Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

The problem that the given paper aims to solve is associated with the need to resolve the contradiction between the requirements of the digital economy for a high level of computational thinking of specialists of the future and an insufficiently developed methodological base for training graduates that meets these requirements. The purpose of the…

In the most general sense, mathematical thinking can be defined as using mathematical techniques, concepts, and methods, directly or indirectly, in the problem-solving process. In this study, efforts were made to include the Graph Theory of mathematics, which is found abundantly in physics, chemistry, computer networks, economics, administrative…

The article outlines ways that teachers could use the content in Biomes and Food Security unit in the Australian curriculum, and its state and territory versions, to encourage their students to engage with higher order thinking. It first briefly discusses how to describe and classify higher-order thinking and argues that concepts are central to…

Practical collaboration at the intersection of education and neuroscience research is difficult because the combined discipline encompasses both the activity of microscopic neurons and the complex social interactions of teachers and students in a classroom. Taking a pragmatic view, this paper discusses three education objectives to which…

Young children are able to categorize animals on the basis of unobservable features such as shared biological properties (e.g., bones). For the most part, children learn about these properties through explicit verbalizations from others. The present study examined how such input impacts children's learning about the properties of categories. In a…

Williams's (2005) study on "learning without awareness" and three subsequent extensions (Faretta-Stutenberg & Morgan-Short, 2011; Hama & Leow, 2010; Rebuschat, Hamrick, Sachs, Riestenberg, & Ziegler, 2013) have reported conflicting results, perhaps in part due to differences in how awareness has been measured. The present…

Computational Thinking is considered a universal competence, which should be added to every child's analytical ability as a vital ingredient of their school learning. In this article we further elaborate on what Computational Thinking is and present examples of what needs to be taught and how. First we position Computational Thinking in Papert's…

The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional…

Purpose: In the current study, the author aimed to determine whether 4- to 6-year-old typically developing children possess requisite problem-solving and language abilities to produce, generalize, and retain a novel verb inflection when taught using an explicit, deductive teaching procedure. Method: Study participants included a cross-sectional…

The optimal timing of feedback on formative assessments is an open question, with the cognitive processing window theory (Doughty, 2001) underlying the interaction approach suggesting that immediate feedback may be most beneficial for language acquisition (e.g., Gass, 2010; Polio, 2012) and two educational psychology hypotheses conversely…

Issues emerging from instructional innovation are inevitable, yet basing any curriculum shift on a theoretical framework is paramount. This paper grounds the case-based pedagogy in three learning theories: behaviorism, cognitivism, and constructivism. The three theories are described and situated in relation to the case study method. An…

The paper presents findings of primary school children's performance on classification and generalisation tasks to demonstrate the fundamental connection between their verbal thinking processes and problem-solving, on the one hand, and the practical activities of their society and culture, on the other. The results reveal that, although children…

Humans reason by analogy (Lakoff and Johnson, 1980; Gentner, 1983; 2003; Hofstadter, 2001, 2006; Pinker, 2007). Some have further argued that analogs can be scientific models (Hesse, 1966, Clement, 1989) although clearly not all analogies are models. Analogies based on mere physical similarity are not equivalent to scientific models but analogies…

The booklet describes the efforts planned by the Washington Research Organization (UWRO) to study ways in which generalization of skills may be facilitated by severely retarded individuals. It is explained that activities of UWRO are organized around four major tasks: descriptive and laboratory research; research in natural educational settings;…