While one branch of literature is replete with investigations of problem solving and another branch frequently investigates student use of dynamic mathematics environments (DMEs), most of the studies in both of these fields consider whether or not students can solve problems. Far fewer number of studies consider the cognitive processes associated…

It is important to support pre-service teachers in terms of mathematical task design so as to increase the success of their future teaching. The purpose of this study was to evaluate mathematical tasks designed by pre-service primary and elementary mathematics teachers within the framework of task design principles. For this purpose, a total of 43…

This study investigates prospective secondary school mathematics teachers' developing conceptions about the meaning of derivative (as rate of change) while working on a series of tasks involving different non-motion real-life contexts. The study was conducted by employing a case study method. The participants of the study were 25 prospective…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

Student problem solving in the context of a dynamic mathematics environment (DME) has previously been investigated primarily through the lens of whether or not the student could complete a problem-solving task. Herein, we investigate what trajectories students employ in the realms of mathematics, technology, and problem solving as they attempt to…

This study investigates representational code-switching (RCS) by considering three high school students' communications in the process of comparing and contrasting pairs of representations (e.g., equation and graph) in the context of rational functions. Supporting this study is research in the realms of students interacting with mathematical…

This study investigates the nature of student errors in the context of problem solving and Dynamic Math Environments. This led to the development of the Problem Solving Action Identification Framework; this framework captures and defines all activities and errors associated with problem solving in a dynamic math environment. Found are three…

The aim of the presented case study is to investigate how coherent analytical instruments may guide the a priori and a posteriori analyses of a didactical situation. In the a priori analysis we draw on the notion of affordances, as artefact-mediated opportunities for action, to construct hypothetical trajectories of goal-oriented actions that have…

In this paper, we examine the ways the history of mathematics is integrated in the national textbooks of Cyprus and Greece. Our data-driven analyses suggest that the references identified can be clustered in four categories: (a) biographical references about mathematicians or historical references regarding the origins of a mathematical concept…

The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

While it is well recognized that students are prone to difficulties when performing linguistic-to-algebra translations, the nature of students' difficulties remain an issue of contention. Moreover, the literature indicates that these difficulties are not easily remediated by domain-specific instruction. Some have opined that this is the case…

Understanding how students translate between mathematical representations is of both practical and theoretical importance. This study examined students' processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the study…

The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9- to 10-year-old students (23 male, 27 female), as they solved items from six distinct graphical languages (e.g., maps) that are commonly used to convey mathematical information. The results of the study revealed:…