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…

Verification and validation are essential aspects of mathematics and beyond in STEM, but these constructs are not consistently defined in research nor in curricula documents. In this theoretical paper, we argue that verification and validation are largely characterized as binary judgments by teachers and researchers about what students do. We then…

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…

In this paper, it was tried to consider the current state of normative support for the development of strategic planning documents in the field of Russian education. The strategy for the development of education (DoE), as an industry document of strategic planning, has not been adopted in the Russian Federation (RF) to date. The article attempts…

The Chinese Radical Assembly Game (CRAG) is an online platform that assesses the lexical competence. In which, individuals select different Chinese radicals to combine them and form a legitimate character. This concept is similar to that of creative synthesis. Therefore, this study aimed to examine whether the CRAG response process involves…

This study aimed to investigate the effects of gender pairings on collaborative problem-solving performance, processes, and attitudes in a social learning context. Three types of pairings (i.e., male-male, female-female, and mixed pairings) were considered in an empirical study with 222 tenth-grade students. The selection of three different…

The mathematics performance of students identified with emotional and behavioral disorders (EBD) is poor. Students identified with EBD require individualized instruction aligned with their unique academic and behavioral needs. One way that teachers can efficiently identify core mathematics deficits and provide individualized instruction is through…

This study aimed to evaluate the effectiveness of the inquiry-based learning method supported by metacognitive strategies on students' problem-solving and problem-posing skills. The research was conducted in two stages using an exploratory sequential design, which is one of the mixed methods research. The case study design was used in the first…

This paper examined the effects of training in creative problem-solving on intelligence. We revisited Stankov's report on the outcomes of an experiment carried out by R. Kvashchev in former Yugoslavia that reported an IQ increase of seven points, on average, across 28 tests of intelligence. We argue that previous analyses were based on a…

This study examined the type of mathematical tasks in two Australian and two Indonesian mathematics textbooks for 7th-grade students. The quantitative data were collected from the coding results of the tasks in the textbooks. The tasks were coded based on six categories: the presentation forms, the cognitive requirements, the contextual features,…

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…

This study addresses how problem-posing seminars provided room for preservice teachers (PSTs) to navigate the disconnect between theory and practice, facilitating reflection on their experiences, and fostering self-efficacy as novice English teachers. Viewing student teaching as identity construction, the authors applied the lens of Lensmire's…

In this brief article, Peter, Larissa and Doug present a single-page scaffold that challenges us to think of the mathematical proficiencies in a whole new way. By thinking of the proficiencies as verbs, they can be seen as purposeful learner actions and offer clues as to what it might mean to be a mathematician.