Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured…

This in-brief technical report documents the results from two different analytic approaches for examining the reliability of the slope for easyCBM® math measures in Grades K-8. Results varied by grade, assessment measure, and the analytic approach. Results patterns are discussed.

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…

This report examines trends in student learning. Using data from the National Assessment of Educational Progress, the first section reports on current trends in reading and mathematics test scores, highlighting arithmetic and noting that student's computation skills have stagnated or declined in recent years. The second section revisits the…

This brief report is a compilation of academic test score data collected on children in the Responsive Educational Programs sponsored by the Far West Laboratory. In some cases sampling was done and statistical tests run. In other situations sampling was not possible and comparisons are made with national norms. Diagrams and figures are given for…

This instructor's guide contains materials for a course designed to prepare employees for statistical process control (SPC) training given at their workplace by refreshing math skills and building the concepts and vocabulary necessary to understand SPC in manufacturing environments. SPC-Prep 1 addresses the math skills necessary to perform SPC…

The purpose of the study was to determine what factors affect success in passing the General Education Development (GED) exam. Using data gathered between 1960 and 1972 from 200 successful GED students at the Mattoon Area Adult Education Center, Ill., the authors developed frequency distribution charts to characterize the students and scattergrams…

In the 1980-81 school year, the Title I program in Lafayette Parish, Louisiana, initiated research into the effectiveness of computer-assisted instruction (CAI) for mathematics in grades 3-6. Children from two lower socioeconomic area schools, who were one or more years below grade placement but were already making gains of 6-9 months due to an…

The study of the public-school system of Wilmington, Delaware, of which this bulletin is a part, was made by the United States Commissioner of Education upon invitation of a committee of 30 citizens of Wilmington appointed by the board of education, by the city council, and by the mayor of the city, and empowered to arrange for such a study. In…