Over the years, we have noticed our students constructing proofs that commutativity is preserved by isomorphism that do not explicitly use the fact that the isomorphism is surjective. These proofs are typically valid otherwise. However, such proofs are invalid because they would prove the false claim that commutativity is preserved by any…

According to Every Student Succeeds Act, schools are accountable for the improvement of all children; including those with disabilities or difficulties, recently arrived English language learners (ELs) as well as long-term ELs, and all students for whom English is not their native language. To meet the accountability requirements, it is essential…

The purpose of this study was to determine the relationship between the problems teachers preferred in mathematics lessons and student achievement in different types of problems. In accordance with this purpose, nine mathematics teachers were interviewed, and corresponding problems were prepared and administered to 225 eighth-grade students. The…

Magic captivates humans because of their innate capacity to be intrigued and a desire to resolve their curiosity. In a mathematics classroom, algorithms akin to magic tricks can be an effective tool to engage students in thinking and problem solving. Tricks that rely on the power of mathematics are especially suitable for students to experience an…

This study explores three aspects of a math emporium (ME), a model for offering introductory level college mathematics courses through the use of software and computer laboratories. Previous research shows that math emporia are generally effective in terms of improving final exam scores and passing rates. However, most research on math emporia…

The link between reading and mathematics achievement is well known, and an important question is whether readability factors in mathematics problems are differentially impacting student groups. Using 20 years of data from the National Assessment of Educational Progress and the Trends in International Mathematics and Science Study, we examine how…

Mathematicians commonly distinguish two modes of work in the discipline: "Problem solving," and "theory building." Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to…

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

This guide is designed for practitioners, including teachers, lead instructors, and professional developers, who are ready to take up the challenge to change how numeracy is taught in adult education. If instructors shift their teaching to focus more on the use of numeracy skills, they might find that their students not only score better on formal…

While mathematics education is key to the post-school outcomes of students with disabilities, it has received less attention in research and practice compared with other aspects of educating this population. Skill maintenance is particularly crucial in mathematics because students build upon prior knowledge across grade levels. They also need to…

Mathematics instruction -- and interventions to support mathematics teaching -- for students with intellectual disability is important yet underexamined. This study explored a graduated instructional sequence referred to as the virtual-representational (VR) as a mathematical intervention. Researchers taught four students with disabilities what…

The current study aimed to reveal the changes to the identities of two tenth graders in mathematics learning at a Japanese high school during the COVID-19 pandemic from the perspective of learning from home versus learning in the classroom. The following research questions are raised: How has the pandemic situation affected and changed Japanese…

The plane problem is a real-world problem, presented without any suggestion as to how it might be solved. It arose unexpectedly as the author was messing around on the internet, not thinking about maths at all. She did not encounter the problem in a maths lesson, nor as homework in the middle of a unit on a particular topic, and so she had no…

In this work, we review and share some useful technology for mathematics educators that can help to enhance their pedagogical practices to motivate students to improve their further understanding of differential equations after an initial exposure to the topic in an undergraduate class. In particular, we present some innovative ways to employ…