This article describes a mathematics session in which students explored a challenging combinatorics task, a topic shown to be difficult for students when taught traditionally. The students developed a progression of personal representations, increasingly symbolic and abstract, which they used to find a solution and justification. (Contains 8…

The Massachusetts Institute of Technology started the first US chemical engineering program six score years ago. Since that time, the chemical engineering curriculum has evolved. The latest versions of the curriculum are attempts to broaden chemical engineering to add product engineering, biology and nanotechnology to the traditional process…

This article reflects on an effort to incorporate constructivist pedagogies (learner-centered, inquiry-guided, problem-based models of teaching) into an introductory class on Christian Ethics in an M.Div. curriculum. Although some students preferred more traditional pedagogies, the majority found that constructivist pedagogies better accommodated…

In this article, the authors discuss the use by teachers of "Type 2 tasks" within the Task Types in Mathematics Learning (TTML) Project, i.e., those in which the mathematics is situated within a contextualised practical problem. It is argued that these kinds of tasks have great potential for challenging and engaging students, and showing…

The Gifted Kids Network is a Web-based, supplemental, gifted and talented programming model that includes standards-based classes, enrichment clusters, and affective programming. Students are encouraged to think critically and creatively and to question the material that is presented to them in order to meaningfully integrate topics covered into…

This paper describes the development of a first-year chemical engineering course over 5 years through action research based on evidence from student feedback. As a result of this research, the course has evolved into a blended approach which incorporates problem based learning (PBL) and online learning tools. Through the use of PBL, the students…

Because the goals of games and the object of school-based learning are fundamentally mismatched, efforts to integrate games into the curriculum have largely fallen flat despite the best intentions of teachers and the gaming industry. Arguing that educational game designers should be investigating ways to get education into games rather than…

In the past, engineering programmes were developed with separate technical learning outcomes supplemented by generic attributes. The latter were in most cases a standalone set of attributes developed by academic institutions or professional societies overseeing engineering accreditation processes. Although the technical learning outcomes were well…

This article draws on the 21st Century Skills Movement and the successful teaching practices of Asian schools in order to provide five suggestions that secondary math teachers can incorporate into their classrooms in order to promote the skill set necessary for an ever-changing global economy. Problem-based instruction, student-led solutions, risk…

This article describes an after-school mathematics program for Latino students. The program focuses on field trips to explore the mathematical practices of the community's businesses. The authors elaborate the project's general structure and illustrate the principles that guided the program. (Contains 3 tables.)

From a review of instructional design theories, research, and practice, the author has derived his "First Principles of Instruction". In this article, he suggests a rubric for using these principles to evaluate existing instruction. The article presents a Course Evaluation form and accompanying demonstration and application rubrics that enable the…

A basic understanding of statistical ideas, and especially the idea of statistical modelling involving exposure to statistical data analysis, is as fundamental to an understanding of modern society and its artefacts as is language literacy. Thus, statistics should become a central feature of the mathematics curriculum. This implies, among other…

Career and technical education (CTE) has a promising future at Darlington (WI) High School. In this article, the author describes how a class bridge project became a real-world, project-based learning opportunity involving higher-level thinking skills that are at the core of CTE at his school. It began when a local citizen approached him at the…

In this article, the author discusses how it is time for higher education to think seriously about alternatives to the traditional undergraduate "major," which, in the large majority of cases, tends to be focused on just a single field of inquiry. The author observes that the current idea of a major (or minor) subject may have made more sense in a…

An increasing variety of professional educational and training disciplines are now problem based (e.g., medicine, nursing, engineering, community health), and they may have a corresponding variety of educational objectives. However, they all have in common the use of problems in the instructional sequence. The problems may be as diverse as a…