The research reported in this article sought to develop a taxonomy of grade 11 students' levels of understanding in algebraic problem-solving tasks. The student sample was from high schools in the province of Ontario in Canada. Problems from four areas in algebra namely, variables, expressions, equations and word problems were chosen to be…

'Mathematical sophistication' behaviours are often exercised by mathematicians in their work. In this article, the importance of mathematical sophistication will be discussed and three mathematics problems that activate mathematical sophistication behaviours will be presented.

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Design science research (DSR) produces knowledge via the design and evaluation of innovative solutions to real-world problems. DSR provides an improved understanding of how and why the solutions work. While DSR is being widely embraced in many research disciplines, its educational pedagogy so far remains immature with little guidance on how best…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

Simplified, reductionist approaches to curriculum design and delivery are pervasive in science education. In ecological curricula--particularly in, but not limited to K-12--biomes, ecosystems, habitats, and other units of study are simplified and presented as static, easily identified and described entities. Characteristics, components, and…

In this article, we present a hierarchical model for teaching scientific thinking to gifted students. This article follows up on an article published 40 years ago in this journal. The problem now, as 40 years ago, is that gifted students often are taught science courses at a more intensive level, but without their truly learning how to think…

It is well accepted that many mechanical engineering (ME) design processes are complex. We believe that many ME design approaches include unnecessary complexity, intended to assist the teaching of engineering knowledge. This technical complexity has contributed to many critical issues in ME education, including decreased enrolments in many…

The concept of Action Competence (AC) has been interpreted in different ways in various domains of the educational sciences. Given the rising scholarly attention to AC, these diverse interpretations are problematic because they hinder a common understanding of the concept among scholars. We unravel the interpretation of AC as a competence of…

In this brief article, Peter, Larissa and Doug present a single-page scaffold that challenges us to think of the mathematical proficiencies in a whole new way. By thinking of the proficiencies as verbs, they can be seen as purposeful learner actions and offer clues as to what it might mean to be a mathematician.

Over the past few years at Columbus State University, the learning support math faculty and director have focused on the importance of training academic coaches to effectively engage students in corequisite support math with key practices implemented in an emporium-based model for our corequisite support math labs. This model consists of…

We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should…

What do people need to learn to engage actively in social action for neighbourhood improvement or development? How important is emergent learning relative to planned learning in this context? Where does first-person knowledge fit into the body of knowledge required for success in bringing about change for the better in neighbourhoods through…

The Individuals with Disabilities Education Act (IDEA) funds programs providing services designed to assist children with a range of delays and disabilities in achieving individualized developmental and functional goals. There are two types of programs. Part C Early Intervention is for children ages birth-2, and Part B Preschool is for children…

Problem solving follows a cycle of inquiry where the individual iterates between finding possible paths and exploring their likely effectiveness before selecting one as a possible solution. The cycle is enhanced through proximal processes because the number of paths that can be explored in depth are greater when more people work on the same…