Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate…

QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper…

This paper analyses how pre-service teachers approach the notion of the infinite limit of a sequence from two perspectives: Specialized Content Knowledge and Advanced Mathematical Thinking. The aim of this study is to identify the difficulties associated with this notion and to classify them. In order to achieve this, an exploratory qualitative…

In this study, we analyzed student participation and success in a college-level Calculus I course that utilized standards-based grading. By measuring the level to which students participate in this class structure, we were able to use a clustering algorithm that revealed multiple groupings of students that were distinct based on activity…

Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

The current study measures the extent to which students' self-regulated learning tactics and learning outcomes change as the result of a deliberate, data-driven improvement in the learning design of mastery-based online learning modules. In the original design, students were required to attempt the assessment once before being allowed to access…

Comparisons are made between the errors obtained when approximating the integral with the midpoint rule, the trapezoidal rule, and Simpson's rule. (MP)

The first section promotes use of student notebooks in mathematics instruction as incentives for pupils to do daily work. Part two looks at a geometric interpretation of the Euclidean algorithm. The final section examines an open box problem that is thought to appear in virtually every elementary calculus book. (MP)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

Very little material exists for utilizing the computer in the physics classroom, and even that little is not widely known. It is hoped that this monograph will provide some stimulus both to innovation and to discussion of the role of the computer in physics education. The paper describes how this might be achieved with a detailed account of one…

Three teaching ideas are presented: how to present changes between scientific notation and decimal form that eliminate some student confusion; an analysis of an incorrect algebra equation that produced a correct answer; and aspects of a standard calculus problem dealing with minimum and maximum values. (MP)

A method of nonmetric multidimensional scaling is described which minimizes pairwise departures from monotonicity. (Author)

An unusual alternative starting point for instruction in a beginning calculus course that focuses on Fixed Point Iteration (FPI) is presented. (MP)