Discusses mathematical thinking and problems posed by seventh- grade students as part of a unit on the study of algebraic ideas. The unit involves showing how variables cause changes and also incorporates the solving of systems of equations by constructing line-graph drawings and combination charts. (AIM)

PLATO Learning, Inc., a developer of computer-based instruction, recently released "Math Problem Solving." This product was designed to teach strategies for solving math problems, and consists of 19 problem-solving activities, ranging from basic math to algebra. Each activity includes tools to help find a solution and rule-based coaching to…

Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…

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…