Despite the accumulation of substantial cognitive science research relevant to education, there remains confusion and controversy in the application of research to educational practice. In support of a more systematic approach, we describe the Knowledge-Learning-Instruction (KLI) framework. KLI promotes the emergence of instructional principles of high potential for generality, while explicitly identifying constraints of and opportunities for detailed analysis of the knowledge students may acquire in courses. Drawing on research across domains of science, math, and language learning, we illustrate the (...) analyses of knowledge, learning, and instructional events that the KLI framework affords. We present a set of three coordinated taxonomies of knowledge, learning, and instruction. For example, we identify three broad classes of learning events (LEs): (a) memory and fluency processes, (b) induction and refinement processes, and (c) understanding and sense-making processes, and we show how these can lead to different knowledge changes and constraints on optimal instructional choices. (shrink)

It is well-documented that mathematics achievement is an important predictor of many positive life outcomes like college graduation, career opportunities, salary, and even citizenship. As such, it is important for researchers and educators to help students succeed in mathematics. Although there are undoubtedly many factors that contribute to students' success in mathematics, much of the research and intervention development has focused on variations in instructional techniques. Indeed, even a cursory glance at many educational journals and granting agencies reveals that there (...) is a large amount of time, energy, and resources being spent on determining the best way to convey information through direct, declarative instruction. The proposed project is motivated by recent calls to expand the focus of research in mathematics education beyond direct, declarative instruction. The overarching goal of the presented experiment is to evaluate the efficacy of a novel mathematics intervention designed using principles taken from the literature on non-declarative learning. The intervention combines errorless learning and structured cue fading to help second grade students improve their understanding of symbolic magnitude. Results indicate that students who learned about symbolic magnitude using the novel intervention did better than students who were provided with extensive declarative support. These findings offer preliminary evidence in favor of using learning combination of errorless learning and cue fading techniques in the mathematics classroom. (shrink)

The cultivation of intellectual character is an important goal within university education. This article focusses on cultivating intellectual humility. It first explores an account of intellectual humility from recent literature on the intellectual virtues. Then, it considers one recent pedagogical approach – Making Thinking Visible – as a means of teaching intellectual virtue. It assesses one particular technique for cultivating intellectual humility arising from this pedagogical literature, and applies it to the teaching of political philosophy. Finally, there is a discussion (...) concerning how to supplement these techniques to best teach political philosophy generally, and for the purposes of cultivating intellectual humility in particular. It is argued that, by introducing the technique of the Circle of Viewpoints, supplemented by techniques from the Compassion in Education literature, the modules I teach can better cultivate intellectual humility in my students. (shrink)