Related papers: Simplifying and Refactoring Introductory Calculus
An active learning physics course (treatment) was re-organized in an attempt to increase students' problem solving abilities. This re-organized course covered all of the relevant concepts in the first 6 weeks with the final 4 weeks spent in…
We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research,…
It is well-known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in quantitative problem-solving process can…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
Math is the backbone of any field. Still its a night mare for many. Recent survey proves that many students become dropouts from their higher education due to math courses. ICT is an enchanted word in the contemporary educational…
An effective weighting scheme for training samples is essential for learning tasks. Numerous weighting schemes have been proposed. Some schemes take the easy-first mode, whereas some others take the hard-first one. Naturally, an interesting…
The following work is written in easy language for college level students. It shows how the first digit probabilities of a group of continuous real-valued functions can be calculated. Thus, examples explaining how the probabilities are…
Software and hardware architectures are prone to modifications. We demonstrate how a mathematically founded powerful refinement calculus for a class of architectures, namely pipe and filter architectures, can be used to modify a system in a…
The Dirac delta function is a standard mathematical tool used in multiple topical areas in the undergraduate physics curriculum. While Dirac delta functions are usually introduced in order to simplify a problem mathematically, students…
We propose a bridge between functional and object-oriented programming in the first-year curriculum. Traditionally, curricula that begin with functional programming transition to a professional, usually object-oriented, language in the…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…
Even though every mathematician knows intuitively what it means to "simplify" a mathematical expression, there is still no universally accepted rigorous mathematical definition of "simplify". In this paper, we shall give a simple and…
This paper provides an overview of common challenges in teaching of logic and formal methods to Computer Science and IT students. We discuss our experiences from the course IN3050: Applied Logic in Engineering, introduced as a "logic for…
Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
Students in introductory calculus-based physics not only have difficulty understanding the fundamental physical concepts, they often have difficulty relating those concepts to the mathematics they have learned in math courses. This produces…
We asked students to explain the structure and execution of their small programs after they had submitted them to a programming exercise. These questions about learner's code (QLCs) were delivered at three occasions in an online and open…
In the last few years appeared pedagogical propositional natural deduction systems. In these systems, one must satisfy the pedagogical constraint: the user must give an example of any introduced notion. First we expose the reasons of such a…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…