The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A…

This project examined three hypotheses: (1) teachers can learn to make explicit their own intuitive knowledge as it relates to specific matters and their teaching practice; (2) once a teacher has gained insight into her own knowledge, she can learn to coordinate it with the privileged descriptions of subject matters she is expected to teach; and…

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,…

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.…

In order to take into account in a more productive, effective manner children's prior science knowledge in the development of science curricula and in the teaching of science, it is important "to know how to explore it, to know about its nature, and to consider the various ways it may, or may not be modified" (Gilbert, Osborne, and Fensham, 1982).…

One of three related documents produced in response to a need for direct instruction in thinking skills, this program for middle school or junior high school students bases its approach on involvement of students in direct experiences. The book contains four units. Focusing on perception, Unit 1: "Experiencing the Arts" begins with ways sensory…

With respect to the innovative roles of technology within the educational realm, an important task of educational research is the investigation of how school children accommodate themselves to innovative computer-based learning environments. This paper describes the strategies and techniques employed and extended by above-average second- through…