This article highlights the study which illustrates how an age-old board games that incorporate numbers and counting have led to better understanding of numbers by young students. Few family rituals have as fixed a place in the American household, and in the popular imagination, as board games, those impromptu or regularly scheduled contests…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and…

This article is the third in a series of articles describing a research project entitled "Entering into Symbols" (EIS) on the use of mathematical applets at key stages 2 and 3. The first two articles, in "MT200" and "MT203", described applets designed to teach place value ("Tuckshop subtraction") and basic algebra ("Matchbox algebra"). In this…

Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n [congruent to] i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also…

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…

Theoretical analyses of the development of numerical representations suggest that playing linear number board games should enhance young children's numerical knowledge. Consistent with this prediction, playing such a game for roughly 1 hr increased low-income preschoolers' (mean age = 5.4 years) proficiency on 4 diverse numerical tasks: numerical…

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…

A sense of number is now generally recognised as a central factor in learning, and later applying, mathematics. Consequently, number sense is increasingly emphasised in curriculum documentation related to mathematics. The "Primary School Curriculum: Mathematics," published by the Government of Ireland in 1999, is no exception. It…

The name of Zoltan P. Dienes (1916- ) stands with those of Jean Piaget, Jerome Bruner, Edward Begle, and Robert Davis as a legendary figure whose work left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the multibase blocks that he invented for the teaching of place value. Among numerous other things,…

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…