This study aimed to examine Grade 7 students' perceptions toward Math word problems to help improve their problem-solving skills since the said skill is important and essential for all students to possess. This study used a descriptive survey made by the researchers and consisted of 15 statements of feelings regarding Math word problems; the…

In this article we critique, disrupt and resist the taken for granted use of the term "fun" in learning; specifically as it is used to justify mathematics education apps that purport to portray maths learning as a fun experience. We accomplish this critique through the creation of a digital artwork called "Arithmomania." This…

In this age of easy access to the internet and to spreadsheets, easy-to-apply numerical methods exist that are vastly superior to Simpson's rule and the (corrected) trapezoidal rule. Gaussian quadrature (GQ) is such a method. What follows tells how enthusiastic Year 9 students with a physics problem provoked a science teacher into re-discovering a…

Let R be an integral domain with quotient field F, let S be a non-empty subset of R and let n = 2 be an integer. If there exists a rational function ?: S [right arrow] F such that ?(a)[superscript n] = a for all a ? S, then S is finite. As a consequence, if F is an ordered field (for instance,[real numbers]) and S is an open interval in F, no such…

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

What is questioned and what is taken for granted when carrying out research into the teaching of a given mathematical topic such as Group Theory? This paper presents two different questioning procedures using the methodological tools provided by the Anthropological Theory of the Didactic (ATD). The first one, leading to an undergraduate…

Observation-based frameworks of instructional quality differ largely in the approach and the purposes of their development, their theoretical underpinnings, the instructional aspects covered, their operationalization and measurement, as well as the existing evidence on reliability and validity. The current paper summarizes and reflects on these…

The continual supply of new items is crucial to maintaining quality for many tests. Automatic item generation (AIG) has the potential to rapidly increase the number of items that are available. However, the efficiency of AIG will be mitigated if the generated items must be submitted to traditional, time-consuming review processes. In two studies,…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…

The purpose of this article is to explore the use of didactical phenomenology as an instructional design heuristic. In doing so, I will articulate ways in which didactical phenomenology can be used in conjunction with the guided reinvention and emergent models heuristics to support instructional design. This discussion will be supported by…

The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from…

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in…

Interactive learning environments facilitate learning by providing hints to fill the gaps in the understanding of a concept. Studies suggest that hints are not used optimally by learners. Either they are used unnecessarily or not used at all. It has been shown that learning outcomes can be improved by providing hints when needed. An effective…

Ratio and proportion have been part of school mathematics since the earliest manifestations of anything like school math in the Middle Ages. In this paper, I compile and comment on statements from primary sources of the last 2300 years to exhibit ideas that appear to have influenced the treatment of these topics in schoolbooks today. Historical…

This proposal explores relationships between young children's unit development/coordination and young children's subitizing. In particular, this theoretical commentary considers students' degrees of abstraction, students' development of actions on units, and students' operations with units when subitizing. As a result of this commentary, this…