In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…

This study analyses the view of students' mental models in solving mathematical problems. The study employed a literature review using well-accepted and robust guidelines. Data were collected by searching books and articles of journals. Data analysis techniques were done qualitatively. The finding of this study showed that the mental model is…

In this paper we examine how facilitators' prior experiences as mathematics teachers frame their work when facilitating a practice-based professional development (PD) for the first time. We focus on the experiences of a novice facilitator of StoryCircles, a professional learning process in which teachers collectively script and visualize a…

The Cognitive Acceleration (or Let's Think) approach to mathematics teaching is a Piagetian programme drawing on Vygotsky's research, developed at King's College London over 30 years ago, along with its associated professional development (PD) programme. This project sought to replicate the original studies conducted 10-15 years earlier and before…

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

The EnCoMPASS project (Emerging Communities for Mathematical Practices and Assessment) at the Math Forum and Drexel University has produced a web-based software tool for the assessment of student work. This paper discusses research on the impact of the tool on teachers' attitudes toward work with students in the software environment. The tool…

This article describes how a teacher in Mexico City worked with two researchers on an instructional design project to help kindergartners become proficient in participating in whole-class mathematical conversations.

Rubric has been associated with the term assessment used for grading and/or scoring. However, it might observe less, but it is also designed as students 'learning tool. This study was conducted to provide empirical facts on its effectiveness as a learning tool in teaching Applications of Derivatives in Basic Calculus. It used the…

This paper reports on a study of collaborative group work in mathematics. Although collaborative group work is known as one of the important approaches in education, it is still uncertain how group thinking can be measured in various learning contexts. We used the Group Thinking Measure (GTM) test developed by [Wegerif, R., T. Fujita, J. Doney, J.…

This paper focuses on pre-service mathematics teachers' geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The…

The present study aims to examine mathematical creativity in students' work in geometry. Research conducted was based on two aspects: (a) examining the influence of geometrical figure apprehension on the production of multiple solutions and (b) how the necessity to construct auxiliary lines in the given shape promotes the production of multiple…

Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…

We discuss classroom activity comprised of small groups of students collaboratively tinkering with programs of dynamically manipulable figural models, posing problems regarding their mathematical properties and behaviors. We analyzed data from students' discourse taken from two classroom interventions employing a framework of creative mathematical…

Elementary and middle school prospective teachers participated in semi-structured problem posing for integer addition and subtraction. The prospective teachers (n = 98) posed a variety of different stories, but this paper focuses on the temperature stories they posed. Results include descriptions of their posed temperature stories through the lens…

Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open…