A teacher-researcher searched for and defined theoretical principles in the literature that could be used as a basis for teaching high-school students who were struggling in mathematics (in a regular-level mathematics classroom) and could offer a framework to design tasks to encourage a problem-solving, thinking classroom. After identifying 13…

The aim of this study is to develop a descriptive framework for teacher educators to assist teachers to plan and realize modelling implementations in their classrooms and for researchers to describe and analyse how modelling is implemented. The planning process and implementations of 12 middle and high school mathematics teachers who conducted…

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…

Problem-solving is an essential part of teaching, learning, and assessment of physics and mathematics. The continuing educational reforms have a deep impact on everyday teaching as well as working with talented students. In the Macedonian educational system, the curricula do not explicitly point out the connection between mathematics and physics,…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

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…

The topic of recurrence relations has recently been introduced in many discrete mathematics textbooks. Recurrence relations are efficient modelling and problem-solving techniques used in mathematics. Combinatorial problems are often used to introduce recurrence relations. However, many textbooks consider problems that can be reduced only to the…

Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically…

Often, straightforward notions from one mathematical domain, when altered even slightly, can become rich and rewarding investigations involving numerous additional domains -- particularly when the investigation includes rigorous proof. This study begins with a familiar high school geometry problem (namely finding the circumcentre of a triangle),…

Mathematical connections play an important role in achieving mathematical understanding. Therefore, in this article, we report research whose objective was to identify mathematical connections that pre-university students make when they solve problems that involve the derivative and the integral. In this research, we consider a mathematical…

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

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…

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students' attention. We present and compare various examples of how…

The purpose of these notes is to provide examples of large-scale geometry problems that have the potential to promote "constructive struggling" in high-school geometry classrooms. These problems are suitable for being explored in a dynamic geometry environment. The notes also contain brief sketches of solutions to the two problems.

This paper describes the main findings of a national action-research project, promoted by Regional School Office of Campania (South of Italy), aimed at improving numeracy and mathematical literacy through supporting schools' activities. The main focus is on processes underlying the creation of capabilities in representation, reasoning and…