In the last two decades, studying the possible relations between the history of mathematics and mathematics education has revealed the importance of certain foundational issues concerning the nature, relevance and validity of historical knowledge vis-à-vis problems of teaching and learning, which call for deeper exploration. Reviewing aspects of…

For quite some time, research on the use of the History of Mathematics in the classroom has confirmed a lot of academic benefits for students. However, the History of Mathematics can also be used as an inclusion tool in classrooms where there are foreign students because it allows working with the specific contexts of other cultures. This article…

Recent scholarship around teaching elementary mathematics supports the learning of early algebra with 5- to 12-year olds. However, in spite of the recognition of the affordances of early algebra, issues about how to introduce it remain open. Within this context, Davydov's work is often cited as a source of impressive demonstration of young…

While classical studies have highlighted the many potential benefits of using original historical sources in the classroom, few studies have documented actual classroom practices outside of research contexts. In this case study, I aim to describe and explain how five French high school teachers autonomously designed and implemented classroom…

This scholarly inquiry critically examines the pedagogical aspects pertaining to the instruction and acquisition of Abstract Algebra within the realm of University Mathematics Education (UME). Drawing upon multiple lenses, including epistemological, cognitive, phenomenological, and institutional perspectives, this study investigates the formidable…

George Spencer-Brown's Laws of Forms was first published in 1969. In the fifty years since its publication, it has influenced mathematicians, scientists, philosophers, and sociologists. Its influence on mathematics education has been negligible. In this paper, I present a brief introduction to the theory and its philosophical underpinnings. And I…

In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the…

This study examined whether there was a significant difference between the End-of-Course Examination scores (EOC) across multiple academic disciplines between students who participated in sports and those who did not participate in athletics at all in three rural high schools in South Carolina. The theoretical foundation for this study was based…

In this article, we describe a collaboratively developed information literacy curriculum that was embedded into three core 8th grade subjects: Algebra, American History, and English Language Arts. The curriculum was rooted in the concept of generalist literacy and supported students as they developed their curiosity, skepticism, commitment to…

This quantitative study explored the relationship between community sociodemographic factors and student outcomes on the 2019 Texas high school mandated end-of-course (EOC) exams for Algebra I, Biology, English I, English II, and U.S. History in Texas midsized high schools. Correlational analysis was run on community sociodemographic factors on…

This paper proposes an experimental path aimed at guiding upper secondary school students to overcome that discontinuity, often perceived by them, between learning geometry and learning algebra. This path contributes to making students aware of how the algebraic language, formalized in the most powerful form by Descartes, grafts itself onto the…

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

This paper constructs an overview of the historical development of the International Journal for Technology in Mathematics Education (IJTME) during the period 2004- 2018. The titles of the published papers in this period are examined, focusing on what technological tools were studied, and what theoretical ideas were used to study the teaching and…

In this paper, we identify, from historical vantage points, the following six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalised arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of…

Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…