Research into the teaching and learning of language and content in mainstream classrooms research tends to treat content as a fixed body of knowledge to be (re)constructed by learners. There is little research which seeks to understand how language and the curriculum are constructed and related in interaction by learners. In this paper, I report…

Large lecture classes can often be quite impersonal. Creating a teaching team, consisting of the instructor, graduate assistants, and a few undergraduates, is one of the ways the University of Arizona has adopted in order to make the large lecture class more personal. As members of the Department of Mathematics we train the undergraduates, who are…

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…

This study involved an investigation of the relationship between the kinds of solution representations Chinese and U.S. students use and the sorts of pedagogical representations Chinese and U.S. teachers use during instruction. The findings suggest that the representations teachers use influence the representations their students use and, hence,…

Herring in the ocean between Iceland and Norway was one of the largest fish stocks in the world until the fishery crashed in the late 1960s. The catch in 1971 was only 20 thousand metric tons in contrast with the record of 2 million tons in 1966 and the spawning stock declined from 10 million tons to 10 thousand tons in 20 years. After 25 years of…

Children's literature can enhance mathematics lessons by providing a meaningful context, demonstrating that mathematics develops from human experiences and contributes an aesthetic dimension to learning mathematics. Written as a series of real life inspired snapshots of mathematical thinking, "Counting on Frank" (Rod Clement, 1990)…

This mixed-methods study assessed the effects of enhanced anchored instruction (EAI) on the math achievement of 17 adolescents who attended an alternative high school for at-risk students with challenging behaviors. EAI is a method specially designed for developing the math skills of low-achieving adolescents that uses multimedia-based and…

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…

Studied were the effects of a knowledge of the behaviors associated with mathematical processes on problem-solving ability. Processes defined for the study were those involving: (1) construction of mathematical models, (2) conjecturing, (3) settling conjectures as being true or false, and (4) application of given axioms and theorems to problems. A…

The purpose of the study was to investigate the effects upon achievement of three levels of sequencing in problem type and two methods of presenting problem solutions. Six treatment combinations of the above were randomly assigned to 18 classes in a school system (grade level unspecified). Results showed that the sequencing called Moderately…

Discusses the nature and role of visualization in the study of mathematics. Also includes a list of seven broad methods (often referred to as the design spectrum) by which individuals solve problems. (JN)

The author criticizes an exploratory study of mathematics curricula for 6-13 year olds for its neglect of the needs of students with learning difficulties. He cites the importance of better assessment strategies, use of the problem-solving approach, development of an intersubject emphasis, and encouragement of estimating abilities. (CL)

A special summer course for mathematically gifted eighth graders used a problem-centered approach to develop abilities to hypothesize and carry out informal deductive proofs. Students responded well to challenging problems and worked best independently rather than in groups. (Author/CL)

A successful three-day enrichment course that introduced primary gifted students to microcomputers involved teamwork on problem solving and basic information on programing. (CL)