In his work leading professional development, Peter Klosterman found that teachers specifically asked for help teaching optimisation more effectively. To address challenges students often experience solving optimisation problems, he explains useful pedagogical strategies to support the teaching of optimisation and student learning in this topic.

Problem solving, and specifically the goal of developing problem-solving competences, is a significant dimension of environmental education. Moreover, human senses and electronic sensors have been recognized as important tools in authentic problem-based learning. The purpose of this paper is to present a model to support teachers in creating…

Word problem solving is the premise for students to generalize their problem solving skills to real world problems. This includes students with autism spectrum disorder (ASD) and intellectual disability (ID). Modified Schema-based Instruction (MSBI) is one strategy that research has shown is effective for teaching students with ASD/ID to acquire…

One hundred years ago, Paul Weiss and Ludwig von Bertalanffy independently proposed that living organisms interact with their environment through systems. In the century that has followed, systems thinking and modeling have grown in tandem with discovery of the vast complexity of the universe at microscopic through astronomic levels. As our…

In this article, the author will demonstrate how gestures--often used in combination with offloading information on scratch paper--can be used to help students with difficulties in mathematics succeed with secondary level algebra. The authors will provide key examples from three studies of the algebra learning of students with mathematics…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Challenging behavior can impact the learning environment and prevent educators and students from demonstrating behavioral and academic success. Schools and districts may implore a framework of tiered systems of support to respond to students struggling behaviorally or academically. These systems provide a decision-making process to aid educators'…

Many music theory courses make use of a textbook with an accompanying anthology of musical examples. Some anthologies include recorded examples, and some do not. Many books address the topics of eighteenth-century theory with exercises for the student to complete at the end of each chapter. This article proposes a music theory pedagogy that honors…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

In this article, the authors define numberless math stories and highlight three strategies for supporting equitable problem solving: (1) The Turn-and-Tell Strategy; (2) Storyboard and Story Mat; and (3) The Act-It-Out Strategy. These three strategies open up problem solving and give every student access to a challenging mathematics curriculum…

The emerging field of social entrepreneurship seeks to address social challenges in environments where traditional public sector institutions are weak or absent. With its explicit focus on solving problems, social entrepreneurship is inherently interdisciplinary. A well-designed undergraduate course in social entrepreneurship can enhance…

Word problem solving is the premise for students to generalize their problem solving skills to real world problems. This includes students with autism spectrum disorder (ASD) and intellectual disability (ID). Modified Schema-based Instruction (MSBI) is one strategy that research has shown is effective for teaching students with ASD/ID to acquire…

A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…