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…

The study examined the ability of preschool-age children to solve five format exemplars of number-numeral correspondence. Results indicated that some children were able to solve number-numeral correspondence problems in some formats and not in others. This deficiency was remediated by training in one, two, or (at most) three format exemplars.…

This article discusses the summability of some divergent series by Cesaro's method of successive arithmetic means. (MM)

Explores whether 5-month-old infants (N=56) develop numerical- or location-based expectations by using a violation of expectation paradigm with possible and impossible events. Reports that infants use a more abstract representation than object location, the numerical nature of which is discussed. Contains 25 references. (Author/ASK)