The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced courses in mathematics. In this study, we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery-based approach where students employ their existing skills as a framework for constructing the solutions of first and second-order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first-year undergraduate class. Finally, we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

We consider Egyptian mathematics from a postmodern perspective, by which we mean suspending judgement as to strict correctness in order to appreciate the genuine mathematical insights which they did have in the context in which they were working. In particular we show that the skill which the Egyptians possessed of obtaining the general case from a specific numerical example suggests a complete solution to the well-known, but hitherto not completely resolved, question of how the volume of the truncated pyramid given in Problem 14 of the Moscow papyrus was derived. We also point out some details in Problem 48 of the Rhind papyrus, on the area of the circle, which have previously gone unnoticed. Finally, since many of their mathematical insights have long been forgotten, and fall within the modern school syllabus, we draw some important lessons for contemporary mathematics education.

Dynamic geometry software (DGS) such as Cabri and Geometers’ Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to students in a deductive manner? Do students have quite different experiences in non-Euclidean environment? This study addresses these questions by illustrating the student mathematics teachers’ actions in dynamic spherical geometry environment. We describe how student mathematics teachers explore new conjectures in spherical geometry and how their conjectures lead them to find proofs in DGS.

In this work, we investigated first-year university students’ skills in using the limit concept. They were expected to understand the relationship between the limit-value of a function at a point and the values of the function at nearby points. To this end, first-year students of a Turkish university were given two tests. The results showed that the students were able to compute the limit values by applying standard procedures but were unable to use the limit concept in solving related problems.

This study documents students’ views about the nature of mathematics, the mathematics learning process and factors within the classroom that are perceived to impact upon the learning of mathematics. The participants were senior secondary school students. Qualitative and quantitative methods were used to understand the students’ views about their experiences with mathematics learning and mathematics classroom environment. Interviews of students and mathematics lesson observations were analysed to understand how students view their mathematics classes. A questionnaire was used to solicit students’ views with regards to teaching approaches in mathematics classes. The results suggest that students consider learning and understanding mathematics to mean being successful in getting the correct answers. Students reported that in the majority of cases, the teaching of mathematics was lecture-oriented. Mathematics language was considered a barrier in learning some topics in mathematics. The use of informal language was also evident during mathematics class lessons.