Futures research involves speculation about alternative developments based upon existing data and potential choices. Effective futures research requires creativity in scientific practice rather than an overemphasis on reason. In discussing the important role of intuition in futures research, characteristics of creative scientists are reviewed and…

Examined the development of proportional reasoning by means of a temperature mixture task. Results show the importance of distinguishing between intuitive knowledge and formal computational knowledge of proportional concepts. Provides a new perspective on the relation of intuitive and computational knowledge during development. (GLR)

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…

Considers the role of evolution and natural selection in the functioning of the modern human brain. Natural selection equipped humans with a mental toolbox of intuitive theories about the world which were used to master rocks, tools, plants, animals, and one another. The same toolbox is used today to master the intellectual challenges of modern…

This study investigated how tacit knowledge was used by expert and novice principals during problem-solving situations. Through the use of a phenomenological, qualitative approach, novice principals were compared with expert principals as both went about their daily tasks of school leadership. Results of the study contribute to the research on…

Abstracts of 12 mathematics education research reports and critical comments (by the abstractors) about the reports are provided in this issue of Investigations in Mathematics Education. The reports are: "More Precisely Defining and Measuring the Order-Irrelevance Principle" (Arthur Baroody); "Children's Relative Number Judgments:…

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,…

Counterintuitive moments in the classroom challenge common sense and practice and can be used to help mathematics students appreciate the need to explore, reflect, and reason. Proposed are four examples involving geometry, systems of equations, and matrices as counterintuitive instances. (MDH)

Three studies examined strategy flexibility in mathematical problem solving among high school students on Scholastic Assessment Test-Mathematics problems and among college students on Graduate Record Examination-Quantitative items. Results suggested that strategy flexibility was a source of gender differences in mathematics ability as assessed by…

Mathematical creativity ensures the growth of mathematics as a whole. However, the source of this growth, the creativity of the mathematician, is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics, a qualitative study involving five creative mathematicians was…

It has been observed that students react in similar ways to mathematics and science tasks that differ with regard either to their content area and/or to the type of reasoning required, but share some common, external features. Based on these observations, the Intuitive Rules Theory was proposed. In this present study the framework of this theory…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

This document focuses on evidence from problem solving case studies which indicate that analogy, extreme case analogies, and physical intuition can play an important role as forms of nonformal reasoning in scientific thinking. Two examples of nonformal reasoning are examined in greater detail from 10 case studies of "expert" problem solving.…

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,…

Creativity in education often takes the form of concentrated periods of arts-based "light relief" from the rigours of the National Curriculum. In psychology, on the other hand, creativity is often associated with a dramatic moment of "illumination" in solving scientific, mathematical or practical problems. This paper explores a third approach…