The learning of calculus concepts is considered challenging for students. This claim is actual for calculus in general and for specific concepts in particular. In this paper, we focus on the concept of the inflection point. We argue that one of the roots of this problem is the lack of a useful and productive meaning of the concept--the…

Calculus is traditionally tested, at least in part, by a closed book written examination taken under secure conditions. In March 2020, two-thirds of the way through a vector calculus course, our institution went into lockdown and all teaching and assessment had to shift online. While some teachers insisted that remotely written non-proctored…

In this study we aimed to capture the characteristics of Chinese high-quality lessons from a lesson structure perspective, specifically addressing the elements of teaching activity and their sequence. Sixteen videotaped middle school mathematics lessons were selected from 224 daily lessons collected from urban districts in five cities located in…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…

This article presents a philosophical and pragmatic critique of critical mathematics (CM) and current vocational mathematics (VM) in the United States. I argue that, despite differences, CM and VM advocates share the view that the inauthentic contextualization of secondary mathematics does particular harm to students from historically marginalized…

Many previous studies have highlighted the influence of learners' affective states on learning with tutoring systems. However, the associations between learning and learners' meta-affective capability are still unclear. The goal of this paper is to analyse meta-affective capability and its influence on learning outcomes as well as the dynamics of…

Digital learning games are designed to foster both student learning and enjoyment. Given this goal, an interesting research topic is whether game mechanics that promote learning and those that promote enjoyment have different effects on students' experience and learning performance. We explored these questions in "Decimal Point," a…

Teachers are responsible for teaching, and when they plan, they are part of a complex non-linear social practice of curriculum making. When planning, teachers draw on curriculum materials, which are often designed to promote reform; however, previous studies show that this is not always the case. A study on planning for mathematics teaching in…

Using videos to supplement live instruction has gained momentum in the past year because teachers often scrambled to find ways to instruct students from different locations. The author, like many of her colleagues, began recording herself teaching short lessons and adding them to her Google Classroom library. But then she realized that despite her…

In mathematics, the keyword strategy involves identifying a keyword and using that keyword to determine the operation needed to find a word problem's solution. We analyzed 747 high-stakes released items across grades 3, 4, 5, 6, 7, and 8. Of these, 57 items did not involve written text. Of the 690 text-based items, we classified 69% as directive…

The COVID-19 pandemic has made mathematical epidemiology a topic of critical importance, providing mathematics educators with an unparalleled opportunity. This opportunity is accompanied by a challenge: how do mathematics educators, some of whom have little personal experience with mathematical modeling, teach mathematical epidemiology to their…

Cornell University has long offered a Calculus for Life Sciences course. In this case study, we report on how a team of pure mathematicians has modernized both the content and teaching methods of this course. The content went from a standard calculus course with few genuine applications in the life sciences to a course focusing on dynamical…

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

This text serves to assist teachers in promoting student ownership of mathematics by synthesizing relevant research into practical classroom strategies across three tiers of student interaction and experience: classwide, peer-to-peer, and individual. Research from across these tiers of student experience is reviewed and synthesized including…

Despite the significance of incorporating technology into geometry instruction, many teachers still find it difficult to teach geometry using technology. This study employed a techno- pedagogical content knowledge (TPACK) survey of 70 pre-service mathematics teachers (29 males, 41 females) from a public university. The goal was to determine which…