The purpose of this study is to examine secondary school students' mathematical reasoning about the area of the circle. Mathematical tasks designed using GeoGebra were performed within the context of the 5E-based flipped classroom approach. The participants of the study are 13 secondary school students. The tasks, video and audio recordings…

A teacher-researcher searched for and defined theoretical principles in the literature that could be used as a basis for teaching high-school students who were struggling in mathematics (in a regular-level mathematics classroom) and could offer a framework to design tasks to encourage a problem-solving, thinking classroom. After identifying 13…

This study aimed to investigate the relative effectiveness of a computer-supported teaching sequence in solving optimization problems in calculus compared to a traditional teaching approach. The participants in the study were 46 first-year prospective mathematics teachers studying in two different classes of a four-year elementary mathematics…

In traditional advanced mathematics lectures the instructor usually provides definitions, theorems, and proofs on the board rather quickly. The students often cannot make sense of these during the lecture as they are busy writing. In order to gain an understanding of the content, an intensive post-class processing on the basis of their notes would…

The process of turning a doctoral student into an independent researcher is usually guided by a professor. In this work, the supervisor-supervisee relationship is represented by a scheme inspired by Michaelis-Menten kinetics, which has been used to determine the rate of enzyme-catalysed reactions. Here, the time evolution of the number of…

An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The…

This study investigates how pre-service mathematics teachers integrate technology into their classroom practices, which normative behaviour they formulate in the classroom and the relationship between such behaviour and the integration process of technology. The study integrates two frameworks, the Instrumental Orchestration and Sociomathematical…

In light of the recent interest in mathematical competencies and the ways in which students communicate their ideas, this study aims to explore how undergraduate students communicate their ideas about mathematical tasks through written texts. Forty-three first-year undergraduate students participated in this study. They were given a graph of a…

The understanding of the relationships between pattern recognition and mathematical abilities is important for students in their learning of mathematics and mathematics teachers in the design of their teaching pedagogies. This study examines the connections between pattern recognition and mathematical abilities of students from four Singapore…

This study investigated the methods that pre-service teachers employed while finding volume using integration and the reasons why they utilized these methods (problems); the accuracy of their solutions was also analyzed in this study. Case study design, a qualitative research method, was used for this study. 45 sophomore pre-service teachers…

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled 'Project Maths' (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). "Report of the…

This paper reports on data obtained during semi-structured interviews with students who had recently experienced a guided inquiry approach to learning ordinary differential equations (ODEs) in a service-taught module. Previous research identified the strengths and weaknesses of similar cohorts of students. The results from that research informed…

In this paper, we explain changes made in an introductory Real Analysis classroom that address common challenges and that may allow for all levels of students to meet a high standard of learning and written work. We aim for this goal by fusing elements of a hybrid course with scaffolded collaborative work to improve student learning. The hybrid…

This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…

In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being…