This paper proposes a philosophical approach to the mathematical engagement involving students and a digital tool. This philosophical proposal aligns with other theories of learning that have been implemented in mathematics education but rearticulates some metaphors so as to promote insight and ideas to further support continued investigations…

This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…

Often solved problems are problems of students' motivation in the process of teaching and learning. Some authors see the solution in creation a more space to students' creativity in teaching and learning. It is the aim of modern pedagogic and humanistic education, too. The submitted study aims to present possibility of how to teach geometric…

Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…

While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the…

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof--statement, proof, and theory--suggested by…

Inferences about student knowledge, skills, and attributes based on digital activity still largely come from whether students ultimately get a correct result or not. However, the ability to collect activity stream data as individuals interact with digital environments provides information about students' processes as they progress through learning…

The aim of this research was to investigate high achievers' erroneous answers and misconceptions on the angle concept. The participants consisted of 233 grade 6 students drawn from eight classes in two well-established elementary schools of Trabzon, Turkey. All the participants were considered to be current achievers in mathematics, graded 4 or 5…

When the National Benchmark Tests (NBTs) were first considered, it was suggested that the results would assess entry-level students' academic and quantitative literacy, and mathematical competence, assess the relationships between higher education entry-level requirements and school-level exit outcomes, provide a service to higher education…

A hands-on symmetry project is proposed as an innovative way of teaching point groups to undergraduate chemistry students. Traditionally, courses teaching symmetry require students to identify the point group of a given object. This project asks the reverse: students are instructed to identify an object that matches each point group. Doing so…

The aim of this study was to determine how successful elementary school teacher candidates are in forming and mathematically defining the surfaces of spheres, cones, cylinders and circular objects with the aid of various geometric elements. The study group consisted of a total of 40 teacher candidates in their fourth year attending a public…

A classic TV commercial once asked, "How many licks does it take to get to the center of a Tootsie Roll Tootsie Pop?" The narrator claims, "The world may never know" (Tootsie Roll 2012), but an Internet search returns a multitude of answers, some of which include rigorous systematic approaches by academics to address the…

Problem Statement: Recent research and evaluation reports show that students are not learning geometry efficiently. One identifier of student understanding related to geometry is teachers' knowledge structures. Understanding what a proof is and writing proofs are essential for success in mathematics. Thus, school mathematics should include proving…

The analytical scheme used in the project The Evolution of the Discourse of School Mathematics (EDSM) was developed to analyse the change over time in examination texts. An adapted version of the EDSM scheme has been deployed to analyse the nature of mathematics construed in Palestinian schools' textbooks and the mathematical activity expected of…

Inventing is fundamental to mathematical activity, should one be a professional mathematician or a primary school student. Research on mathematical creativity generally is organized along three axes according to its focus on the final product, the overall process, or the individual person. Through these conceptualizations, however, research rarely…