The article deals with issues concerning the abductive-inductive reasoning of 42 preservice elementary majors on patterns that consist of figural and numerical cues. We discuss: ways in which the participants develop generalizations about classes of abstract objects; abductive processes they exhibit which support their induction leading to a…

There has been a lot of material written about logarithmic spirals of golden proportion but this author states that he has never come across an article that states the exact equation of the spiral which ultimately spirals tangentially to the sides of the rectangles. In this article, the author intends to develop such an equation. (Contains 5…

Two related sequences of definite integrals are considered. By mixing hand-work, computer algebra system assistance and websurfing, fine connections can be studied between integrals and a couple of interesting sequences of integers. (Contains 4 tables.)

A functional magnetic resonance imaging (fMRI) study was performed on a 4-year-old girl with autism. While sedated, she listened to three utterances (numbers, hello, her own first name) played through headphones. Based on analyses of the fMRI data, the amount of total brain activation varied with the content of the utterance. The greatest volume…

Children differ in how much they spontaneously pay attention to quantitative aspects of their natural environment. We studied how this spontaneous tendency to focus on numerosity (SFON) is related to subitizing-based enumeration and verbal and object counting skills. In this exploratory study, children were tested individually at the age of 4-5…

The fourth of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Topics include ratio, proportion, and percentage…

This numeracy package, which is intended for use by facilitators in group or tutoring situations, consists of materials designed to help adult literacy students understand number systems, appreciate the different roles that numbers play in daily life, and gain the confidence needed to work with numbers in everyday situations. Part 1, which…

In this paper four programs are described in which children learn multidigit number concepts and operations with understanding: (1) the Supporting Ten-Structured Thinking projects, (2) the Conceptually Based Instruction project, (3) Cognitively Guided Instruction projects, and (4) the Problem Centered Mathematics Project. The diversity in these…

This set of 13 activities, adapted from "Mathmatters: Developing Computational Skills with Developmental Activity Sequences (by Randall Souviney, Tamara Keyser, and Alan Sarver) was designed to help teachers using the Indigenous Mathematics Project materials (in Papua New Guinea) understand the basic processes involved in computation with…

A model for multiplication is described and used to discuss the properties of division. (SD)

The first edition of the counting workbook centers around the numbers from 1 to 100 and focuses on number and set concepts. The workbook introduces the Makah spelling of each number and reinforces the spelling with exercises such as matching words to numbers, writing the words, counting symbols, and circling the correct number. Spaced throughout…

A method for generating 3x3 magic squares is developed. A series of questions relating to these magic squares is posed. An invesitgation using matrix methods is suggested with some questions for consideration. (LS)

The development of number concepts from conservation through order and place value notation is discussed in the context of applications to classroom instruction. Activities designed to motivate, build, and reinforce these concepts are described, and a list of objectives is presented in the form of a suggested progress record. (SD)

Directions are presented for the construction and use of line-segment strips. Examples demonstrate activities, integrate elementary geometry and arithmetic instruction. (JP)

Topics that deal with prime numbers are presented with the intent of allowing the student to re-create the excitement of the original investigation. Suitable for advanced high school students as an introduction to number theory at the college level or as a text for courses in teacher education, the book covers the following topics: (1) the number…