Le Châtelier's principle is used as a basis to derive an expression to calculate solution pH during titrations that involve only strong acids and strong bases. Central to this model are the reaction quotient and a re-equilibration term that represents the extent of neutralization during a titration. Unlike the method traditionally taught to…

Mathematics is full of mystery. We illuminate the myth to expose two conflicting senses of mystery at work in mathematics and its education practices. There is a sense of boundlessness with mathematics--the idea that we never fully know. There is also a practice of concealment, in which an answer or solution is known by special people who may…

This paper discusses authenticity from the perspective of mathematics education. Often, school mathematics offers students inauthentic word problems, which don't show the authentic usefulness of mathematics in real life. In some tasks, authentic aspects are combined with inauthentic ones (e.g., an authentic context, but the question is artificial…

Most questionnaires construe avoidance as resulting from a problem-solving process and analyse only a few, single-factor and mostly non-adequate, forms of avoidance. The aim of the present study was to develop a multi-dimensional questionnaire to measure avoidance among adolescents. We tested the Avoidance Questionnaire for Adolescents (AQA) with…

In a games-based approach, the idea of understanding is located within the concept of games as decision-laden, problem-solving contexts. However, the concept of "understanding" is largely implicit in much of the germane literature. We are arguing for a more deliberate framework to approach the concept of understanding. We propose that…

Children's early mathematical abilities are fundamental to their later academic achievement. An interest in mathematics in the early years is likely to establish a positive attitude to later mathematical learning, hopefully sustaining continued interest in mathematics and mathematical learning. Approaches to early mathematics teaching in the early…

A prevailing theory of mathematical problem solving predicts that children will be less accurate solving a + b = c + __ problems versus a + b = __ + c. However, this has never been tested directly. Because of low base rates, information combined from multiple studies can help improve estimation accuracy and precision. This study compared…

The development of universal learning actions [universal'nye uchebnye deystviya] in logic is one of the most important tasks of education. This article explores logical problems as an effective tool for developing logical thinking and the underlying universal learning actions. We outline the basic principles of learning to solve logical problems.…

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs,…

Through critical interpretation, this paper aims to critically think about some points of Paulo Freire's critical pedagogy and its educational implications. Firstly, this paper explores the influence of life experiences and the Frankfort School on the development of Freire's critical pedagogy. Secondly, it aims to critically assess some points of…

In this age of science, there is a need for rational individuals who are open to innovations to be able to limit and combine information and establish inter-system relationships. Problem solving is considered to be the most important cognitive activity that requires mental effort and will-power. The processes applied in mind when solving a…

An important but challenging problem-solving technique in introductory mechanics is that of using "tilted axes." For inclined plane and centripetal motion problems, using axes that are aligned relative to the ramp direction or the radial direction (rather than the horizontal and vertical) yields equations that are conceptually more…

The role that the mental, or internal, representation plays when people are solving hard computational problems has largely been overlooked to date, despite the reality that this internal representation drives problem solving. In this work we investigate how performance on versions of two hard computational problems differs based on what internal…

Studies of African indigenous games often focus on a specific game or on games from different regions. This article, rather, examines five popular African board games in order to find the similarities and differences among these games. The analysis shows similarities among them. However, these similarities do not necessarily mean that these games…

For students working on realistic complex modelling problems as autonomously as possible the support by a tutor is indispensable for the students. However, how this support can be realised is still a question that has not been sufficiently answered. Based on prior research, it turned out that teacher interventions based on heuristic strategies…