Simple harmonic motion (SHM) is a common topic for many students to study. Using the free, though versatile, motion tracking software; "Tracker", we can extend the students experience and show that the general equation for SHM does lead to the correct period of a simple pendulum.

Many poverty measures are estimated by using sample data collected from social surveys. Two examples are the poverty gap and the poverty severity indices. A novel method for the estimation of these poverty indicators is described. Social surveys usually contain different variables, some of which can be used to improve the estimation of poverty…

The meaning given to letters is significant for students' ability to be successful with algebraic tasks. Recent studies have noted that even when students have a sense of generalised number, they often have a natural number bias in the values they think a letter can take. This study analyses interviews from 13 students across two schools to…

According to what is now commonly referred to as "the Equation" in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of…

Pythagoras' theorem in two and three dimensions appears in General Mathematics, Units 1-2, section 6 (Geometry and trigonometry: Shape and measurement) in the Victorian Certificate of Education Mathematics Study Design (Victorian Curriculum Assessment Authority, 2010). It also comes in Further Mathematics, Units 3-4 (Applications: Geometry and…

The assessment of the achievement of students and the quality of schools has drawn increasing attention from educational researchers, policy makers, and practitioners. Various test-based accountability and feedback systems involving the use of value-added techniques have been developed for evaluating the effectiveness of individual teaching…

This article analyzes the use of the software Grid Algebra with a mixed ability class of 21 nine-to-ten-year-old students who worked with complex formal notation involving all four arithmetic operations. Unlike many other models to support learning, Grid Algebra has formal notation ever present and allows students to "look through" that…

Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…

Inspection of thousands of student responses to computer-marked assessment questions has brought insight into the errors made by adult distance learners of science. Most of the questions analysed were in summative use and required students to construct their own response. Both of these things increased confidence in the reliability of the…

Early in 2010, a group of year 11 students (age 15-16) studying GCSE (General Certificate of Secondary Education) Astronomy at The Radclyffe School, Oldham, in the UK, teamed up with a similar age group from Tianyi High School, Wuxi City, in China, to undertake a joint astronomy investigation. This article outlines the outcome of the first stage…

James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other…

This is the second of three articles that draw on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". The report was soundly based on research about how children learn mathematics, much of it done in the UK in the '80s. Most of the findings about algebra are very…

We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation,…

For their course, mathematics students at Bath Spa University were asked to choose a topic and explore the mathematics. As well as learning some mathematics, the author hoped that the assignment would shed light on the process of mathematical investigation itself. Their course leader had suggested that the topic of conic sections was rich, and…

In this article, the author looks at some of the aspects of the equals sign. He shares several insights from his colleagues on the meaning of the equals sign. He also discusses how children view "=" as a sign which is written before "the answer," and, in the recording of the many practical activities that form the basis for the…