A robust finding in cognitive psychology is that training children's spatial abilities is an effective route to improving mathematics performance. Despite this finding, there is limited representation of spatial reasoning in school curricula. To bridge this gap between research and practice, we created the Spatial Reasoning Toolkit (SRT; Gifford…

The mathematics of budgeting and space can lead to a justice-oriented experience for elementary students as they design a proposal for an inclusive playground. The authors' work focused on creating the space for elementary children to see the interconnectedness between mathematics and a community social injustice, lack of inclusive playground…

The aim of the study is to examine how lesson study activities affect primary school preservice teachers' noticing of students' misconceptions. A qualitative research approach was adopted and action research method was used. The study was conducted with 9 primary school preservice teachers. The data were obtained from the observation form, video…

This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

Creativity and problem solving are considered to be twenty-first-century competencies, therefore promoting mathematical creativity should be an important part of school mathematics. The study presented in this paper is inspired by the notion of mathematical creativity and the utilization of multiple solution tasks (MSTs) to investigate students'…

Previous literature has indicated a lack of information available regarding virtual schooling and how it compares to traditional schooling in terms of the academic achievement of students (Angiello, 2010; Brady, 2012; Dichev, Dicheva, Agre, & Angelova, 2013; Molnar et al., 2019; Molnar, 2021). This study aimed to examine differences among…

A central aspect of reform-minded mathematical teaching is training and developing teachers' ability to notice vital aspects in the classroom and more specifically, students' mathematical thinking. As there is an abundance of evidence and research that support the benefits for teachers to elicit and use students' ideas and thinking during…

Family characteristics such as socioeconomic status (SES) and migration background (MiBa) predict children's early mathematical skills. This study investigated the associations between SES and MiBa and children's mathematical precursor skills, mediated by different facets of the home numeracy environment (HNE) in a German sample (N = 500). In…

Reducing learning time or training time in intelligent tutors is a challenging research problem. In this study, we aim to reduce training time while maintaining student performance in intelligent tutors. We propose a Deep Reinforcement Learning (DRL) based method to determine when students need more training and when they don't. We design an…

Recent developments in Augmented Reality (AR) headset technologies have allowed for users to see and manipulate the same 3D hologram at the same time, allowing for collaborative, embodied interactions using gestures and actions. Three-dimensional geometry has traditionally been taught largely through 2D projections of 3D figures on pages or…

In Advanced Calculus, our students wonder if it is possible to graphically represent a tornado by means of a three-dimensional curve. In this paper, we show it is possible by providing the parametric equations of such tornado-shaped curves.

A negative correlation between math anxiety and mathematics performance is frequently reported. Thus, some may assume that high levels of mathematics anxiety are associated with poor mathematical understanding. However, no previous research has clearly measured the association between mathematics anxiety and mathematical learning disability. To…

This longitudinal study examined the influence of prekindergarten teacher characteristics and classroom instructional processes during mathematical activities on the growth of mathematics learning scores in prekindergarten, kindergarten, and first grade. Participants attended state-funded and Head Start prekindergarten programs. Mathematical…

Originally written 30 years ago, this paper is an analysis of the central challenge of schooling--that of engaging fully the powers of students' minds in classroom learning. This challenge maintains its relevance today. The work of engaging what John Dewey referred to as students' "inner attention" becomes the focus of an investigation…

Introduction: Differences in learning mathematics between boys and girls are being controversial according to different studies. However, those divergences are not always supported by empirical studies. One of the specific sources of difficulties on this topic is the fluency calculation learning, where performance differences between boys and…