We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

Demonstrates that an elementary understanding of computer programing and the development and illustration of the structure of computer program analysis will be valuable assets in the understanding and teaching of mathematics and may be used as modeling devices to simulate the stages of learning. (Author)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

The time at which component skills are taught is studied to see whether it is a significant instructional variable. This research involved the instruction of a multiplication algorithm to 15 below-average first graders. (MP)

A survey of general mathematics students whose teachers were taking an inservice workshop revealed that they had not yet mastered division. More direct introduction of the standard division algorithm is favored in elementary grades, with instruction of transitional processes curtailed. Weaknesses in transitional algorithms appear to outweigh…

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

The instruction of finger counting and finger calculation, also known as Chisanbop, is promoted as a natural method of introducing and teaching the basic processes of addition, subtraction, multiplication and division to children, particularly to those who are mentally and physically handicapped. The sequential process for teaching finger…

This document analyzes one chapter of a textbook for college remedial mathematics. This analysis is done by one of the textbook authors. The chapter under discussion deals with fractions. The text authors, writing from a constructivist perspective, attempted to write problems which not only developed specific conceptual and heuristic objectives…

The results of an investigation of the development of children's knowledge of addition and subtraction concepts before they start school are detailed. The purpose of the study was to test the predictions of the three-stage model about the distinctions between the last two stages. Twenty-four children participated in the investigation. None of…

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Creole language edition are identical to the English language and…

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Italian language edition are identical to the English language and…

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate and secondary students. The contents of this French language edition are identical to the English language and…

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Spanish language edition are identical to the English language and…