Related papers: Complexity in Mathematics Education
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…
This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in…
We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of…
This article is a part of the report for the research project ``Reform of the Course System and Teaching Content of Higher Mathematics (For Non-Mathematical Specialties)'' in 1995, supported by the National Ministry of Education. There are…
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
The paper describes methodology of math education for students interested in chemistry. Suppose we have mathematical circle 2 hours per week. What can be done? We can not provide any systematic study, but we can choose one subject and show…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
This paper examines the integration of STEAM (Science, Technology, Engineering, Arts, and Mathematics) into education, emphasizing the inclusion of the Arts to foster creativity alongside traditional STEM skills. STEAM encourages…
As several critical issues in computing such as algorithmic bias, discriminatory practices, and techno-solutionism have become more visible, numerous efforts are being proposed to integrate criticality in K-16 computing education. Yet, how…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
In a previous paper, we described the set of words that appear in the coding of smooth (resp. analytic) curves at arbitrary small scale. The aim of this paper is to compute the complexity of those languages.
This article is a theoretical study on the effectiveness of educational research in the context of Philosophy of science. This topic of discussion, in the area of educational research, has been the subject of intellectual debate and arises…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…