In this paper, we propose that an increasingly regarded theoretical framework in neuroscience--the predictive processing framework--can help to advance an understanding of the foundations of critical thinking as well as provide a mechanistic hypothesis for how education may increase a learner's subsequent use of critical thinking outside of an…

The logos of many atomic energy regulatory bodies present a paradox in that the depictions of atomic structure that they portray tend to be 'wrong' in relation to the rules that govern pictorial representations of atomic structure that we teach. These logos present chemistry educators with excellent classroom resources to enhance critical thinking…

Sprego is programming with spreadsheet functions. The present paper provides introductory Sprego examples which have so far only been available in Hungarian. Spreadsheet environments offer both a programming tool which best serves beginner and end-user programmers' interest, and an approach which lightens the burden of coding and language details.…

Student errors are springboards for analyzing, reasoning, and justifying. The mathematics education community recognizes the value of student errors, noting that "mistakes are seen not as dead ends but rather as potential avenues for learning." To induce specific errors and help students learn, choose tasks that might produce mistakes.…

By following learned rules rather than reasoning, students often fall into common error patterns, something every experienced teacher has observed in the classroom. In their effort to circumvent the developing common error patterns of their students, the authors decided to supplement their math text with two weeklong investigations. The first was…

"Focus in Grade 2: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 2 Focal Point as presented in 'Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics". It includes representational supports for teaching and learning that can facilitate…

There is a pressing need for an evaluation rubric that examines all aspects of educational apps designed for instructional purposes. In past decades, many rubrics have been developed for evaluating educational computer-based programs; however, rubrics designed for evaluating the instructional implications of educational apps are scarce. When an…

This article presents a framework for the cognitive diagnosis of learners' errors in an interactive learning activity occurring in an intelligent learning environment. The proposed framework supports the implementation of an authoring tool. This tool helps instructional designers to specify the features of a component for cognitive diagnosis. Two…