A method of using a modified number line to illustrate concepts of addition, subtraction, multiplication, and division in a modular system is presented. (DT)

Illustrated are the discovery and verification of new patterns in Pascal's Triangle. Discovery activities appropriate for students when they are learning to expand binomials are provided. (JP)

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 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…

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…

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,…

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

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

After prime factors of a set of numbers are listed, geometric shapes are used to find the prime factors of the least common multiple (LCM). (MNS)

A distinction is made between an algorithm and the justification for the algorithm. Examples of both are given for the operations with whole numbers. (DT)

This paper describes the PD program that was delivered during the first year of the study. The main goal of the intervention was to increase teachers' capability to teach positive rational number topics effectively. The program included a 3-day summer institute (18 hours per teacher), five 1-day seminars held during the school year (30 hours per…

The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an…

In this second of a series of four articles, the author deconstructs the primary national strategy's (PNS) approach to written subtraction. The approach to subtraction is divided into three stages: using the empty number line; partitioning; and expanded layout leading to column methods (called "standard methods" in the consultation document). The…

Described is an activity in which students develop their own number system. This activity allow students to examine the structure and history of number systems and to discover the power and respectable efficiency of the number system used today. (KR)