This paper provides principles which can be used to mark mathematics papers in secondary schools. Sections included are: (1) "Drafting the Marking Scheme" (describing 15 general considerations); (2) "Calculations" (listing 16 grading principles on computation papers); (3) "Graphs" (providing four guidelines on graph papers); (4) "Constructions"…

This document is part 1 of the workbook for grade 2 pupils in the Comprehensive Instructional Management System, a unified mathematics curriculum for kindergarten through grade 7. Each objective is developed by a variety of strategies, with mastery of objectives diagnosed through a testing component. The activities in the student workbook are…

This is the teacher's manual to accompany part 2 of the workbook for grade 5 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fraction ideas and to emphasize estimation. It was determined that all students possessed a rich store of prior…

Some recent research findings with implications for improving mathematics instruction are reviewed in this report. The focus is on two topics: computation, in particular subtraction and estimation, and problem solving. Findings about each are listed, with references for each cited study included. Effective algorithms and strategies used by…

Following instructions provided in the teacher's manual, the SCOPE Mathematics Achievement Test booklet for grade 2 presents 10 mathematical concepts. Testing items are: counting number of objects in a set to 100; using ordinals to the 31st; forming numerals correctly; writing number words to 10; identifying and naming the number of 10's and 1's…

To determine how children cope with some of the demands imposed on them by arithmetic word problems, 200 sixth-graders were asked to solve prolems modeled after those used by the National Assessment of Educational Progress. A quantitative demand was imposed on the children by adding extraneous information to the problems, and a verbal demand was…

Parents have many opportunities every day to develop, nurture, and refine their children's mathematics skills. This pamphlet was designed to help parents become aware of these opportunities and to encourage them to participate in their children's learning process. Estimation is the skill of making a reasonably accurate guess and is prominently…

In the spring of 1977, the University of Washington Faculty Senate revised the undergraduate admissions system to include equitable means for admitting freshmen and transfer students. Generally, the University adopted the position that it is the best qualified individuals who should be admitted, with best qualified being defined as those having…

This report presents a theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction. The best-fitting distribution of fixation durations with a relatively simple theoretical justification…

This document focuses on one child's skip counting methods. The pupil, a second grade student at Steuben School, in Kankakee, Illinois, was interviewed as she made several attempts at counting twenty-five poker chips on a circular piece of paper. The interview was part of a larger study of "Children's Conceptions of Number and Numeral,"…

Many children are known to leave school with mathematical deficiencies, particularly from the inner city. While manipulatives are generally used to teach and reinforce understanding of operations, concepts, and abstractions, the use of concrete objects is not viewed to fully involve the student in the learning process. A finger system of…

This document consists of a list of the references on calculators which were collected by the Calculator Information Center prior to June 1979. Included are references which previously appeared on bulletins distributed by the Center, plus articles from newsletters and similar less readily available sources and from non-American sources. Most…

This is unit three of a fifteen-unit secondary mathematics textbook. This unit contains two chapters. The first chapter discusses integers and the second chapter discusses rational numbers. Operations with both types of numbers as well as the structure of the systems are discussed. (MK)

Research on the structures and processes involved in simple mental arithmetic is reviewed. Results suggest that mental arithmetic is a memory retrieval phenomenon, which develops with the experiences of elementary school and can be understood in general as retrieval from organized network representations. Simple mental addition with basic facts…