For a given rational number r, a classical theorem of Niven asserts that if cos(rp) is rational, then cos(rp) [element-of] {0,±1,±1/2}. In this note, we extend Niven's theorem to quadratic irrationalities and present an elementary proof of that.

A premise of this article is that the current methods used in mathematics education research may be preventing researchers from adequately addressing the body and, in particular, the alignment of acting and knowing. Pursuing a non-dualistic and non-hierarchical approach to learning and knowing, I experiment with new methods that aim to increase…

In this paper we deal with a geometric machine that has gone somewhat unnoticed in mathematics education: the Perfect Compass. It allows conics to be drawn using a special two aperture compass, based on Apollonius' conic sections. Proposed in the 10th century, it seems that it was never built in medieval times--at least no archaeological remains…

Throughout the years of the history of the development of mathematics, starting with the ancient mathematicians, new things were discovered from time to time, which made it a central component of the computerized world, which serves us in many fields, with the young "swimming" in it, and the adults asking: how could we live without it!…

A single discrete random variable is depicted by a stick diagram, a 2D picture. Naturally, to visualize a bivariate discrete distribution, one can use a bivariate stick diagram, a 3D picture. Unfortunately, many students have difficulty understanding and processing 3D pictures. Therefore, we construct an alternative 2D disc plot to depict the…

Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, the authors share a process for revising them using Universal Design for Learning (UDL). Outlined in detail here are problems for kindergarten, grades 5 and 7, and high school (algebra).

This article presents a didactic situation focused on geometric reasoning using 3D GeoGebra, using the concepts Theory of Didactical Situations (TDS). The objective of this work is to bring a didactic proposal for the teaching of Spatial Geometry, working with the students' geometric perception, oriented and elaborated based on the dialectic of…

National mathematics achievement results show that elementary students in the United States are not increasing in cognitive ability or critical thinking skills (NAEP, 2020). For this increase, mathematically promising students require more opportunities for cognitively demanding mathematics instruction. As a result, this descriptive study focused…

Examples are an essential part of mathematics teaching and learning, used on a daily basis to teach and practice content. Yet, selecting good examples for teaching is complex and challenging. This article presents ideas to consider when selecting examples, drawn from a research study with algebra 2 teachers.

The aim of this study is to examine the problem-solving processes and problem-posing skills of pre-service mathematics teachers, which consists of four stages (understanding the problem, preparing a plan for the solution, applying the plan, evaluating) defined by Polya (1997) with the progressive scoring scale based on the alternative assessment…

The teaching guides that complement textbooks have key importance in the assessment of competence in problem solving, because these materials contain the assessment tools that teachers frequently use to quantify the achievements of their students. In this paper, we set two aims: to analyze which curriculum contents are given priority in the…

This research study explored the experiences of this teacher-researcher and eight student-participants in a Montessori-inspired, nature-based mathematical environment. I utilized an action research study framework with a critical event narrative analysis to describe mine and my student-participants' experiences throughout this study, using…

Almost 70% of college students in California are required to take at least one remedial education course in mathematics or English, and of those students, only 40% continue to succeed in their educational goals of transfer or receiving a degree ("Student Success Scorecard," n.d.). Corequisite support remediation is an alternative to…

African American learners deserve liberating learning experiences, yet rarely receive them. We argue that the framework of Afrofuturism is a productive strategy for reconceptualizing the work of mathematics teaching as liberating and empowering for African American learners and the Rights of the Learner Framework offers useful tools to enable…

Probability literacy has gained importance in educational curricula. The aim of this research was to analyse secondary education teachers' attitudes towards probability and its teaching and to examine differences across the factors of gender, academic training, and work experience. From a positivist paradigm, a quantitative methodology was used.…