We review the history and previous literature on radical equations and present the rigorous solution theory for radical equations of depth 2, continuing a previous study of radical equations of depth 1. Radical equations of depth 2 are equations where the unknown variable appears under at least one square root and where two steps are needed to…

In this document, we search for and define an infinite limit of sequences that is correct and accepted by the mathematical experts, the final purpose of which is to analyze its phenomenology, in Freudenthal's sense. To make the choice, experts were consulted on two issues. The first one was not decisive because of the effect that the divergence…

This paper discusses a concept that we call "'m'-tile means," which are the arithmetic mean of data values that break a data set into "m"-1 equal parts. Studying "m"-tile means can engage students' critical thinking skills and demonstrate the concepts underlying commonly used measures of central tendency, and so they…

The objective of the study was to characterise how pre-service kindergarten teachers used a Hypothetical Learning Trajectory on length and its measurement to notice children's mathematical thinking. A total of 64 pre-service kindergarten teachers enrolled in an Early Years Education mathematics teaching course were asked to notice teaching…

This article reports on a study of Kuwaiti college students' knowledge about the concept of functions. It also shows the connections these students make between different representations of functions. The results indicated that most students (96%) were unable to provide a definition of a function and only a third could provide examples of a…

In this study, it was aimed to examine the probability problems which were posed based on continuous sample space and discrete sample space. Participants of the study consisted of 48 university students selected by using the convenience sampling method. Eight tasks related to continuous and discrete variables were designed by the researcher. Eight…

Peer-mediated instructional strategies (e.g., peer tutoring) have been effective at teaching academic responses in previous research. This study extended the literature by programming for inference-making, or derived relations. Across two experiments, researchers investigated the use of peer tutoring and inference-making to teach…

Around the globe, young students are expected to learn about time, yet how is it that they themselves make sense of this topic? From a sociocultural perspective, sense-making about time emerges in relation to properties of available tools and representations, such as analog clocks or digital notation. Such interactions with the symbols and…

Undergraduate students' choices and success in their career and life is influenced by their mathematics achievement and perception of themselves in life. Conceptual understanding of topics in undergraduate mathematics such as quantitative reasoning can be difficult for students with less sophisticated multiplicative reasoning than others. This…

The teacher must, first of all, have a good knowledge of mathematics to detect the errors in the student's mathematical knowledge and to identify the general situation in the classroom. This depends on the mathematical knowledge gained in the teacher training schools. General mathematics topics occupying an important place in the departments of…

This paper describes a process of developing dance performance based and inspired by mathematical concepts and development of mathematics through history. The performance was included in the manifestation of the May month of mathematics in Serbia and prepared in collaboration with mathematicians, choreographers, dancers, science communicators and…

Many studies have investigated students' problem-posing activities. However, there has not been a strong focus on affective aspects in mathematical problem-posing. Also, students' understanding of the function concept whilst generating functions has not previously been investigated. This paper investigated students' misconceptions of the function…

In this paper, we examine the national curricula for primary mathematics for each of the four constituent nations of the United Kingdom (England, Northern Ireland, Scotland and Wales) for the estimation-related opportunities they offer children. Framed against four conceptually and procedurally different forms of estimation (computational,…

Modern economics courses require high mathematical proficiency, and low proficiency may reduce grades or cause students to avoid economics courses. The article's authors sought to improve students' mathematical skills and grades with a simple intervention based on repeated quizzing of building-block concepts. They analyzed data from four semesters…

We discuss the evolution of an instructional unit for supporting prospective elementary and middle grades' teachers' conceptions of fractions as measures. We first studied prospective teachers' conceptions of fractions using a task-based written assessment with discrete, linear, and circle representations. We designed an instructional unit that…