This paper associates the findings of a historical study with those of an empirical one with 16 years-old students (1st year of the Greek Lyceum). It aims at examining critically the much-discussed and controversial relation between the historical evolution of mathematical concepts and the process of their teaching and learning. The paper deals…

The impulse to investigate the natural world is deeply rooted in our earliest childhood experiences. This notion has long guided researchers to uncover the cognitive mechanisms underlying the development of scientific reasoning in children. Until recently, however, research in cognitive development and education followed largely independent…

Students with mathematical learning disabilities (MLDs) experience persistent challenges learning even the most elementary mathematics. While prior research on MLDs has classified students on the basis of test scores and documented performance differences between groups, this dissertation focuses on the qualitative differences in individual…

Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical…

The emergence of technology has led to numerous changes in mathematical and statistical teaching and learning which has improved the quality of instruction and teacher/student interactions. The teaching of statistics, for example, has shifted from mathematical calculations to higher level cognitive abilities such as reasoning, interpretation, and…

In this article we describe our experiences using picture books to provide young children (five- to six-year-olds) with a learning environment where they can explore and extend preliminary notions of mathematics-related concepts, without being taught these concepts explicitly. We gained these experiences in the PICO-ma project, which aimed to…

Mathematical proofs are not only the focus of every country's mathematics curriculum reforms, but also the subject of research on mathematics education. This paper is based on a survey of mathematics teachers, the goal of which was to investigate the understanding of mathematical proofs of secondary school math teachers, their levels of…

Background: Trigonometry is an area of mathematics that students believe to be particularly difficult and abstract compared with the other subjects of mathematics. Trigonometry is often introduced early in year 8 with most textbooks traditionally starting with naming sides of right-angled triangles. Students need to see and understand why their…

The focus of this paper is the use of National Assessment Program in Literacy and Numeracy (NAPLAN) items to develop students' competence in reading mathematical text, to promote thinking strategies including estimation, and to evaluate alternative solutions for errors and misconceptions. Showing students test items and discussing strategies for…

The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology (APT) curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who…

Solving true problems requires persistence. The National Council of Teachers of Mathematics (NCTM) states that "problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process they will often develop new mathematical…

The present study takes an interdisciplinary mathematics-physics approach to the acquisition of the concept of angle by children in Grades 3-5. This paper first presents the theoretical framework we developed, then we analyse the concept of angle and the difficulties pupils have with it. Finally, we report three experimental physics-based teaching…

One of the core courses in the undergraduate mechanical engineering curriculum has been completely redesigned. In the new numerical methods course, all assignments and learning experiences are built around a video/computer game. Students are given the task of writing computer programs to race a simulated car around a track. In doing so, students…

Technology according to the National Council of Mathematics plays a special role in teaching and learning mathematics. Technology when used effectively can deepen mathematical understanding and lead to greater abstraction. But, not all uses of technology lead to this desired result. Defining cognitive and mathematical fidelity and using it to…

The present study explores students' abilities in conversions between geometric and algebraic representations, in problem-solving situations involving the concept of "limit" and the interrelation of these abilities with students' constructed understanding of this concept. An attempt is also made to examine the impact of the…