The purpose of this study is to investigate students' thinking of direct, inverse and nonproportional problems. Thirty two seventh grade students from three different government schools participated in this study. To collect the data, the participants were asked to solve 9 open-ended problems, including 3 direct, 3 inverse and 3 non-proportional…

This qualitative study aimed to examine: (1) the manner in which kindergarten children and first graders make sense of the term "area" regarding optimization problems; (2) how this manner is manifested in their decision-making and "STEAM" (science, technology, engineering, art and math) skills; and (3) how kindergarten children…

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for…

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…

The present study aimed to examine the effect of proficiency on the pragmatic comprehension of speech acts, implicatures, and routines, as well as the way learners of different proficiency levels employ strategies when comprehending a pragmatic task. Thirty-three high-proficiency and forty-one low-proficiency Chinese learners of English completed…

The present study uses the intuitive rules theory as a framework to examine whether some of the difficulties in dealing with errors and uncertainties observed among students in the university physics laboratory can stem from their use of intuitive rules. The study also examines the relationship between the use of intuitive rules and laboratory…

The phenomenon of insight is frequently characterized by the experience of a sudden and certain solution. Anecdotal accounts suggest that insight frequently occurs after the problem solver has taken some time away from the problem (i.e., incubation). However, the mechanism by which incubation may facilitate insight problem-solving remains unclear.…

The observation that the human mind operates in two distinct thinking modes--intuitive and analytical- have occupied psychological and educational researchers for several decades now. Much of this research has focused on the explanatory power of intuitive thinking as source of errors and misconceptions, but in this article, in contrast, we view…

The term of implicit learning is still subject to controversy. "At least a dozen different definitions have been offered in the field" (Frensch & Rünger, 2003 p.13). While some scholars consider it downright inexistent (see Chun & Jiang, 1998), many others are trying to identify how we seem to acquire knowledge in absence of…

Understanding contingency table analysis is a facet of mathematical competence in the domain of data and probability. Previous studies have shown that even young children are able to solve specific contingency table problems, but apply a variety of strategies that are actually invalid. The purpose of this paper is to describe primary school…

Educators in many disciplines are too often forced to rely on intuition about how students learn and the effectiveness of teaching to guide changes and improvements to their curricula. In computer science, systems that perform automated collection and assessment of programming assignments are seeing increased adoption, and these systems generate a…

The purpose of this paper is to explore the use of a new coding system that incorporates the various types of metatalk that occurred during paired learners' engagement in a consciousness-raising task. On the basis of previous studies, metalanguage (e.g. with or without terminology), knowledge sources (e.g. intuition), and verbalisation strategies…

In the present article, we articulate three assumptions underlying theories proposing that restructuring processes play a key role in insightful problem solving: representational difficulty, representational change, and discontinuity in solution processes. We argue that these assumptions need empirical validation to justify the proposition of…

Sixty-three college students worked with a computer simulation in which gradually increasing model complexity (model progression), model progression plus small assignments, or a control condition without either were used. Definition knowledge increased for all three conditions, but intuitive knowledge gain was greater for the two experimental…

This article looks at how children in preschool through second grade intuitively solve mathematical problems rather than using textbook strategies with a single path to a solution. The authors discuss Cognitively Guided Instruction (CGI), a curriculum approach that helps teachers understand and encourage children's use of intuitive strategies.…