Recent research shows that teachers' level of Mathematical Knowledge for Teaching (MKT) and their beliefs about teaching and learning effect teaching practices and student achievement. Higher levels of MKT typically lead to more effective teaching abilities in terms of helping students make meaning of mathematical concepts, but beliefs seem to be…

Reasoning, our ability to solve novel problems, has been shown to improve as a result of learning experiences. However, the underlying mechanisms of change in this high-level cognitive ability are unclear. We hypothesized that possible mechanisms include improvements in the encoding, maintenance, and/or integration of relations among mental…

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Research in physics education has contributed substantively to improvements in the learning and teaching of university physics by informing the development of research-based instructional materials for physics courses. Reports on the design of these…

This research study explored robotics as the catalyst for computational thinking (CT) by sixth-grade students as they are engaged in a science lesson. The interactions, understandings, and applications are discussed, along with the participants' connections and implementations of CT concepts (decomposition, abstraction, pattern recognition, and…

Systems and system models are recognized as a crosscutting concept in the newly released framework for K-12 science education (NRC [National Research Council], 2012). In previous work, I developed a learning progression for systemic reasoning in ecology at the elementary level. The learning progression captured five levels of students' reasoning…

The paper focuses on student-teachers' geometric diagrams to mediate the emergence of different proofs for a geometric proposition. For Peirce, a diagram is an icon that explicitly and implicitly represents the deep structural relations among the parts of the object that it stands for. Geometric diagrams can be seen as epistemological tools to…

Purpose: This study examined bilinguals' performance on functional executive function map tasks such as the Zoo Map from the Behavioural Assessment of the Dysexecutive Syndrome and the extent to which working memory, set-shifting, and inhibition measures predicted bilinguals' performance on these tasks. Additionally, we explored the utility of…

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…

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…

Inequalities are everywhere, yet little is known about how children respond to people affected by inequalities. This article explores two responses--minimizing inequalities and favoring those who are advantaged by them. In Studies 1a (N = 37) and 1b (N = 38), 4- and 5-year-olds allocated a resource to a disadvantaged recipient, but judged…

It is commonly accepted in the academy that developing a critical thinking capacity and related capabilities will make students more effective thinkers and writers, and that these are desirable traits for graduates to have no matter what path they take after graduation. While most academics agree that critical thinking is an essential component of…

Abstraction is a key adaptive mechanism of human cognition and an essential process in the personal construction of mathematical knowledge. Based on the notion of abstraction, this paper aims to conceptualise a framework for analysing textbooks. First, I search for the meaning of abstraction from a constructive-empirical and a dialectic…

The present study addressed the effectiveness of an educational math game for improving proportional reasoning in prevocational education, and examined the added value of support in the form of reflection. The study compared four conditions: the game with reflection prompts, the game with reflection prompts plus procedural information, the game…

Using an ethnographic approach, the aim of this study was to explore how social workers learn and make sense of experiences in their daily practices. Five events that took place during an ordinary day of child investigation work are described and serve as the basis for the analysis. The findings imply that investigation work is largely a social…

The labels used to describe patterns and relations can influence children's relational reasoning. In this study, 62 preschoolers (M[subscript age] = 4.4 years) solved and described eight pattern abstraction problems (i.e., recreated the relation in a model pattern using novel materials). Some children were exposed to concrete labels (e.g.,…