In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

Following employers' criticisms and recent societal developments, policymakers and educators have called for students to develop a range of generic skills such as critical thinking ("twenty-first century skills"). So far, such skills have typically been assessed by student self-reports or with multiple-choice tests. An alternative…

Two different tools for assessing pedagogical content knowledge (PCK) of mathematics teachers used in the framework of the COACTIV study are systematically compared in this paper, namely the paper-and-pencil test consisting of items on the three facets "knowledge of explaining and representation," "knowledge of student thinking and…

Curricula authoring is a complex process, involving different actors and different kinds of knowledge. Learners aim at acquiring expertise about some topic of their own interest, and need to perceive that the curriculum they attend will lead them toward their goal; when this does not happen, they become demotivated. Learners are all different, not…

Technology has been part of the language learning process, both inside and outside the classroom, for decades, helping to bridge the gap between different contexts of learning. At the same time, the concept of lifelong-learning has widened our understanding of what learning is, what different forms it can take, and of the importance of considering…

The child welfare system in Germany has been described as family service-oriented because families in need are entitled to request family support services. If there is any form of child maltreatment, there may be some kind of mandatory state intervention to protect the child. Using trends in the number of children affected by maltreatment, the…

The evaluation of government-financed research has become increasingly important in the last few decades in terms of increasing the quality of, and payoff from, the research that is done, reducing the cost of doing it, and lending public credibility to the manner in which research is funded. But there are very large differences throughout the…

Stimulated by a picture of a Sierpinski-pyramid and an article by Stewart, students were asked about a connection between this pyramid and the well-known trinomial formula. The results of all the work done with students are presented in this note. (Contains 8 figures.)

Describes Assessment Center (AC) programs that are used in Germany to prepare university business graduates making job applications to large companies. The simulation of real-life application procedures is explained, problems associated with the validity of the AC are addressed, and the roles and attitudes of students and experts are discussed.…

The subject of q-calculus is a rich source of learning activities that address concept formation, exploration, variation, rich training and proof. This paper is a survey of the subject that shows how high school students using a computer algebra system can explore the field and prove some results. (Contains 7 figures.)

The paper's aim is to note a remarkable (and apparently unknown) relation for right triangles, its generalisation to arbitrary triangles and the possibility to derive these and some related relations by elimination using Groebner basis computations with a modern computer algebra system. (Contains 9 figures.)

Recommends confronting the problem of validity in intercultural research by adopting research approaches that focus on the problem (for example, ethnopsychoanalysis, intercultural psychology). Briefly reviews the current debate on intercultural-comparative research. Concludes with examples and a discussion of the recent developments in comparative…

Criticizes and examines the motives behind Charles Murray's "The Bell Curve." Murray's book claimed that many social problems, including crime and poverty among blacks, could be explained by African Americans' lack of intelligence as evidenced by testing. Reveals the book's skewed methodology as well as its interest-guided financial…