The focus of this report is children's construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in their strategies for dealing with isomorphic combinatorial problems presented in "hands-on" and written form. Case studies of 9-year-olds, one low and one high achieving in school…

This manual is part of a series of materials designed to reinforce essential concepts in physical science through interactive, language-sensitive, problem-solving exercises emphasizing cooperative learning. The manual is intended for limited-English-proficient (LEP) students in beginning physical science classes. The materials are for teams of two…

A course of study was researched, designed, and implemented by the writer to learn mathematics apprehensions of fifth grade students. The primary goal was to reduce mathematics apprehension through positive mathematics experiences at home as well as in school. The objectives of the program were to develop a more positive feeling about mathematics…

Despite suggestions for incorporating students' experiences into school math lessons, mathematics education seems to be the last bastion of formalism. This paper reports on a sociocultural study of the use of students' personal experiences in early childhood elementary mathematics lessons. This study documents the use of students' personal…

Presents the teaching strategy of having first grade students write their own word problems. Suggests the use of calculators to permit students to create problems with larger, more realistic numbers. Gives examples of student-generated problems and discusses students' attempts to solve the problems. (MDH)

Reports a study to examine careless errors fifth-grade students (n=58) make while solving mathematical word problems and explores the type of student who frequently makes such errors. Results indicated that frequency of these errors was significantly related to the noncognitive variables of the study. Discusses implications for remediation. (20…

Detection of calculation errors, operation errors, and unanswerable problems was studied for 78 third graders and 77 fifth graders. The relationship between mathematics achievement and error detection was also examined. Older children and high achievers detected more errors than did younger students and low achievers. (SLD)

This report describes the development of a new tool for assessment research in graduate education. The tool, the Algebra Assessment System, is based on GIDE, a pre-existing program that diagnostically analyzes complex constructed responses to algebra word problems. The project had three goals. The first goal was to build a generically usable…

This paper reports on five related studies on upper elementary school students' beliefs about the role of real-world knowledge in solving mathematical word problems, and on possibilities of overcoming their unrealistic mathematical modeling. Findings from the first study of 75 Belgian fifth-grade students showed that as a consequence of current…

Imagery use in high school mathematics classrooms was studied. A visual image was defined as a mental scheme depicting visual or spatial information, but this definition was not spelled out to teachers or students, in order to learn what they meant by the concept. Subjects were 13 high school teachers and 54 of their students interviewed over 3…

A study investigated how elementary school students form a mental representation of simple addition and subtraction word problems, focusing on critical elements in the problems' semantic structure, and the extent to which the accuracy of the solutions found was related to the students' English language proficiency when the problems were presented…

Whether or not working with more realistic and lengthier problems during instruction would make students better able to solve similar problems on achievement tests was studied for 82 seventh graders (50 in the experimental condition and 32 in the control condition) in general mathematics classes at an urban middle school. The study also…

This guide is designed to help classroom teachers implement the Alabama Course of Study: Mathematics K-12. It is inclusive also of the objectives tested by the Stanford Achievement Tests and the Alabama Basic Competency Tests. One characteristic of the curriculum guide is that it clearly states what students should learn in each grade level. These…

The paper describes the rationale and 10-day implementation in a 5th-grade classroom (n=19) of an experimental ratio-and-proportion instructional design. In this constructivist-phenomenological design, coming from our theoretical perspective, design research, and domain analysis, students: (1) link "real-world" and "mathematical" objects…

Results of a comparison of Papua New Guinea bilingual and monolingual students' (n=232) mathematics achievement indicated that bilingual students competent in both languages scored significantly higher on two different types of mathematical tests than both low-competent bilingual students and monolingual students. (32 references)