Background and aims: In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between…

One of the four cornerstones of the National Council of Teachers of Mathematics (NCTM) "Curriculum and Evaluation Standards for School Mathematics" asserts that connecting mathematics to other subjects in the curriculum and to the everyday world is an important goal of school mathematics. This yearbook is designed to help classroom…

This computer software is a tool designed to help teachers help children in grades 1 through 7 construct their own knowledge of whole numbers and fractions. This software is the first in a series of new, dynamic computer microworlds that allow teachers to interact with students and students to interact with each other as they engage in…

This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…

This book contains real-life mathematics problems and is designed to conform to the National Council of Teachers of Mathematics' (NCTM) goals as outlined in the NCTM Curriculum and Evaluation Standards for School Mathematics. The problems come from each person's day-to-day experiences in their careers. Persons from various careers represented are…

This book provides regular classroom and special education teachers with alternative, individualized methods of teaching math computation skills. Learning activities are designed to appeal to auditory, visual, and kinesthetic learning modalities. Six mathematics topics addressed include modeling addition and subtraction, basic facts for addition…

This study investigated hearing-impaired students' understanding of the mathematical concept of fractional numbers, as measured by their ability to determine the order and equivalence of fractional numbers. Twenty-one students (ages 10-16) with hearing impairments were compared with 26 students with normal hearing. The study concluded that…

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book…

A randomized pretest-posttest-control group design study, replicated three times, each time with 24 subjects randomly selected and assigned to either a treatment or control group of 12 subjects each, was conducted to determine the effectiveness of a modified instructional strategy for accelerative and mastery learning of basic arithmetic by a male…

This book of supplemental exercises is one of a series of books designed to provide educational materials for students in addition to the instructional texts in the Adult Learning Skills Program. Exercises in this basic level book are for the mathematics subject area. Course numbers and exercise topics are: 301 (vocabulary and reading in math,…

The Enright Arithmetic Program is a diagnostic-prescriptive program designed to facilitate an effective remedial effort. This paper evaluates the effect of the use of the program on the performance of students needing remedial education in mathematics. The program begins by establishing for each student the exact set of skills that the student…

Because little is presently known about changes in children's knowledge of the logical principles of arithmetic and, more specifically, about how children's developing knowledge is reflected in the use of solution procedures, two types of three-term arithmetic problems were presented for solution to 6-, 7-, 9-, 11-, and 20-year-olds. Problems were…

This resource package deals with elementary level mathematics in daily living, substituting newspapers as a refreshing change from mathematics texts. A total of 40 exercises are intended to provide review and reinforcement for skills previously taught in formal lessons. Skill or concept areas included are: reading large numbers; basic operations;…

This program is designed to enable students to master the competencies and skills which reflect the learning goals and objectives developed by the Illinois State Board of Education. This document lists the learning objectives by grade level and reporting period for kindergarten through grade three. Topics included are arithmetic, measurement,…

This review of the relevant literature in the area of numerical facility attempts to clarify the construct of numerical facility and provide guidance for items tapping this ability. The review is presented in five parts. The first section introduces two approaches that can be used to investigate numerical facility, including factor analysis.…