This study investigates the analogies used by a sample of secondary mathematics teachers when they described the concept of function. The study is concerned with understanding what analogies were used by the participant teachers and conceptions of functions positioned in those analogies. Using examples from a set of responses to five open-ended…

This article is intended to contribute to greater knowledge regarding the importance of flow and the time used to perform an activity, with a focus on students' mathematical experiences of 3D bodies. Thirty-one 9th-grade students took part in the study. Flow and variation theory was used in the analysis of lesson observations, submission tasks,…

When students encounter challenging problems, difficulty or errors in the problem solving process, they must have the ability to adapt or change their problem solving methods; in other words, they must possess strategic flexibility. The aim of this study was to determine the strategic flexibility indicators displayed by gifted children in solving…

Prior research has suggested that mathematics specific anxiety and self-efficacy are strong predictors of mathematics performance. The purpose of this study was to examine this relationship using two nationally representative samples of Greek students in 2003 and 2012. Findings indicated that both mathematics anxiety and mathematics self-efficacy…

The field of mathematics education has seen an increase in research focused on the concept of identity, with many researchers focusing on the role of teacher pedagogies in shaping learners' identities and their participation in and engagement with mathematics. In this paper, the actual and narrated practices of two teachers, which incorporate…

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

This article attempts to identify the kind of arguments that lower secondary school-level pupils use when they apply programming to solve a mathematical problem. By analyzing the data from one group of three pupils working together with Processing (Processing is a Java based tool primarily to learn programme visual effects supported and…

In this paper, we pursue a materialist approach to tool use to account for the material dimensions of learning mathematics with technology while decentralizing the human body from activity. We root this vision in theoretical advances on embodied mathematics learning and tool use that have been recently offered as alternatives to traditional…

The aim of this study was to observe the development process of the concept of a parabola in Taxicab geometry. The study was carried out in two stages. First, some activities related to Euclidean geometry and Taxicab geometry were designed based on concept development and real-life applications, and they were administered to a ninth-grade student.…

This paper explored variation of strategy use in pattern generalization across different generalization types and across grade level. A test was designed to assess students' strategy use in pattern generalization tasks. The test was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. The findings of this study…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

This study presents a subset of factors and their association with students' achievement in school algebra. The participants were students who had enrolled in 2007 at the ninth year of Greek public education (third year of middle school). A total of 735 students participated (aged 14-15 years) from 37 public secondary schools. The sample consisted…

One of the efforts to improve and enhance the performance and achievement in mathematics of learners is the incorporation of life-related contexts in mathematics teaching and assessments. These contexts are normally, with good reasons, decided upon by curriculum makers, textbook authors, teachers and constructors of examinations and tests.…

Against the backdrop of half a century of research in mathematics problem solving, Polya's last stage is especially conspicuous--by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, "Conditions for promoting reasoning in problem solving: Insights from a longitudinal…

The purpose of the study reported herein was to identify the common mistakes made by junior secondary students in Hong Kong when learning algebra and to compare teachers' perceptions of students' ability with the results of an algebra test. An algebra test was developed and administered to a sample of students (aged between 13 and 14 years). From…