Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

In this article, the author describes an occurrence of the golden ratio in the context of regular hexagons. The method described can be used to construct the golden ratio. This is one of many ways one can construct the golden ratio.

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students' awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design…

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…