The purpose of the two studies reported was to develop and validate clinical assessment instruments designed to identify both the progress of learners through a hierarchy of mathematics content and the mode of presentation through which learners can best handle the content. In Study 1, 73 second graders were given one of two forms of a 15-item…

This volume consists of the following ten papers, which were presented at the second Hokan-Yuman Languages Workshop, held at the University of California at San Diego in June 1976: (1) "The Havasupai Writing System," by Rena Crook, Leanne Hinton, and Nancy Stenson; (2) "The Upland Yuman Numeral System," by Martha B. Kendall;…

This guide contains an outline of topics to be included in individual subject areas in secondary school mathematics and some specific suggestions for teaching them. Areas covered include--(1) fundamentals of mathematics included in seventh and eighth grades and general mathematics in the high school, (2) algebra concepts for courses one and two,…

This book is part 1 of a 2-part manual for teachers using SMSG text materials for grade 6. The purpose for each of 5 chapters is stated and mathematical background for the teacher is presented. Detailed lesson plans are then provided, including sequences of statements and questions, activities, and exercise sets with answers. Needed materials and…

The title of this mathematics text for preservice elementary teachers is intended to suggest the book's theme of mathematics as an abstraction from human experience with sticks (lines, segments), stones (sets, counting) and other objects. An introductory chapter which describes the objectives of the author and discusses learning and attitudes…

The primary aim of this guide is to aid teachers in planning and preparing a senior high school mathematics course for students preparing for college work. It is divided into separate one-semester courses of seven chapters each. The first-semester course consists of a traditional approach to the introduction of trigonometry and trigonometric…

This curriculum guide for grades K-6 is the first volume of a two-part series. It is meant to provide an ordered sequence of mathematical concepts from which teachers may organize an arithmetic program allowing for individual student progress with the greatest amount of individual attention. Each topic is arranged into levels based on the topic's…

This paper seeks to formulate a principle that explains the working of the Japanese number system with respect to Japanese nouns and that defines the kinds of nouns and contexts that condition the forms of number expressions. It is the author's theory that in applying numbers to nouns, the Japanese make a formal distinction between things they…

MIDDLE-CLASS, FIRST-GRADE STUDENTS (100) WERE TESTED INDIVIDUALLY ON 4 ITEMS OF CONCEPT OF ADDITION AND CONSERVATION OF NUMBER. THE TEST ITEMS WERE IDENTICAL EXCEPT FOR THE NUMBER OF OBJECTS INVOLVED. FOR EACH ITEM, TWO PILES OF CANDY WERE PLACED BEFORE EACH CHILD AND THEN MOVED TOGETHER. THE STUDY SHOWED NO MAJOR DIFFERENCE IN THE MEAN…

This volume presents a partial description of the lessons in the preliminary version of the PLATO fractions curriculum. Each lesson has three parts: review, new material, and a student-selected option. Students receive immediate feedback from the computer as they progress through each lesson. Five groups of lessons are described: meaning of…

The introduction of prime numbers in the intermediate grades should be handled with care or the concept will appear arbitrary, artificial, and unreal to the pupils. The approach suggested here is in the form of a game-like activity. A knowledge of multiplication and factors is a prerequisite. (BB)

College students, in three experiments, learned to recite a counting pattern in the base three number system. Although all subjects learned to a criterion of two errorless trials, learning with different rule systems resulted in different levels of understanding and performance on transfer tasks. (GDC)

The emergence and differentiation of partitioning as a process that leads young children to construct ideas of rational numbers was traced through clinical sessions with 43 primary children as they manipulated objects. The data analysis led to a five-level theory of the partitioning process. (MNS)

While most elementary teachers experience little difficulty using the decimal system for whole numbers, many do not have the desired depth of understanding for teaching the system. The focus of the material is stage-by-stage creation of a hypothetical numeration system. (MP)