Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

The achievement of deep learning by secondary students requires teaching approaches that draw students into task commitment, integrated curricula, and analytical thinking. By using real-world data sets in project based instructional units, teachers can guide students in analyzing, interpreting, and reporting quantitative data. Working with…

Are there different kinds of design problems? Jonassen (2011) argued that problems vary in terms of structuredness, complexity, and context. On the structuredness and complexity continua, design problems tend to be the most ill-structured and complex. Brown and Chandrasekaran suggest that design problems may vary along a continuum from…

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

Teaching mathematics using graphic calculators has been an issue of didactic discussions for years. Finding ways in which graphic calculators can enrich the development process of creative activity in mathematically gifted students between the ages of 16-17 is the focus of this article. Research was conducted using graphic calculators with…

A quasi-experiment was conducted at an elementary school to investigate if guided collaboration would facilitate programming learning of 6 graders. Sixty-six students of two intact classes learned to program in KPL (kid's programming language) for 18 weeks during the experiment. One class was randomly assigned to the control group (i.e.,…

The design of problems is crucial for the effectiveness of problem-based learning (PBL). Research has shown that PBL problems have not always been effective. Ineffective PBL problems could affect whether students acquire sufficient domain knowledge, activate appropriate prior knowledge, and properly direct their own learning. This paper builds on…

The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…

Problem-based learning (PBL), initiated when learners meet the problem scenarios, develops learners' skills and subject matter content to make the transition from beginner to more expert problem solver. Beginning students might benefit from simple, well-structured problems, in which the understanding of sets of rules and principles results in a…

The problem-of-the-week (POW) and problem-solving class openers are exemplified as methods for the integration of course-relevant problem solving into a first-year algebra classroom without sacrificing time spent on developing skills and learning concepts. Illustrated examples, as well as problem sources, are included. (JJK)