A collection of word problems for fifth and sixth grade students are presented. The problems, which are divided into four sections and which get progressively more difficult in each section, include: (1) 38 problems on ratio and proportion; (2) 40 multistep problems (problems which require more than one calculation); (3) 40 problems on geometry…

Determines effect of a process-oriented science curriculum on students' (N=83) ability to transfer and utilize problem-solving skills, and the relation of basic and integrated processes to the development of those skills. Discusses methodology and implications for teaching problem solving, stressing the need for process-oriented curricula.…

Students in Grades six, seven, and eight were asked to integrate existing information and initially unknown answers to prose-related questions for answering superordinate questions. Results suggest that grade level development of hypothetico-deductive skills interacts with instructional prompt levels and that these skills are essential to…

A pilot study was conducted to examine the information with respect to the modes, referents, and relationships that a given teacher acquires through the examination of her students' written responses to open-ended tasks and how the teacher uses this information. The participating teacher taught sixth grade in a public elementary school in a…

This paper reports a study to address two questions concerning children's understanding of average: How do children construct and interpret representativeness within the context of data sets? and How do children think about the mean as a particular mathematical definition and relationship? Twenty-one students (seven each of 4th, 6th, and 8th…

This handbook is part of a series of three, corresponding to the three grades (4, 6, and 8) at which Mastery Tests are administered. This publication was written as a resource for teachers developing mathematics programs for students in grades 4, 5, and 6. The Mastery Test in Mathematics at Grade 6 assesses student performance for 36 instructional…

This document provides a description of the competitions involved in the Mathematics Olympics held in the Springfield Public Schools (Missouri). It provides descriptions of the team events (which involved a scavenger hunt, computers, and computations) and the individual events (which involved applied geometry, calculators, conversion from ratio to…

This paper examines sixth-grade children's thinking related to solving ratio and proportion problems before these children had received any instruction in the domain. It explores unitizing and norming, one of the processes identified by both content analyses (Behr, Harel, Post, & Lesh, 1990); Harel, Behr, Post & Lesh, 1990) and research in…

The Mathematics Pentathlon is a tournament of mathematics games held each spring since 1979 to promote the development of mathematical concepts and skills while fostering interaction among the educational community. There are five games in each of four divisions, for grades K-1, 2-3, 4-5, and 6-7. The focus is on active problem solving and…

THE PURPOSE OF THIS STUDY WAS TO INVESTIGATE SPECIFIC METHODS OF DEVELOPING THE INQUIRY SKILLS OF ELEMENTARY SCHOOL CHILDREN. ACTIVITIES INVOLVED SELECTING SPECIFIC METHODS, GATHERING MATERIALS, AND TRAINING QUALIFIED TEACHERS. A 24-WEEK, INQUIRY TRAINING PROGRAM WAS GIVEN TO FIFTH- AND SIXTH-GRADE CHILDREN WHICH INCORPORATED--(1) ANALYSIS, (2)…

THE OBJECTIVES OF THIS STUDY WERE TO DEVELOP A PROGRAM OF CLASSROOM SIMULATION FOR THE PRESERVICE EDUCATION OF ELEMENTARY SCHOOL TEACHERS AND TO CONDUCT A TEST OF THAT PROGRAM. A SINGLE SIXTH-GRADE CLASSROOM WAS SIMULATED THROUGH THE USE OF FILMS AND PRINTED MATERIALS. A TEST GROUP OF 40 STUDENTS, DIVIDED INTO 4 GROUPS, WAS PRESENTED WITH 60…

In a test the presence or absence of a "structure" in the individual's cognitive processes of formal operations thinking, 61 fourth, fifth, and sixth grade students were administered three tasks supposedly requiring such a method of thinking. The three tasks were (1) a problem solving task (PS), (2) a chemistry task requiring a certain combination…

Two studies are reported that explore the effectiveness of instruction in promoting students' conceptual understanding of the average concept using a leveling model and an open-ended problem-solving approach. One teacher and her 46 sixth-grade students participated in the first study. One year later, the second study was conducted with the same…

Interviews with (n=21) fourth, sixth, and eighth graders, who were asked to construct their own notion of average and representativeness in open-ended problems, identified five basic constructions of average as mode, an algorithmic procedure, what is reasonable, midpoint, and a mathematical point of balance. (16 references) (MKR)

Describes a study of fifth- and sixth-grade students that investigated the patterns of peer interaction among students working cooperatively in small groups on a computer-based problem-solving task and the effects of gender and group composition on peer interaction. Suggestions for future research are included. (Contains 86 references.) (LRW)