Different types of reasoning, such as intuitive, inductive, and deductive, are used in the generalization of figural patterns, as an important part of patterns in school mathematics. It is difficult to demarcate the constructive patterns where the regularity observed in the first few sentences is generalizable to the other sentences and each…

Functional thinking is an established route into algebra. However, the learning mechanisms that support the transition from arithmetic to functional thinking remain unclear. In the current study we explored children's pre-instructional intuitive reactions to functional thinking content, relying on a conceptual change perspective and using mixed…

Recent studies of second language (L2) construction learning using artificial linguistic systems have begun to closely examine the role of individual differences, including personality. In such studies, adult participants learn form-meaning mappings after exposure, with scores on generalization tests as a standard criterion for learning. This…

Abilities in scientific thinking and reasoning have been emphasized as core areas of initiatives, such as the Next Generation Science Standards or the College Board Standards for College Success in Science, which focus on the skills the future will demand of today's students. Although there is rich literature on studies of how these abilities…

Generic statements express generalizations about categories and present a unique semantic profile that is distinct from quantified statements. This paper reports two studies examining the development of children's intuitions about the semantics of generics and how they differ from statements quantified by "all," "most," and…

Despite many years of investigation into implicit learning in nonlinguistic domains, the potential for implicit learning to deliver the kinds of generalizations that underlie natural language competence remains unclear. In a series of experiments, we investigated implicit learning of the semantic preferences of novel verbs, specifically, whether…

This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

Different morphological theories assign different status to parts of words, roots and affixes. Models range from accepting both bound roots and affixes to only assigning unit status to standalone words. Some questions that interest researchers are (1) What are the smallest morphological units, words or word parts? (2) How does frequency affect…

Examined how 3- and 5-year-olds and adults extend names for human-made artifacts. Found that even 3-year-olds were more likely to provide artifact names (e.g., "knife") when they believed objects were intentionally created and to provide material-based descriptions (e.g., "plastic") when they believed objects were accidentally…

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)