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.…

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…

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…

Considers 33 preservice secondary mathematics teachers' solutions to a famous sampling problem with particular interest on the use of intuition and/or formal mathematics in reaching a conclusion. Considers the relationship of solution strategy to students' background in formal mathematics and gender. Discusses implications for teaching statistics…

This paper further develops an instructional method called here "process-object linking and embedding". The idea is to link the familiar mathematical processes to objects in a familiar situation, then re-embed the new link through mathematical symbols into their mathematical construction. It makes use of children's extra-mathematical,…

Concerns about students' difficulties in statistical reasoning led to a study which explored form five (14- to 16-year-olds) students' ideas in this area. The study focussed on descriptive statistics, graphical representations, and probability. This paper presents and discusses the ways in which students made sense of information in graphical…