Mathematics learning is not only about knowledge but also cultivating mathematical thinking and how to think solve problems. Unfortunately, the way teachers evaluate students still based on student’s academic achievement. Many learn by rote, which unsuitable for developing their ability at different levels. With advent of era big data, teaching has become more accurate convenient. In this paper...

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and ma...

The point of view of the book derives from Leopold Kronecker (1823-1891), whose views were quite consonant with those of MAP. Kronecker resisted the overthrow of the Aristotelian (and Gaussian) prohibition of completed infinites on the ground that the overthrow was unnecessary. In other words, he committed himself to doing mathematics without completed infinites, basing his work on algorithmic ...

This paper presents a new type of programming language (also called modeling language) which allows a modeler to combine declarative and algorithmic knowledge, that is, mathematical-logical constraints on the one hand and an instruction sequence defining an algorithm on the other hand. The approach is new in the sense that it strictly separates syntactically and sematically the declarative from...