In Stanovich's (2009a, 2011) dual-process theory, analytic processing occurs in the algorithmic and reflective minds. Thinking dispositions, indexes of reflective mind functioning, are believed to regulate operations at the algorithmic level, indexed by general cognitive ability. General limitations at the algorithmic level impose constraints on, and affect the adequacy of, specific strategies ...

This is an expository article the aim of which is to introduce interested students and researchers to the topic of tensor rank, in particular to the construction of explicit tensors of high rank. We try to keep the mathematical concepts and language used as simple as possible to address a broad audience. This article is thought to be an appetizer and does not provide by any means a complete cov...

The mathematical concept of topology has brought about significant advantages that allow for a fundamental understanding of the underlying physics of a system. In magnetism, the topology of spin order manifests itself in the topological winding number which plays a pivotal role for the determination of the emergent properties of a system. However, the direct experimental determination of the to...

This study combines elements of the Japanese Lesson Study approach and teachers’ professional development. An explorative research design is conducted with three upper level high school teachers in the light of educational design research, whereby design activities will be cyclically evaluated. The Lesson Study team observed and evaluated two different research lesson cycles. The first one focu...

In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners’ concept images. We report a case study with a first year undergraduate student and place this i...