The purpose of this study was to examine the effects of researcher-developed lessons on students' understanding of two- and three-digit numeration. Digit-correspondence tasks, often used for individual interview assessment of place value understanding, were adapted to be used as problem-solving tasks. The tasks were presented to three classes,…

In six parts, this research panel report focuses on numerous aspects of an institutionally-supported project in Writing and Problem Solving across Disciplines conducted by four teachers at Central Oregon Community College in Bend, Oregon. The report's first section, "Introduction," is descriptive and gives some background on the research…

Findings from two studies of fourth grade children learning the concept of mathematical equivalence are presented. The questions studied were: (1) Can knowledge conveyed in gesture but not in speech be tapped by a recognition technique; and (2) Does having implicit knowledge that is expressed in gesture but not in speech have implications for…

A study was conducted in Israel to determine effects of external similarity in problem structure on students' responses. Fifty students from each of the 7th, 8th, 10th, and 12th grade levels were presented with three problems involving successive divisions that were similar in structure. The problems asked separately whether the processes of…

Through timely questioning, teachers can estimate a child's understanding of mathematical ideas. Hence, the type of question asked by the teacher must be connected to the student's present thinking about a solution. This paper illustrates and analyzes how timely questioning on the part of teachers helped third, fourth, and fifth grade students…

This document is the teacher's guide for a curriculum designed to teach mathematics in a social studies context. It provides mathematical experiences in real world contexts that help students interpret, experiment, communicate, and look for multiple solutions to complex problems. The curriculum uses mathematics in context to help students develop…

This handbook offers teachers suggestions for ways to help students become risk-takers. Five levels of risk-taking behavior are identified: the uninhibited risk-taker, the analytical risk-taker, the cautious risk-taker, the inhibited risk-taker, and the nonrisk-taker. The importance of risk-taking for problem solving, and the teacher's role in…

Mathematics problem solving skills need to be developed through meaningful interactions. Computer simulations combined with cooperative learning methods provide students a context within which to construct an understanding of mathematics problem solving. This study examines the distribution and sequence of events that result in acquisition of…

Computer courseware appropriate for instruction in grades K-12 is listed in this document. Entries are classified by subject or application: (1) communication skills, which include instruction in reading, writing, and research sources; (2) mathematics; (3) college selection services; (4) problem solving; and (5) social studies. Information on each…

This paper documents the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to ten instructional units on sentence-writing for verbal problems and algorithms specified test content. Tests measuring…

The curriculum guide for gifted and talented third and fourth grade students was developed in a 1-week teacher workshop. Introductory sections specify tasks and timelines, review characteristics of gifted and talented students, and describe the district's screening and identification process. The curriculum is based on a combination of…

Over a l0-week period, an elementary school teacher designed and implemented a practicum study intended to help a target group of 24 kindergartners develop crucial mathematical problem-solving skills and to prepare them for taking the Stanford Achievement Test. The objective was addressed through implementation of direct instruction, modeling,…

The purpose of this study was to describe and compare kindergarten and first-grade children's performance on addition and subtraction problems presented in two contexts: verbal (in which problem data were linked to physical referents such as objects or people and their actions), and abstract (in which no such links to physical situations…

Methodological issues in the use of protocol analysis for research into human problem solving processes are examined through a case study in which two students were videotaped as they worked together to solve mathematical problems "out loud." The students' chosen strategic or executive behavior in examining and solving a problem was…

This document focuses on four children in a small group, solving word problems aloud. Different aspects of how children in small groups approach problems were revealed; certain characteristics of their attempts to solve problems suggest a variety of questions for further research. These pupils were part of a project that involved six groups of…