Electricity and magnetism are fundamental areas of physics and are integral to science curricula at various educational levels. However, this area has been reported to contain several concepts that students find challenging, leading to perspectives that diverge from scientifically accepted views. This study examines the errors made by physics…

Object-oriented programming distinguishes between instance attributes and methods and class attributes and methods, annotated by the "static" modifier. Novices encounter difficulty understanding the means and implications of "static" attributes and methods. The paper has two outcomes: (a) a detailed classification of aspects of…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

Research Findings: This study investigated teachers' Concept development (CD) strategy use in whole-group math teaching and its associations with children's higher-order thinking processes in 25 Chinese preschool math lessons. We utilized the CD dimension within the Classroom Assessment Scoring System (CLASS) to guide our exploration. CD…

The purpose of this study was to improve children's cognitive ability of Group A in ECE Yasmin Jember, which was focused on (1) the ability to recognize simple concepts in daily life; (2) the ability to observe and curiosity; (3) the ability to classify; (4) the ability to relate cause and effect. This study was conducted by using qualitative…

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.,…

This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

The Vygotsky Blocks Test assesses problem-solving styles within a theoretical framework for the development of higher mental processes devised by Vygotsky. Because both the theory and the associated test situate cognitive development within the child's social and linguistic context, they address conceptual issues around the developmental relation…

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

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…

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that…

The author was asked to develop a list of actions that teachers could take to build students' mathematics abilities. Too many students fail to graduate and fail to pass state assessments as a result of weak mathematics skills. Even many students who do graduate leave high school lacking sufficient understanding of mathematics to pass college…

Synthesizing a decade of research, the author describes a taxonomy of meaningful learning. The most meaningful learning outcome is problem solving. In this taxonomy, four different kinds of problem solving are arranged in a hierarchical manner. Prerequisite/corequisite with problem-solving outcomes are two fundamental reasoning skills that…

Forty second- and third-graders were placed into two groups, classifiers and non-classifiers (determined by Piagetian tasks). Twenty of the subjects were then trained to use feedback to manipulate stimulus attributes, in order to determine whether the effect of the training on concept attainment was similar to that predicted by the application of…