According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

The ray tracing method is widely used in teaching geometrical optics at the upper secondary and university levels. However, using simple and straightforward examples may lead to a situation in which students use the model of ray tracing too narrowly. Previous studies show that students seem to use the ray tracing method too concretely instead of…

A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans versus Zombies moderated tag game played on the Utah State University campus. We discuss…

This article examines the issues of how Common Core State Standards (CCSS) will impact adaptive teaching. It focuses on 2 of the major differences between conventional standards and CCSS: the increased complexity of text and the addition of disciplinary literacy standards to reading instruction. The article argues that adaptive teaching under CCSS…

Purpose: Apprenticeships are now usually seen as a model of education focused on occupational preparation, albeit manifested in different ways across nation states. However, throughout human history, the majority of occupational preparation has been premised upon apprenticeship as a mode of learning. That is, a preparation arising mainly through…

A growing body of academic literacies research has enhanced our understanding of university writing as contested, institutionally situated practice with important consequences, particularly for students as they learn to negotiate the writing demands of university study. Less empirical attention has been paid to the practices of subject academics…

The calculus concepts of concavity and inflection points are often given meaning through the shape or curvature of a graph. However, there appear to be deeper core ideas for these two concepts, though the research literature has yet to give explicit attention to what these core ideas might be or what it might mean to "understand" them.…

Many scientific theories and discoveries involve reasoning about extreme scales, removed from human experience, such as time in geology, size in nanoscience. Thus, understanding scale is central to science, technology, engineering, and mathematics. Unfortunately, novices have trouble understanding and comparing sizes of unfamiliar large and small…

Online planning of good teaching sequences has the potential to provide a truly personalized teaching experience with a huge impact on the motivation and learning of students. In this work we compare two main approaches to achieve such a goal, POMDPs that can find an optimal long-term path, and Multi-armed bandits that optimize policies locally…

Teachers involved in New Zealand research conducted to develop forward-looking literacy pedagogy explained they needed ongoing support to make their new practices sustainable. This article responds to that request. We begin with a whistle-stop tour of the rapidly evolving literacy landscape, briefly reviewing key concepts of critical…

Background: Productive learning processes and good learning outcomes can be attained by applying the basic elements of active learning. The basic elements include fostering discussions and disputations, facing alternative conceptions, and focusing on conceptual understanding. However, in the face of poor course retention and high dropout rates,…

Teacher leaders are often responsible for providing professional development to improve teacher effectiveness and student learning. Leading professional development for teachers can be highly effective when the focus is on student learning in on-going and relevant contexts. This article describes a school-based, teacher-led collaborative process…

Direct instruction approach has been widely used in higher education. Many studies revealed that direct instruction improved students' knowledge. The characteristics of direct instruction include the subject delivered through face-to-face interaction with the lecturers and materials that sequenced deliberately and taught explicitly. However,…

The purpose of this study was to determine the effectiveness of an instructional package, Self-Regulated Strategy Development, a cognitive strategy instructional model (POW + TREE), in combination with video self-modeling (VSM) on the improvement on the written expression of three third-grade students with learning disabilities (LD). This…

This small-scale design study describes disciplinary learning in mathematical modeling and science from an authentic engineeringthemed module. Current research in tissue engineering served as source material for the module, including science content for readings and a mathematical modeling activity in which students work in small teams to design a…