This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

This article explores relationships between designing and making in the work of children within the age range 5-11 when engaged in practical modelling tasks. The notion of the model is explored from the perspective of concrete representations. It is suggested that concrete models may be used as hypotheses from which to test ideas about the nature…

Extends prior theory and research by postulating the existence of an intermediate class of concepts called 'hypothetical'. Investigates the hypothesis that three kinds of scientific concepts exist by constructing and administering a test on concepts introduced in a college biology course. Supports the hypothesis that intellectual development…

The constructivist hypothesis that the acquisition of domain-specific conceptual knowledge (declarative) requires the use of general procedural knowledge was tested. Students (n=314) were classified as reflective, transitional, or intuitive thinkers and presented with four concept-acquisition tasks. Skill in hypothetico-deductive reasoning…

Describes a study that investigated probabilistic intuitions held by students (N=98) from grade 7 through college through the use of a questionnaire. Of the misconceptions that were investigated, availability was the only one that was stable across age groups. Contains 20 references. (DDR)

Achievement in science depends among other factors on hypothetico-deductive reasoning ability; that is, on the developmental level of the students. Recent research indicates that developmental level of the students should be studied along with individual difference variables such as Pascual-Leone's M-capacity (information processing) and Witkin's…

Examines 11 elementary science texts in terms of conceptual structure and reasoning demands using concept maps. Reports that (1) the conceptual structures vary widely across texts; (2) most of the structures are well defined; and (3) the reasoning demands are above the developmental capabilities of most of primary-level children. (Author/YP)

The reasoning abilities to be expected of the concrete operational and formal operational student, the percentage of secondary science students that are capable of each type of reasoning pattern, and effective strategies to teach science to concrete reasoners are described. Implications for curriculum development are discussed. (KR)

Five- to six-year-old children estimated the size of Euclidian objects using an addition rule of Height plus Width, rather than a multiplying rule. Within the framework of information integration theory, tested whether intensive handling of objects would facilitate shift from addition rule to multiplication rule. Found that following handling,…

Analogies and examples from student's experiences are frequently cited as important to teaching conceptual material. This study was conducted in order to explore the effectiveness of an analogical teaching technique, which uses a connected sequence of "bridging" analogies, compared with a more standard teaching-by-example technique. The…

The purpose of this descriptive study was to investigate the developmental patterns in logical reasoning of students in grades 6-10 over a span of 20 months. The Group Assessment of Logical Thinking (GALT) was administered to the sample (N=84) during the fall of 1986, the fall of 1987, and the spring of 1988. The GALT measures six reasoning modes:…

Describes a study which was designed to determine the effect of a 25-hour introductory qualitative analysis course on high school students' understanding of formal concepts related to electrolytes. Suggests that introductory concrete experiences better prepare students to deal with more formal abstract concepts. (TW)

The constructs of concrete and formal operational reasoning were examined in 459 15-year-old secondary school students (234 males and 225 females) in Singapore. Log linear models were used to explore the relationships between Piagetian level of reasoning, the level of intelligence, gender, and type of home-speaking environment among these…