This article is the first of a two-part series that explores science teachers' and their pupils' experiences of using different pedagogical approaches based on understandings of how brains learn. For this case-study research, nine science teachers were interviewed and four teachers self-selected to trial a pedagogical approach, new to them, from…

Manipulating algebraic expressions is guided by students' structure sense and the individual process of relating subexpressions to each other. This paper presents a framework for identifying the underlying cognitive processes of manipulating algebraic expressions, based on 'basic structures' and 'giving relevance'. A design-research case study…

Prior studies suggest that struggling to make sense of mathematics is a necessary component of learning mathematics with understanding. Little research exists, however, on what the struggles look like for middle school students and how they can be productive. This exploratory case study, which used episodes as units of analysis, examined 186…

To investigate relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems…

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the "cognitive type" refers to the kind of teacher content knowledge and thinking processes required to accomplish…

The purpose of this study was to examine preservice mathematics teachers' knowledge about common (mis)conceptions and difficulties of elementary students. In addition, it was aimed to investigate preservice teachers' knowledge about the possible sources of these misconception/difficulties, and their suggested strategies to overcome those…

Variability stands in the heart of statistics theory and practice. Concepts and judgments involved in comparing groups have been found to be a productive vehicle for motivating learners to reason statistically and are critical for building the intuitive foundation for inferential reasoning. The focus in this paper is on the emergence of beginners'…

These proceedings contain the papers of the IADIS International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2013), October 22-24, 2013, which has been organized by the International Association for Development of the Information Society (IADIS), co-organized by The University of North Texas (UNT), sponsored by the…