Solving many quantitative problems does not necessarily lead to an improved Physics understanding. However, physicists, who have learned physics largely through quantitative problems solving, often have a refined physical intuition. Assuming that the refinement of physical intuitions occurs, to a great extent, during problem solving, the question…

Error analysis is the study of errors in learners' work with a view to looking for possible explanations for these errors. It is a multifaceted activity involving analysis of correct, partially correct and incorrect processes and thinking about possible remediating strategies. This paper reports on such an analysis of learner tests. The tests were…

As a contribution to honour the foresight of Ken Clements and John Foyster in founding MERGA [Mathematics Education Research Group of Australasia] so many years ago this paper is not a research paper in the usual sense. Rather it sets out to sample the context of Mathematics Education in Australasia and beyond (then and now) and to highlight some…

The aim of this study was to investigate the use of the "dual mathematical modelling cycle framework" as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an "Oil Tank Task" that required them to develop two…

We adopted Brown's (1987) conceptualisation of metacognition to examine how student teachers can be taught metacognitive control while solving mathematical problems. In addition, tasks given to these student teachers were in-built with opportunities for them to be aware of the need for metacognition. We describe the use of the Practical Worksheet…

We describe an attempt by a former mathematics teacher to read an undergraduate mathematics proof aided by discussions with a mathematician using the language of mathematical problem solving. The literature on successful approaches to reading mathematics is scarce at the secondary and undergraduate levels. Shepherd, Selden and Selden (2012)…

We report on a long-term study which was executed in a German secondary school with 128 eights graders (ages 14 to 15) in four different classes. Two of these classes served as control groups. The mathematics lessons of the other two classes (treatment groups) were frequently enriched by distinguished phases in which structured argumentation and…

We encounter ratios on a daily basis. They also play an important role as a basic construct of thinking in many areas of school mathematics. For example, a fraction can be interpreted as the ratio of a part to the respective whole. Many children appear to have difficulties with fractions and although the concept of ratios is crucial for this…

Despite their apparent simplicity, the concepts of square numbers and square roots are problematic for high school students. I inquired into students' understanding of these concepts, focusing on obstacles that students face while attempting to solve square number problems. The study followed a modified analytic induction methodology that included…

This paper describes how the global education community can prepare for the future of education. With the aim of promoting global education and creativity, the paper leverages case studies on Korea's education reform, including the Free Semester Program (FSP) and the SMART Initiative using ICT, which are new education initiatives focused on…

This article describes the implementation of an interdisciplinary design studio as a means to teach creative problem-solving through project-based learning. "Learning and Innovation Skills" has been designated as a core skill that students need to be successful in today's world, and project-based learning is one approach to helping…

This study aimed at developing a module in physics based on the assessment of the learning progression of students in physics and science teachers' formative assessment practices. The participants in this study were the Grade 11 students and Junior High School science teachers for the data gathering, science teachers for the design and development…

Acceptance and commitment therapy asserts that in clinical problems such as rumination and depression, making sense continues despite accompanying aversive consequences, because sense-making is reinforcing, particularly when it leads to experiential avoidance. The following series of experiments aimed to provide preliminary empirical evidence for…

When Martin Gardner first presented the Two-Children problem, he made a mistake in its solution. Later he corrected the error, but unfortunately the incorrect solution is more widely known than his correction. In fact, a Tuesday-Child variation of this problem went viral in 2010, and the same flaw keeps reappearing in proposed solutions of that…

Background: A potential problem of low-stakes large-scale assessments such as the Programme for the International Assessment of Adult Competencies (PIAAC) is low test-taking engagement. The present study pursued two goals in order to better understand conditioning factors of test-taking disengagement: First, a model-based approach was used to…