This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

A key challenge in implementing inquiry-based learning in mathematics has been raising teachers' confidence and skills with unfamiliar pedagogical practices. The nature of inquiry in particular challenges traditional notions of teaching mathematics that dominate the field. Few studies have explored how teachers' perceptions of the nature of…

Mastery of mathematical literacy is essential for developing life skills in the 21st century. Mathematical literacy is even more critical in elementary schools as it forms the basis for mastery at the junior and senior high school levels. Elementary school students differ in their characteristics from students at the higher education level. They,…

Nutrition facts are the details on food packaging that describe its nutritional value, including serving size, calories, macronutrients like carbohydrates, protein, and fat, and micronutrients such as vitamins and minerals. These facts have mathematical concepts that can be utilized as a context for prospective teachers to create mathematical…

Can You Build It? is an engaging Improve It! task that asks children to construct 3D shapes based on 2D depictions. Students' initial 3D creations often need revision, and as they build and re-build, they develop spatial relationships. This task was implemented in a first-grade class, connected to composing 3D geometric shapes to address the…

Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

Although kindergarteners often are excited to share their mathematical ideas, they may not be sure how to explain the underlying reasoning that brought them to their answers. Teachers seeking to use literacy skills in mathematics to support kindergarteners' reasoning can use writing to provide each student an avenue to communicate their individual…

Incremental rehearsal (IR) has consistently been shown to improve students' math fact retention and fluency (Maki et al., Journal of Behavioral Education 30:534-558, 2021). However, less is known about how intervention modifications may support longer-term skill maintenance. The purpose of this study was to compare traditional IR with a modified…

Preschool students' mastery of early numeracy skills is important, so they enter kindergarten with the necessary prerequisite skills, which are predictive of achievement in later elementary grades. The purpose of this study was to examine the effects of a concrete-representational-abstract (CRA) instructional package on the foundational early…

Nearly half of all students in the United States are placed into at least one developmental course in college. Many of these students fail to complete developmental course sequences and persist to degree completion. First-Year Seminars are one of several high-impact practices associated with increased persistence, retention, and graduation rates…

Young children often explore partitioning as the idea of fair sharing in contexts where equal parts are created and distributed based on spatial constructs of the objects, rather than enumerating parts or collections. However, the presence of spatial reasoning in children's early fraction experiences is implicit within much of the literature and…

This sequential explanatory mixed methods study explores elementary mathematics teachers' perceptions regarding their mathematical self-efficacy, how teachers describe their perceptions about their prior mathematical learning experiences and their impact on their instructional practice in the elementary mathematics classroom. In support of this…

Rising numbers of English learners (ELs) being placed in general education high school mathematics classrooms with underprepared teachers is an increasing concern in U.S. public schools. Despite its importance, there has been little research on how to best support high school mathematics teachers in their attempt to teach both the highly…

Research on mathematics learner identity often relies on interview data and presents case studies of individuals. This method allows an in-depth understanding of the person and their relationship with mathematics, but fails to generate a larger picture of identity with more breadth. In this paper we propose a method that blurs the boundaries of…

This study investigates the effectiveness of a Low-Cost Single-Channel BCI system in improving mathematical learning outcomes, self-efficacy, and alpha power in university students. Eighty participants were randomly assigned to either a BCI group receiving real-time neurofeedback based on alpha rhythms or a sham feedback group. Results showed that…