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…

Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

The purpose of this study was to identify the use of number sense strategies by pre-service teachers studying at the department of elementary education. Compared to the previous one; new mathematics curriculum places more emphasis on various strategies such as estimation strategies, computational estimation strategies, rounding and mental…

A survey ("n" = 410) revealed statistically significant gender differences between middle school students' preference for playing particular types of games. Subsequent instrumental case studies theorised the "within-game" and "out-of-game" experiences of two middle school students as they played a digital hand-held…

This article presents ideas behind science and technology challenges and shares experiences of "egg races." Different challenges were set, but there was always the need to transport an egg across some obstacle course without breaking it. It was so popular in the 1980s that the term "egg race" came to mean any kind of simple…

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

Permutations and combinations are used to solve certain kinds of counting problems, but many students have trouble distinguishing which of these concepts applies to a given problem. An "order heuristic" is usually used to distinguish the two, but this heuristic can cause confusion when problems do not explicitly mention order. This…

WebQuests have been a popular alternative for collaborative group work that utilizes internet resources, but studies have questioned how effective they are in challenging students to use higher order thinking processes that involve creative problem solving. This article explains how different levels of inquiry relate to categories of learning…

Complex Problem Solving (CPS) skills are essential to successfully deal with environments that change dynamically and involve a large number of interconnected and partially unknown causal influences. The increasing importance of such skills in the 21st century requires appropriate assessment and intervention methods, which in turn rely on adequate…

The present study investigated the problem-solving performance of 101 university students and their interactions with a computer modeling tool in order to solve a complex problem. Based on their performance on the hidden figures test, students were assigned to three groups of field-dependent (FD), field-mixed (FM), and field-independent (FI)…

Debates about the role of the university in society have been going on for many decades. There have been several calls for a more "engaged" form of scholarship which applies itself consciously to the pursuit of applied knowledge which can contribute towards solving some of the most pressing societal challenges. Closer collaboration…

The TRIPSE (tri-partite problem solving exercise), a process-oriented exam that mimics the scientific process, was used previously in small classes (15-25). Provided limited data, students frame explanations and design experimental tests that they later revise with additional information. Our 6-year experience using it with larger numbers…

Semantic studies on diagrammatic notations (Barwise & Etchemendy,; Shimojima,; Stenning & Lemon, ) have revealed that the "non-deductive," "emergent," or "perceptual" effects of diagrams (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler,; Kulpa,; Larkin & Simon,; Lindsay, ) are all rooted in the…

The purpose of this article is to promote the use of GIS and place-based education (PBE) in rural mathematics classrooms. The pedagogy of place is disappearing from rural communities because of declining enrollments, lack of support, and federal mandates to focus more on basic academic skills. However, PBE does not stand in opposition to…

An experiment published in this "Journal" has been revisited and it is found that the curve pattern of the anodic polarization curve for iron repeats itself successively when the potential scan is repeated. It is surprising that this observation has not been reported previously in the literature because it immediately brings into…