A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and…

This article considers a set of well-researched default assumptions that people make in reasoning about complex causality and argues that, in part, they result from the forms of causal induction that we engage in and the type of information available in complex environments. It considers how information often falls outside our attentional frame…

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of…

Checklists that focus attention on key variables might allow clinicians to find and fix their mistakes. However, whether this approach can be applied to clinicians of varying degrees of expertise is unclear. Novice and expert clinicians vary in their predominant reasoning processes and in the types of errors they commit. We studied 44 clinicians…

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

Researchers taking a domain-general approach to the development of scientific reasoning long thought that the ability to engage in scientific reasoning did not develop until adolescence. However, more recent studies have shown that preschool children already have a basic ability to evaluate evidence and a basic understanding of experimentation.…

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

There is substantial variance in the age at which children construct and deploy their first explicit theory of biology. This study tests the hypothesis that this variance is due, at least in part, to individual differences in their executive function (EF) abilities. A group of 79 boys and girls aged 5-7 years (with a mean age of 6½ years) were…

Preschool children can navigate by simple geometric maps of the environment, but the nature of the geometric relations they use in map reading remains unclear. Here, children were tested specifically on their sensitivity to angle. Forty-eight children (age 47:15-53:30 months) were presented with fragments of geometric maps, in which angle sections…

Current adolescent literacy rates cause concerns at the number of students who graduate high school with basic or below-basic reading skills. The Common Core State Standards promote disciplinary literacy, which presents advanced literacy skills embedded in content area instruction. Disciplinary literacy is argued as a way to raise adolescent…

Mobilizing scientific knowledge for understanding the natural world and for critically appraise socio-scientific situations and make decisions are key competencies for today's' society. Therefore, it is essential to understand how students at the end of compulsory schooling use scientific knowledge for understanding the surrounding…

This study examines the ways in which teachers provide students with written scaffolds in assessment tasks and the impact of these on students' abilities to demonstrate a core disciplinary proficiency--constructing evidence-based explanations. Data include 76 assessment tasks designed by 33 science teachers and 707 samples of student work. We…

Elementary science standards emphasize that students should develop conceptual understanding of the characteristics and life cycles of plants (National Research Council, 2012), yet few studies have focused on early learners' reasoning about seed structure and function. The purpose of this study is twofold: to (a) examine third-grade…

If students really understand the systems they study, they would be able to tell how changes in the system would affect a result. This demands that the students understand the mechanisms that drive its behaviour. The study investigates potential merits of learning how to explicitly model the causal structure of systems. The approach and…

This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…