Practical problem solving is not common in many mathematical classes in Malaysian upper secondary schools. Usually, students receive the mathematical concepts through abstract materials (students cannot see some of them in their daily life). Thus some students believe that 'mathematics is not necessary for human life'. In this article, the…

Prior research substantially overstates the cost of retention under test-based promotion policies to both taxpayers and students who delay labor market entry because it omits two important factors. First, there is a delay between the intervention and the taxpayer's expenditure. Second, on average, the treatment leads to less than a full year of…

In this work, we have developed an alternative device composed by an Arduino board and an INA219 sensor to experimentally obtain the mathematical formulas describing the charge and discharge of the capacitor for educational proposes. We have obtained excellent agreement between theoretical prediction and experimental measurements. The INA219 DC…

The present work presents a proposal for study and investigation, in the context of the teaching of Mathematics, through the history of linear and recurrent 2nd order sequences, indicated by: Fibonacci, Lucas, Pell, Jacobsthal, Leonardo, Oresme, Mersenne, Padovan, Perrin and Narayana. Undoubtedly, starting from the Fibonacci sequence, representing…

There has been widespread interest in the study of oxoacids of phosphorus owing to their characteristic structures and uses in various areas of daily life. In this article, a new strategy is recommended to determine their structures. This strategy will help to develop problem-solving skills and creativity among students. The strategy is based on…

This paper describes the implementation of problem-based learning in chemical education with regard to the impact that protolytic reactions have on equilibria. The problem-based task presented here is focused on extremely weak acids and calcuation of the pH value of their aqueous solutions. The task is based on comparisons of K[subscript a] ranges…

The private company SpaceX regularly launches satellites into geostationary orbits. SpaceX posts videos of these flights with telemetry data displaying the time from launch, altitude, and rocket speed in real time. In this paper this telemetry information is used to determine the velocity boost of the rocket as it leaves its circular parking orbit…

By using high-leverage models to connect student learning experiences to overarching concepts in mathematics, teachers can anchor learning in ways that allow students to make sense of content on the basis of their own prior experiences. A rectangular area model can be used as a tool for understanding problems that involve multiplicative reasoning.…

This article uses dynamic software in Excel to demonstrate several ways in which graphical and numerical approaches can be introduced both to enhance student understanding of l'Hopital's Rule and to explain why the Rule actually works to give the "right" answers. One of the approaches used is to visualize what is happening by examining…

Earlier "Discovery" articles (de Mestre, 1999, 2003, 2006, 2010, 2011) considered patterns from many mathematical situations. This article presents a group of patterns used in 19th century mathematical textbooks. In the days of earlier warfare, cannon balls were stacked in various arrangements depending on the shape of the pile base…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…

A video is taken of a road-sign mirage from the passenger seat in a car traveling at constant speed on a highway. The video spans the duration of seeing the mirage of the sign, viewing the vanishing of the mirage as the car approaches, and passing the road sign. The mirage angle, defined as the angle with respect to the horizontal at the moment…

While tutoring his granddaughter in second-year algebra recently, the second author lamented that every textbook he could find expresses the quadratic formula as probably the most common form of the formula. What troubled him is that this form hides the meaning of the various components of the equation. Indeed, the meaning was obscured by the…

Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.

An introductory course in algebra may cover various types of polynomial manipulation, here we cover the background of these topics and a relatively unknown property of polynomials, namely Viete's relations. We define relevant operations and properties of polynomials over the real numbers as well as their algebraic forms, divisibility properties,…