In a first proof-oriented mathematics course, students will often ask questions--for example, "What is this problem asking me to do?" or "What would a proof of this even look like"--that have more to do with logic than mathematics. The logical structure of a proof is a dance involving those basic logical forms--such as "p…

These notes discuss several related problems in geometry that can be explored in a dynamic geometry environment. The problems involve an interesting property of hexagons.

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…

Contemporary scholars describe mathematical modeling as a transformation of a real-world problem to a mathematical problem and back again. This paper treats a critical issue in the modeling process: how modelers determine if the transformation from the real world to mathematics was carried out well. I present an empirically derived typology of…

The new method of teaching the problems with a parameter was designed based on the identification of the reasons for the low success rate of the kids in solving the problems. In order to identify these causes and to find ways of their elimination, pedagogical research was carried out in two phases at selected universities of Slovakia (126…

Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of…

Motivation: This research investigates the transformative impact of integrating AI into mathematics education, aiming to enhance students' conceptual understanding and self-efficacy. It addresses the crucial need for innovative teaching methods in response to contemporary challenges in education and aims to fill gaps in understanding the potential…

Over the past few years at Columbus State University, the learning support math faculty and director have focused on the importance of training academic coaches to effectively engage students in corequisite support math with key practices implemented in an emporium-based model for our corequisite support math labs. This model consists of…

In this paper, we present an activity to introduce the idea of public-key cryptography and to make pre-service STEM teachers explore fundamental informatics and mathematical concepts and methods. We follow the Theory of Didactical Situations within the Didactical Engineering methodology (both widely used in mathematics education research) to…

Supporting young students in developing meanings for the set-theoretic function definition is emphasized in 6th-12th grade curricula around the world. In prior work, we have highlighted how covariational reasoning supports college students in constructing relationships that afford considering mathematical properties important for a set-theoretic…

Determining "when" and "whether" to provide personalized support is a well-known challenge called the assistance dilemma. A core problem in solving the assistance dilemma is the need to discover when students are unproductive so that the tutor can intervene. Such a task is particularly challenging for open-ended domains, even…

The purpose of this study was to describe students' thinking processes in relating quantities to the problem of covariation in the process of solving mathematical problems. This study used a descriptive exploratory approach within the scope of qualitative research involving 87 students as prospective subjects from three different high schools. The…

This study aimed to examine the inversion skills of preschool children. Within the framework of the main objective of this study, the differentiation of children's inversion skills was analyzed according to various variables (age, gender, school type, mother's and father's education level). The study group consisted of a total of 80 children (40…

This study proposes "task of teaching" as an organizer of dimensionality in teachers' subject matter knowledge for teaching (SMK) and investigates it in the context of measuring SMK for teaching high school geometry (SMK-G). We hypothesize that teachers use different SMK-G in different aspects of their teaching work and that such…

This study explores student teachers' views regarding problem solving in mathematics classrooms. The participants in the study were Bachelor of Education students registered for their second year of teaching practice (at a distance institution) who were asked about their experiences of teaching a mandatory mathematics problem-solving lesson while…