Related papers: Mathematical analysis in high school : a fundament…
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
Statistical hypothesis testing, as formalized by 20th Century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in…
In this paper, we describe the possibilities of using a rapid mental computation system in elementary education. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly.…
System dynamics is a methodology that is widely used in many academic fields. It explains the behavior of social and economic systems with models that capture complex causality and feedback effects. This 'practice paper' discusses the…
Implementation of a STEAM Makerspace to dynamize the teaching and learning processes of mathematics (with emphasis on geometry) of second-year students in the upper secondary level.
We present two add-ons for Mathematica for teaching mathematics to undergraduate and high school students. These two applications, M@th Desktop (MD) and M@th Desktop Tools (MDTools), include several palettes and notebooks covering almost…
Evaluation of students' performance for the completion of courses has been a major problem for both students and faculties during the work-from-home period in this COVID pandemic situation. To this end, this paper presents an in-depth…
This paper discusses an instructional strategy which explores eventual similarities and/or analogies between familiar problems and more sophisticated systems. In this context, the Atwood's machine problem is used to introduce students to…
We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding…
In accordance with Bloom's taxonomy, a four-level evaluation abstraction was generated with the objective of structuring and hierarchizing curricula knowledge, allowing students to dominate a subject and progressively reach the top of…
In the field of evaluation research, computer scientists live constantly upon dilemmas and conflicting theories. As evaluation is differently perceived and modeled among educational areas, it is not difficult to become trapped in dilemmas,…
In recent years, computing has become an important part of the way we teach and learn physics. Teachers, both at high school and college levels, now use computational activities in many of their courses. Physics departments are offering…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
We review the role of mathematics from a historical and a conceptual perspective in the light of modern data science.
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…