The purpose of this article was to summarize results from 5 randomized control trials assessing the effects of intervention to improve the fraction performance of 4th-grade students at-risk for difficulty in learning about fractions. We begin by explaining the importance of competence with fractions and why an instructional focus on fractions…

In this article, associate professor Chrystal Dean describes how teachers can challenge their upper elementary students' understanding of area beyond a memorized formula. Herein she describes an activity that will show students the "why" behind using A = l × w to solve rectangular area problems. The activity will help deepen…

In this paper we introduce a new collaborative technique in teaching and learning the epsilon-delta definition of a continuous function at the point from its domain, which connects mathematical logic, combinatorics and calculus. This collaborative approach provides an opportunity for mathematical high school students to engage in mathematical…

This teaching brief describes a method for finding an approximately optimal combination of order quantity and reorder point in a continuous review inventory model using a discrete expected shortage calculation. The technique is an alternative to a model where expected shortage is calculated by integration, and can allow students who have not had a…

We discuss the importance of the ordering of symbols in physics formulas and identify implicit conventions that govern the "standard" form for how formulas are written and interpreted. An important part of writing and reading this form is understanding distinctions among constants, parameters, and variables. We delineate these conventions and…

As teachers, we want to encourage our students to ask searching questions on topics like how old the Universe is, how much of the Universe we can actually see and how far away the cosmic microwave background radiation is. But how many of us can honestly say we know the answers? And, even if we know the answers, how are we going to respond to the…

This paper being an extension of Bhattacharjee (2012) is very much relevant to Year 9 to Year 10A in the "Australian Curriculum: Mathematics". It also falls within the purview of class IX to class XII curriculum of Mathematics in India (Revised NCERT curriculum) for students aged 14-17 years. In Bhattacharjee (2012), the discovery of…

We discuss a general formula for the area of the surface that is generated by a graph [t[subscript 0], t[subscript 1] [right arrow] [the set of real numbers][superscript 2] sending t [maps to] (x(t), y(t)) revolved around a general line L : Ax + By = C. As a corollary, we obtain a formula for the area of the surface formed by revolving y = f(x)…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

In e-learning systems, the tutors play many roles and carry out several tasks that differ from one system to another. The activity of tutoring is influenced by many factors. One factor among them is the assignment of the appropriate profile to the tutor. For this reason, the authors propose a new approach for modeling and evaluating the function…

A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

Evidence of confusion in intermediate accounting textbooks regarding the annual percentage rate (APR) and annual effective rate (AER) is presented. The APR and AER are briefly discussed in the context of a note payable and correct formulas for computing each is provided. Representative examples of the types of confusion that we found is presented…

The goal of the study was to reconstruct and dismantle a sequence of events that preceded an insight solution to a challenging problem by a ninth-grade student. A three-week long solution process was analysed by means of the theory of shifts of attention. We argue that concurrent focusing on what, how and why the student attends to when working on…

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

This paper presents views on the teaching of chemistry and directions for its further development. A detailed critical analysis is offered for the inadequacy of much of the current teaching, weighed that it is by a conventional, traditional and, as it turns out, rather outdated sense of the material to be covered. The ambient meta-discourse on the…