the relationships between mathematical modeling and problem solving. Eight secondary teachers participated in semi-structured, think-aloud individual interviews. Some conceptualizations include (a) modeling and problem solving are two distinct processes; (b)…

The aim of this study is to determine the effect of teaching based on mathematical modeling on the students' academic achievement in mathematics and science education through meta-analysis. In this study, experimental studies carried out in the national and international literature were included in the meta-analysis. As a result of the literature…

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…

The COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach the principles of mathematical modeling in epidemiology. Compartmental epidemiological models, such as the SIR (susceptible-infected-recovered), are widely used by…

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…

Although the secondary-tertiary transition has been investigated in mathematics education research with different focuses and theoretical approaches, it remains a major issue for students in the transition. With success in a science, technology, engineering, or mathematics (STEM) major at stake, we investigated a novel approach to support the…

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…

The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

A sense of belonging in mathematics--feeling accepted and valued in the field (Good et al., 2012)--is a powerful predictor of student success. However, many students, particularly those from marginalized backgrounds, often lack this feeling as a result of limited representation in curricula and school cultures (Barbieri & Miller-Cotto, 2021).…

When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for…

Using mathematical modelling to solve problems appears in all year levels in the Australian Curriculum: Mathematics (v. 9), and is probably the most authentic way of teaching mathematics in context. However, the term mathematical modelling, even if familiar to teachers, may not be well understood or enacted confidently by teachers in their…

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.…

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…

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…