The author describes a Piaget based curriculum involving three main themes (classification, number measurement/space, and seriation) for young mentally retarded children. Students solve problems by doing something physically and mentally to the data, shuffling the facts about in their minds, so that they will come to a logical solution. Language…

THE THIRD YEAR OF ARITHMETIC INSTRUCTION SHOULD UTILIZE SOCIAL SETTINGS FOR LEARNING AS WELL AS MANIPULATIVE AND GRAPHIC MATERIALS. THE NUMBER SYSTEM, IN COUNTING, SHOULD DEVELOP THE SKILLS OF COUNTING BY 3'S AND 4'S AND OF RECOGNIZING ODD AND EVEN NUMBERS. CHILDREN SHOULD GAIN THE ABILITY TO READ AND WRITE NUMBERS TO FOUR PLACES. THE WHOLE…

Thirteen research reports related to mathematics education are abstracted and critiqued in this publication. The topics of the research include counting, addition, subtraction, ratio, proportion, geometry, problem solving, and teaching strategies. Also included is an editorial comment by T. Kieren on mathematics education research. Research…

To ascertain if children's use of manipulatives and/or the teacher's presentation of the problem in parts (chunking) affect children's ability to model and/or solve addition and/or subtraction problems, 146 first-grade subjects were administered the Houston Addition and Subtraction Problem-Solving Test which provided accuracy and modeling scores…

This study compared the error patterns of third- and fourth-grade children on addition, subtraction, and multiplication exercises in horizontal and vertical formats. The research design used parallel eight-item tests for each operation; the only difference between items on parallel forms was the formal (horizontal or vertical) of the computational…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include the decimal system, exponential notation, base seven, and the binary and duodecimal…

This is part one of a three-part SMSG mathematics text for seventh-grade students. The text was written for those students whose mathematical talent is underdeveloped and is essentially the same subject matter presented in the SMSG text. Chapter topics include: (1) what is mathematics; (2) number symbols; (3) whole numbers; (4) non-metric…

This is a first-grade manual for teachers using SMSG elementary school text materials. For each chapter background information is given; for each section, objectives, vocabulary, materials, suggested procedures, and further activities are listed. Chapter topics include: (1) pre-number experiences; (2) recognizing geometric shapes; (3) building…

This publication identifies some of the underlying ideas relevant to improved mathematics programs of the elementary school. This publication does not prescribe a course of study. It does, however, provide ideas to assist school personnel in their analysis of mathematics programs and textbooks. It presents an orderly outline of topics and concepts…

The Materials in this bulletin indicate suggested teaching procedures needed to implement the teaching of "mathematics, 9th Year" as outlined in Curriculum Bulletin No. 3, 1958-59 series, Course of Study Mathematics 7-8-9. Whereas the course of study suggests the application of mathematical principles such as commutativity,…

This paper notes three objections to the use of hand-held calculators in schools: they would (1) block reasoning, (2) make individuals machine-dependent, and (3) broaden the gap between developed and underdeveloped nations. Each is addressed, with specific examples used to refute them. The belief is strongly expressed that calculators can aid in…

This book is part 1 of a 2-part manual for teachers using SMSG text materials for grade 4. 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 need to promote mathematical creativity and suggestions for developing it are discussed in this document. The largest portion of this document consists of a collection of problem sheets, arranged according to 26 content areas. Puzzles, activities, and a variety of problems are included, with an answer key. An annotated bibliography of selected…

The author investigates elementary school students' performance when solving selected open distributive sentences in relation to three factors (Open Sentence Type, Context, Number Size) and identifies and classifies solution methods attempted by students and students' errors in performance. Eighty fifth-grade students participated in the…

The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection…