The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

This study explored the potential connections between secondary in-service (ISTs) and preservice (PSTs) mathematics teachers' anticipations and their noticing of student thinking in technology-mediated learning environments, a topic with limited prior research. Specifically, the study examined how teachers (ISTs and PSTs) anticipate student…

This study investigated the effects of working memory load (WML) and automaticity on mental addition through an examination of both task and individual characteristics within the framework of cognitive load theory. Results from 73 fourth graders showed that WML, automaticity, and their interaction had significant effects on mental addition.…

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240…

Understanding exponential growth is a fundamental aspect of developing critical numeracy skills; however, typically, exponential growth is introduced in curricular documents to secondary students. Moreover, such introductions tend to be in the context of formal mathematical modeling, divorced from a sense of quantity. The authors argue that, given…

This study explored the use of Indigenous storytelling in the planning and teaching of mathematical content. In collaboration with Indigenous and non-Indigenous educators, a culturally inclusive mathematical lesson was developed, implemented, and reviewed in an elementary school in Northern Ontario. This study used a culturally authentic approach…

A common approach to scaling up a professional development program is for the researchers who designed the program to prepare teacher leaders to facilitate it at their schools. When researchers eventually leave, however, teacher leaders may receive less support. To ensure that teacher leaders continue receiving support, researchers can prepare…

In this study, it was aimed to experiment a new method to increase the quality of the history of mathematics course instruction in the primary mathematics education. The method composed by synthesizing project-based and collaborative learning methods was named "Newspaper Preparation Method," and the course was delivered using this…

In this paper, the authors discuss their experiences with ungrading at a small public university in the U.S. and a large public university in Germany. The courses described are Calculus 1 and a content course for pre-service secondary teachers of mathematics. The professors teach differently: one with lecture, the other with inquiry-based…

Mathematical writing is one way for primary students to communicate their mathematical thinking. Research in the field of writing has shown that to become an effective teacher of writing, preservice teachers must have experience engaging in the kinds of writing given to their students. The study reported in this paper explored how 27 preservice…

Because deficits in executive functions (EFs) characterize most neurodevelopmental disorders, it is appropriate to question the value of EFs for understanding learning disabilities. Two types of studies--those testing whether EFs moderate treatment effects and those testing the direction of effects between EFs and academic skills--are presented to…

Like K-12 mathematics teachers, for whom effective instruction requires a full suite of pedagogical and mathematical knowledge and skills, Mathematics Teacher Educators (MTEs) also need a professional knowledge base to facilitate the development of future educators capable of supporting K-12 students' mathematical learning. In this paper, we…

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…