We applied overlapping waves theory and microgenetic methods to examine how children improve their estimation proficiency, and in particular how they shift from reliance on immature to mature representations of numerical magnitude. We also tested the theoretical prediction that feedback on problems on which the discrepancy between two…

In this article, we show how "Laplace Transform" may be used to evaluate variety of nontrivial improper integrals, including "Probability" and "Fresnel" integrals. The algorithm we have developed here to evaluate "Probability, Fresnel" and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals…

Number processing is characterized by the distance and the size effect, but symbolic numbers exhibit smaller effects than non-symbolic numerosities. The difference between symbolic and non-symbolic processing can either be explained by a different kind of underlying representation or by parametric differences within the same type of underlying…

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

These Proceedings are a written record of the research presented at the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2011) held in Reno, Nevada, October 20-23, 2011. The theme of the conference is Transformative Mathematics Teaching and Learning. The Proceedings…

Observation of patterns constructed on geoboards can lead to discussions of properties of primes, number sequences, and complex numbers. (SD)

Five open-ended problems are suggested which lead students to investigate basic number properties and numeration characteristics. (JP)

This is volume one of a three-volume set for teachers using SMSG junior high school text materials. Each unit contains a commentary on the text, answers to all the exercises, a copy of the questionnaire used for evaluating the material, and a summary of comments by the teachers using the text. Unit topics include: (1) numeration; (2) natural…

This text is one of the sequence of textbooks produced for low achievers in the seventh and eighth grades by the School Mathematics Study Group (SMSG). There are eight texts in the sequence, of which this is the sixth. This set of volumes differs from the regular editions of SMSG junior high school texts in that very little reading is required.…

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…

Describes a three-week summer course for academically talented high school students which explored the integers and some classical topics from number theory. (PK)

A chart is described which gives children an opportunity to discover prime and composite numbers and which leads to discussions of the associative and commutative laws, multiplication by 1, and powers and exponents. (DT)

In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…

Reviewing addition through the use of palindromes is discussed. A rule for converting any number into a palindrome is presented. (MP)