This article demonstrates how to consider differentiating instruction for diverse learners while maintaining the cognitive demand of a mathematics task. The authors present scenarios involving hypothetical cases of students in inclusive classrooms who engaged in productive struggle within the differentiated task. The authors specifically focus on…

The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…

Design thinking is a methodology that emphasizes reasoning and decision-making as part of the problem-solving process. It is a structured framework for identifying challenges, gathering information, generating potential solutions, refining ideas, and testing solutions. Design thinking offers valuable skills that will serve students well as they…

Gifted middle school students in sixth, seventh, and eighth grades engaged with a community activism curriculum designed and implemented by the author, their gifted education facilitator, as part of their gifted programming. This authentic learning experience asked students to follow a creative problem-solving process that fostered thoughtful…

Computational thinking is an important and necessary way of thinking for computer programmers and other professionals in science, technology, engineering, and mathematics (STEM). Research on emerging practices around computational thinking that is developed through coding initiatives in schools reports that elementary children typically learn how…

This article describes the implementation of a collaborative--competative pedagogy in a Year 10 class and the productive motivational outcomes that followed.

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

The Mathematics Practicum has been offered at St. Olaf College for over 30 years. The Practicum is a 4-week, January Interim course where three teams of five students work on consulting problems solicited from area businesses, government agencies, and non-profit organizations. These problems have significant mathematical, statistical, and…

The Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…

The concept of the Citizen Scholar highlights the potential for universities to act as vehicles for social change by supporting the development of active, engaged graduates who are geared to respond to current and future global challenges. This demands a radical shift in teaching towards more interactive pedagogies, which may prove difficult for…

Many general and special education teachers teach mathematics word problems by defining problems as a single operation and linking key words to specific operations. Unfortunately, teaching students to approach word problems in these ways discourages mathematical reasoning and frequently produces incorrect answers. This article lists eight common…

Problem solving in groups can be rich with tension for students. This tension may arise from conflicting approaches (conceptual and/or epistemological) and/or from conflict emerging in the social relations among group members. Drawing on video records of undergraduate students working collaboratively, we use three cases to illustrate the…

Data-based problem solving within a multi-tiered system of support (MTSS) can help state education agencies and local education agencies (LEAs) improve graduation rates for students with disabilities. To facilitate problem solving within an MTSS, states and LEAs need efficient systems and processes for analyzing and integrating data across…

As outlined by many of the social and political movements happening around us today, now more than ever, youth need to be critically conscious of their world in order to navigate it successfully. The Toronto District School Board, where Armen Shahnazarian teaches uses the hybrid model of culturally responsive and relevant pedagogy (CRRP), based on…

This paper outlines a seven-step process for developing problem-solving tasks informed by cognitive load theory. Through an example of a task developed for Year 2 students, we show how this approach can be used to produce challenging mathematical tasks that aim to optimise cognitive load for each student.