It is important for students to develop critical thinking and other higher-order thinking skills during their tertiary studies. Along with the ability to think critically comes the need to develop students' meta-cognitive skills. These abilities work together to enable students to control, monitor, and regulate their own cognitive processes and…

A present-day engineer has a large scientific knowledge; he is a team-player, eloquent communicator and life-long learner. At the Katholieke Universiteit Leuven, the course "Problem Solving and Engineering Design" introduces engineering students from the first semester onwards into real engineering practice and teamwork. Working in small…

For over a decade it has been a common observation that a "fog" passes over the course in linear algebra once abstract vector spaces are presented. See [2, 3]. We show how this fog may be cleared by having the students translate "abstract" vector-space problems to isomorphic "concrete" settings, solve the "concrete" problem either by hand or with…

Education in this 21st century is concerned with developing intelligences. Problem solving in real-world contexts involves multiple ways of knowing and learning. Intelligence in the real world involves not only learning how to do things effectively but also more importantly the ability to deal with novelty and growing our capacity to adapt, select…

This paper reports on an ongoing project to develop an "eLingua" Latin language-learning application that combines natural-language text-input with computer game-based approaches to discovery learning. The program aims to create a content-based immersive environment within which to test the hypothesis that second-language learning is more…

Speaking at a Harvard University commencement 60 years ago, Secretary of State George C. Marshall proposed a massive program of aid and redevelopment--since known as the Marshall Plan--to bring a war-ravaged Europe back to economic health, political stability, and peace. Today colleges and universities need a new such plan, with university…

In this article, the author describes a 200-year-old ladder problem that can carry learners to high levels of mathematical thinking and activity. This problem requires learners to go from a word problem to an equation to a graph and from there to a solution. As this problem of specifics is turned into a problem using variables, technology,…

For the last four years, Soenderholm School, near the town of Aalborg, Northjutland, Denmark, has had an optional subject in the seventh grade called First "Lego" League (FLL). FLL is an international contest which aims to advance pupils' scientific interest. The task is for participants to build and program a "Lego" robot able…

When students are engaged in learning environments that allow for the practice of problem-solving skills, they are able to connect the classroom to the real world. Students with disabilities need to develop the skills of problem solving, and they need to know how to identify a problem, find the answer, and evaluate their choice. This article…

A major preoccupation in assessment is connecting examinees' performance in assessment and nonassessment contexts. This preoccupation has traditionally been framed in terms of generalizability. This article reconceptualizes this problem from a qualitatively different perspective on human abilities and their development, namely, the Sociocultural…

The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as…

One way of providing middle-school students with the opportunity to engage in realistic activities is to ensure that mathematical concepts and ideas can be taught and expressed in contexts closer to students' own experiences. Students are expected to learn serious, substantive mathematics in classrooms in which the emphasis is on thoughtful…

The idea of problem posing is not new, but it has received increased attention in light of new approaches to mathematics education. Mathematical problem posing builds on young children's natural curiosity. It promotes children's "engagement in authentic mathematical activity"; enables children to "encounter many problems, methods, and solutions…

West outlines the scientific method as a proven problem-solving method for young children across the curriculum and in all areas of life and learning. She emphasizes that doing, thinking, and talking with peers when problem solving are as important as writing conclusions. The article walks readers through a second grade class's experiment in…

In this article we present a structured set of Design Patterns (DPs) that deals with tracking students while they solve problem in specific domains such as programming or mathematics. Our collection of 17 DPs yields a three step approach: First step: to collect and analyze information on each student for each exercise; Second step: to build a…