Off-task activity is ubiquitous in classrooms, yet little understood. Building on recent work that illustrates the utility of off-task activity to disrupt relations of power among students, this article explores the potential functions of off-task participation during collaborative mathematics problem-solving. We examined 56 instances of off-task…

The purpose of this article is to demonstrate how exponential functions and patterns can be taught by well-structured lessons composed of classroom activities, mathematical questions, discussions, and solving problems. Sawyer (1943) used a rope-and-post system to introduce the concept of logarithms and to calculate a product by adding the…

This article discusses how technology, in conjunction with carefully designed tasks and orchestrated discussions, has the potential to both reveal students' mathematical practices and to provide opportunities to shape those practices. Four specific mathematical practices that tend to be associated with problem-solving situations are examined: (1)…

Background: As engineers solve problems that are ill-structured and require collaboration, a common goal of engineering programs is to develop students' competencies for solving such problems in teams, often using cornerstone design experiences. Purpose: With the goal of designing effective learning environments, this study identifies…

This paper builds on two concepts, the first of which is the extended information processing model of expert design cognition. This proposes twelve internal psychological characteristics interacting with the external world of expert designers during the early phases of the design process. Here, I explore one of the characteristics, hierarchical…

Ensuring that students reach the determined goals of the courses at the desired level is one of the primary goals of teaching. In order to achieve this purpose, educators use a variety of teaching strategies and methods, and teaching materials appropriate to the content and the subject of the courses in the teaching process. As a matter of fact,…

This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments.

This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated…

Computational Thinking is a skill that guides the 21th century individual in the problems experienced during daily life and it has an ever-increasing significance. Multifarious definitions were attempted to explain the concept of Computational Thinking. However, it was determined that there was no consensus on this matter in the literature and…

Education policies today aim to raise individuals with 21st Century skills considered as a universal necessity and problem-solving skill is the one of the skills that have emerged as a requirement of the 21st century. Teaching problem solving is one of the most important topics of physics education, it is also the field where students have the…

Schacter's (2001) work on "The Seven Sins of Memory" conceptualized and communicated many of the failures of memory and their critical role in cognition. At the heart of the framework is the idea that memory often fails not because it is dysfunctional or maladaptive, but because it prioritizes flexibility and the ability to think and…

This paper describes the implementation of problem-based learning in chemical education with regard to the impact that protolytic reactions have on equilibria. The problem-based task presented here is focused on extremely weak acids and calcuation of the pH value of their aqueous solutions. The task is based on comparisons of K[subscript a] ranges…

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we…

People frequently gesture when problem-solving, particularly on tasks that require spatial transformation. Gesture often facilitates task performance by interacting with internal mental representations, but how this process works is not well understood. We investigated this question by exploring the case of mental abacus (MA), a technique in which…

Touch technologies have become ubiquitous, motivating researchers to explore their potential--especially in collaborative scenarios. Studies on collaboration using joint visual spaces like multi-touch tables have demonstrated positive effects on performance. Yet, factors like prior knowledge and preferences, resulting in cognitive biases, were…