In this note properties of two sequences generated by the recurrence relation G[subscript n] +2 = 4 G[subscript n] +1 - G[subscript n], are studied. It is shown that one of the sequences leads to a family of diophantine triplets. Some interesting properties of these sequences are also established.

The present study focused on two main goals. One was to test the "representational mapping hypothesis": The greater the transparency of the mapping between physical materials and desired internal representations, the greater the learning of the desired internal representation. The implication of the representational mapping hypothesis in the…

This dissertation investigated the conceptual schemes children constructed as they related division number sentences to various types of fractions: Proper fractions, improper fractions, and mixed numbers in both contextual and abstract symbolic forms. It was hypothesized that student's understanding depends heavily on the role played by factors…

This paper discusses some issues that arose in the context of a three-year research project on Indigenous mathematics teacher education in the Northern Territory of Australia. The project was based on the premise that Indigenous student numeracy outcomes are more likely to be improved where students can work on key number ideas and strategies in…

The high incidence of number transcoding deficits in aphasic subjects suggests there is a strong similarity between language and number domains. However, recent single case studies of subjects who showed a dissociation between word and number word transcoding led us to hypothesize that the two types of stimuli are represented independently in the…

We report a patient (MT) with a highly specific alexia affecting the identification of letters and words but not numbers. He shows a corresponding deficit in writing: his letter writing is impaired while number writing and written calculation is spared. He has no aphasia, no visuo-perceptual or -constructional difficulties, or other cognitive…

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…

This paper describes a study that examined parents' beliefs about children's number skill development. Twenty-seven parents of 4- and 5-year-olds were interviewed about number tasks that could be solved by children between the ages of 4 and 7 years. In addition, parents were asked a series of open-ended questions about how they would answer a…

Hypothesizing that subtraction of (negative) integers requires formal operations, the author describes a study of children's understanding of related concepts. The study involves the use of apparatus embodying properties of the number line. (SD)

The author describes a model for operations on the set of rationals. Thi s model, used by students in a laboratory situation, is based on an easily constructed number balance. (SD)

By varying task conditions and constraints on subjects, this study attempted to extend and refine a developmental theory of partitioning as a foundational process undergirding children's construction of a rational number. Subjects were 31 preponderantly higher-grade pupils enrolled at an elementary school in Nova Scotia, Canada. Two tasks were…

A two-year study was conducted with fourth-grade children in the context of extensive teaching experiments concerned with the learning of rational number concepts. Representational difficulties in using the number line model were investigated. While instruction in the second year attempted to resolve observed learning difficulties, the results of…

The activities presented are all designed to encourage children to learn about the structure of whole numbers by looking at number patterns in various ways. (DT)

Instruction on properties of whole numbers, the meanings of operations on whole numbers, symbolic representation and algorithms for completing these operations is discussed. Many activities appropriate to each of these topics, and suitable for primary school children, are presented. (SD)