The present study investigated the development of possibility-judgment strategies between the ages of 4 and 8. In Experiment 1, 48 children and 16 adults were asked whether a variety of extraordinary events could or could not occur in real life. Although children of all ages denied the possibility of events that adults also judged impossible,…

Participants learned about a structure without explicit explanation, either by using relational schema induction (G. S. Halford, J. D. Bain, M. T. Maybery, & G. Andrews, 1998), which requires completion of instances of the structure, or by memorizing instances. Emergence of structured knowledge over trials was assessed by ability to map the…

Recent research has demonstrated the transfer of induced mood functions through equivalence relations by means of a musical mood-induction procedure. The research described in this article replicated and extended such work, primarily with the inclusion of a baseline and two types of reversal procedures. First, 16 adult participants were trained…

Here is a distinction that appears very simple, looks compelling and seems to be deeply rooted in our reflections on learning. The distinction is between activities of learning that involve training and those that involve reasoning. In the former, the pupil is a passive recipient of habits of mind and action. The mechanism by which they acquire…

Four experiments examined the development of property induction on the basis of causal relations. In the first 2 studies, 5-year-olds, 8-year-olds, and adults were presented with triads in which a target instance was equally similar to 2 inductive bases but shared a causal antecedent feature with 1 of them. All 3 age groups used causal relations…

The period from adolescence through young adulthood is one of great promise and vulnerability. As teenagers approach maturity, they must develop and apply the skills and habits necessary to navigate adulthood and compete in an ever more technological and globalized world. But as parents and researchers have long known, there is a crucial dichotomy…

It is desirable that reasoning, problem-solving and decision-making skills should form an integral part of our private and professional lives. Here we show how these skills can be improved through the use of the ARDESOS program. To test the effect of the program, we have also developed an assessment test (PENCRISAL). Our results are going in the…

The following study describes design research in an elementary school near the metropolitan D.C. area with a diverse student population. The goal of the project was to design tasks that leveraged technology and enhance the access to critical thinking in specific mathematical concepts: data analysis and probability. It highlights the opportunities…

Meaningful learning is the fundamental process that underlies the acquisition of useful information and the construction of new knowledge. By creating meaningful relations, learners are able to organize the information in bigger and more organized chunks of information; an organization that reduces memory overload and increases processing…

Different technological artefacts may offer distinct opportunities for students to develop resources and strategies to formulate, comprehend and solve mathematical problems. In particular, the use of dynamic software becomes relevant to assemble geometric configurations that may help students reconstruct and examine mathematical relationships. In…

When Paul Hirst and Wilfred Carr squared up to each other a few years ago on the issue of the role of philosophical theory in educational practice, it became clear that theory itself had become a troubled term. The very fact that Wilfred Carr could argue for the end of educational theory recalls Paul Feyerabend's fiery argument for the end of…

In this article, the authors argue that there are a range of effects usually studied within cognitive psychology that are legitimately thought of as aspects of critical thinking: the cognitive biases studied in the heuristics and biases literature. In a study of 793 student participants, the authors found that the ability to avoid these biases was…

Computational models of analogy have assumed that the strength of an inductive inference about the target is based directly on similarity of the analogs and in particular on shared higher order relations. In contrast, work in philosophy of science suggests that analogical inference is also guided by causal models of the source and target. In 3…

Reversing is the notion of thinking or working in reverse. Computer science textbooks and tutors recognize it primarily in the form of recursion. However, recursion is only one form of reversing. Reversing appears in the computer science curriculum in many other forms, at various intellectual levels, in a variety of fundamental courses. As such,…

Upper secondary students' task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a…