In this study, we investigated prospective secondary mathematics teachers' development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written…

The worked example effect has been well documented within the framework of Cognitive Load Theory (CLT), which suggests that teaching with examples would be superior to engaging in unguided problem solving, particularly for novices, as using worked examples would reduce their cognitive load, compared to solving problems, thus facilitating knowledge…

Matters of identity are personally and socially constructed and do not always align with teacher perceptions. When this occurs, it can cause internal tensions in ways students navigate their sense of being in schooling and in society as a whole. These tensions can also impact students' mathematical identity and their motivations within mathematics…

Situations where students encounter mathematical "impasses" -- instances where their current discourse is incommensurable with the discourse demanded to solve a task -- have the potential to stir emotional responses of different types. They can engender feelings of confusion and bafflement, or even embarrassment, or alternatively open…

Using narrative inquiry, I share the beginning stories of the instructional visions of secondary mathematics teachers throughout their undergraduate studies of pedagogy and content-specific methods and evidenced in undergraduate coursework and student teaching experience. Guided by Munter's (2014) Visions of High-Quality Mathematics Instruction…

How teachers can experience adaptive professional development (PD) experiences is still understudied in the literature on teacher learning, which for the most part reflects an emphasis on learning outcomes rather than the process of learning. In this study, we use a situated perspective on teacher learning to investigate the coevolution of a…

This paper introduces two theoretical constructs, open-loop covariation and closed-loop covariation, that combine covariational reasoning and causality to characterize the way that three preservice mathematics teachers conceptualize a feedback loop relationship in a mathematical task related to climate change. The study's results suggest that the…

This commentary was written by ChatGPT, an artificial intelligence language model developed by OpenAI. It was conceived by the first author as a test for how the advent of predictive language modeling will create opportunities and challenges for researchers and teachers in mathematics education. The paper consists of a commentary that was written…

In this article, the authors share the instructional moves that a fifth-grade teacher, made to simultaneously develop the mathematical reasoning of multilingual learners and the mathematics register required to write a multiplication story. The teacher incorporated tasks in her lessons that fostered students' mathematical reasoning consistent with…

One perceived advantage of computer-based testing is that accessibility tools can be embedded within the testing format, allowing students with disabilities to use them when necessary to remove unique barriers within testing. However, an important assumption is that students activate and use the tools when needed. Initial data from large-scale…

In numerous studies, intelligent tutoring systems (ITSs) have proven effective in helping students learn mathematics. Prior work posits that their effectiveness derives from efficiently providing eventually-correct practice opportunities. Yet, there is little empirical evidence on how learning processes with ITSs compare to other forms of…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

This paper presents results from research that investigated the participation and attrition rate of male and female candidates in two post-secondary mathematics courses (Pure Mathematics and Applied Mathematics). The data for this study consisted of the course results over five years from 2013-2017 for 15,220 candidates (N = 19,585) from 71…

This action research study examines the use of professional development to build the self-efficacy of secondary math teachers in culturally responsive mathematics teaching (CRMT), with the hope to address achievement gaps of Black and Hispanic students. Seven math teachers from a school division in Southwest Virginia participated in a 9-week…

Students determined to be underprepared for college-level mathematics would be enrolled in a sequence of developmental mathematics courses before taking their college-level mathematics course. Students who started in the lowest level of developmental mathematics had a twenty percent chance of completing their college-level mathematics credits…