We discuss mathematical tasks used in a first mathematics content course for elementary teachers at our university to foster a deep conceptual understanding of early arithmetic, including basic concepts of number, number relationships and strategies, and coordinating units of different rank. Our approach is to immerse our students in a base 8…

This study examined the neuronal correlates of reading Roman numerals and the changes that occur with extensive practice. Subjects were scanned by functional Magnetic Resonance Imaging (fMRI) three times the first day of the experiment and once following two to three months of practice. This allowed comparison of brain activations with varying…

In this study, Piagetian theory is extended to explore ways in which children construct their understanding of our notational system and place value. Eighty children aged 4 to 9 were asked to group objects, draw pictures of grouped quantities, write numerals to indicate amounts, and theorize about the relationship between their written numerals…

The system of International Standard Book Numbers uses a check code based on modular arithmetic. This system, the use of a simple machine to compute check digits, and related classroom activities are described. (SD)

Activity questions based on the prime factorization of numbers can be answered by reference to the lattice structure of factors. (SD)

Activities involving set union and intersection, graphing solutions of open sentences, and negation are described. These activities afford students with opportunities for computational practice as well as instruction on equations and inequalities. (SD)

The author observes that checking the closure property is redundant for most number systems and therefore hard for students to understand. He defines several systems which are not closed, develops two concepts related to closure, and provides many related examples. (SD)

The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

A GROUP OF REPRESENTATIVES FROM FIVE SCHOOLS MET FOR TWO WEEKS TO DISCUSS MEANS OF IMPROVING ARITHMETIC TEACHING. THE CONTENT OF EACH GRADE WAS EXAMINED. THE PURPOSE WAS TO DETERMINE VARIOUS APPROACHES TO MOTIVATE BETTER LEARNING. NOTES OF THESE MEETINGS HAVE BEEN REPRODUCED AND SUGGESTIONS FOR TEACHERS OFFERED. TEACHERS SHOULD PROVIDE MANY…

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 a new kind of addition and multiplication, operations, closure, identity, mathematical…

This is part one of a two-part SMSG elementary school text for fifth-grade students. The content is aimed at the development of some of the fundamental concepts of mathematics such as number, numeration, the operations of arithmetic, and intuitive geometry. Chapter topics include extending systems of numeration, factors and primes, extending…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

Chapters 7-8 of the special materials for low achieving students in grades 7-8 by SMSG deal with properties of the rational numbers and elementary probability. Included for each chapter are pretest exercises, a self-test, instructional lessons and exercises, and a chapter test. (CT)

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and…