In their recent article on teachers' proportional reasoning, Copur-Gencturk et al. (2022) draw attention to a type of strategy that they call "relative", lodged right between additive and multiplicative thinking. This strategy raised interest in our research team, as it aligned well and helped give stronger meaning to some strategies…

The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students' structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers' structural reasoning for the purposes…

Covariational reasoning (or the coordination of two dynamically changing quantities) is central to secondary STEM subjects, but research has yet to fully explore its applicability to elementary and middle-grade levels within various STEM fields. To address this need, we selected a globally referenced STEM assessment--the Trends in International…

This article analyzes how three mathematics preservice teachers (PSTs) reasoned quantitatively and covariationally while making sense of the Earth's energy budget (EB)--a model of energy circulation within the Earth's climate system--and discusses how their quantitative and covariational reasonings influenced their understanding of climate change.…

Many studies have characterized students' difficulties in understanding and reasoning about scientific mechanisms. Some of those studies have drawn implications on teaching mechanisms and how to guide students while reasoning mechanistically. In this theoretical article, I claim that one component that has not garnered much attention in the…

Diagrams and in general the use of visualization and manipulative material play an important role in mathematics teaching and learning processes. Although several authors warn that mathematics objects should be distinguished from their possible material representations, the relations between these objects are still conflictive both from an…

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the…

Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…

Transfer of structural math knowledge to physics is difficult for students. While research suggests various improvement techniques, enhancing parallelism of algebraic structures used in physics to those studied in mathematics courses seems underrepresented. This paper proposes an alternative way of introducing wave functions as a set of parametric…

In Canada, kinesiology academic units are undergoing change. The growth of kinesiology as a health profession is reflected in increased clinical course offerings to train student clinicians. These courses require clinical educators, however, not all programs have clinical staff and faculty with the required knowledge or experience. In particular,…

How anthropomorphic reasoning functions in scientific thinking has been a controversial topic. There is evidence it is problematic as well as evidence it can play productive roles, for scientists and for students. In science education, however, the prevailing view remains that it is an impediment. For this study, we have chosen examples of what we…

Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in…

Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

This article focuses on preservice and in-service teachers' pedagogical reasoning, decision making and action concerning technology integration for learning. We examine this topic in light of three contemporary barriers in policy, practice and research, namely: the lack of an integrative model that considers how teachers come to shape their…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…