In research on mathematical problem posing, a broad spectrum of different situations is used to induce the activity of posing problems. This review aims at characterizing these so-called problem-posing situations by conducting three consecutive analyses: (1) By analyzing the openness of potential problem-posing situations, the concept of…

The Campbellian validity typology has been used as a foundation for outcome evaluation and for developing evidence-based interventions for decades. As such, randomized control trials were preferred for outcome evaluation. However, some evaluators disagree with the validity typology's argument that randomized controlled trials as the best design…

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

The requirement to assure the teaching of critical thinking put the school in front of its own weaknesses. A profound criticism highlights limitations, hindrances and obstacles that are difficult to pass without the personal efforts of the teachers. Following criticism, one can identify a set of requirements that would allow for improvement and…

Molecular orbital configurations give rise to electronic terms comprising corresponding electronic states. Electronic terms possess symmetry classifications, which are denoted by a term symbol, based on the symmetry properties of the electronic wave functions associated with the states. Using the methylene radical, and both planar and twisted…

In the context of curriculum change within English education, and beyond, this article explores the cultural historical roots of design and technology as an educational construct, distinct from design or engineering, which exist as career paths outside of the school curriculum. It is a position piece, drawing on literature from a wide range of…

In recent decades, technology has influenced various aspects of assessment in mathematics education: (1) supporting the assessment of higher-order thinking skills in mathematics, (2) representing authentic problems from the world around us to use and apply mathematical knowledge and skills, and (3) making the delivery of tests and the analysis of…

In this paper we offer a review of sorts of the studies conducted around issues of problem posing in mathematics education research. We first ground the work on problem posing in the seminal work of Polya and of Brown and Walter, which influenced most studies on this subject. We then propose two perspectives taken on problem posing: the implicit…

Courses on computer programming are included in the curricula of almost all engineering disciplines. We surveyed the research literature and identified the techniques that are commonly used by instructors for teaching these courses. We observed that visual programming and game-based learning can enhance computational thinking and problem-solving…

This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

Humans routinely make inductive generalizations about unobserved features of objects. Previous accounts of inductive reasoning often focus on inferences about a single object or feature: accounts of causal reasoning often focus on a single object with one or more unobserved features, and accounts of property induction often focus on a single…

In recent years, a number of models concerning problem solving systems have been put forward. However, many of them stress on technology and neglect the research of problem solving itself, especially the learning mechanism related to problem solving. In this paper, we analyze the learning mechanism of problem solving, and propose that when…

A seminal study by Chi "et al." firmly established the paradigm that novices categorize physics problems by "surface features" (e.g., "incline," "pendulum," "projectile motion," etc.), while experts use "deep structure" (e.g., "energy conservation," "Newton 2," etc.). Yet, efforts to replicate the study frequently fail, since the ability to…

Since it was first published 30 years ago, the seminal paper of Chi "et al." on expert and novice categorization of introductory problems led to a plethora of follow-up studies within and outside of the area of physics [Cogn. Sci. 5 121 (1981)]. These studies frequently encompass "card-sorting" exercises whereby the…