Abstract International curriculum and policy directions have called to embed critical thinking across discipline areas including mathematics; however, conceptually, this is under-theorised under-researched in the field of mathematics education. This paper presents conceptualisation mathematical (CMT) application a literature informed conceptual framework; particular, it examines what CMT capabi...

Our purpose in this chapter is to propose that the concept of reflective abstraction can be a powerful tool in the study of advanced mathematical thinking, that it can provide a theoretical basis that supports and contributes to our understanding of what this thinking is and how we can help students develop the ability to engage in it. To make such a case completely, it would be necessary to do...

This paper describes one department's attempt to deal with one of the most salient aspect of the secondary-tertiary interface, namely, students' lack of previous experience with mathematical discourse, notion of proof, and proof-techniques. A proactive approach is taken by devoting a one-semester course speci cally for discussing proofs. Examples of the approach taken as well as of some of the ...

Undergraduate students often start their academic course of studies with inadequate learning and thinking skills. Our college has a policy of setting high standards and demands, while supporting students' learning in a variety of ways. In this paper we present a distinctive course designed to aid students develop algorithmic problem-solving skills. The course is taught in parallel to a CS1 cour...

Computational algorithmic thinking (CAT) is the ability to design, implement, and assess the implementation of algorithms to solve a range of problems. It involves identifying and understanding a problem, articulating an algorithm or set of algorithms in the form of a solution to the problem, implementing that solution in such a way that it solves the problem, and evaluating the solution based ...

Granular computing becomes known as an innovative multidisciplinary study and has established much attention in recent years. The framework shared multiple views and multiple levels of understanding in each view from many fields. The three components of the theory are labeled as the philosophy, methodology and the computation, the integration of the above view of granular computing as a way of ...

General wisdom is, mathematical operation is needed to generate number by numbers. It is pointed out that without any mathematical operation true random numbers can be generated by numbers through algorithmic process. It implies that human brain itself is a living true random number generator. Human brain can meet the enormous human demand of true random numbers. Number as well as a string of n...