Constantly on the lookout for Canadian mathematics education matters, because if Canadian mathematics education matters then Canadian mathematics education matters, three young university bookstore employees, university students, unable to make proper change when I handed them a five dollar bill for a sticker I was purchasing for my laptop,…

This commentary summarizes emerging research into fractions instruction for students who are at risk for failure. Each of the three articles emphasizes a measure conception of fractions. Teaching fractions as measurement helps students learn the magnitude of rational numbers. However, measurement is only part of the way that students should…

In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…

It is of deep interest to both linguists and psychologists alike to account for how young children acquire an understanding of number words. In their commentaries, Barner and Butterworth both point out that an important question highlighted by the work of Syrett, Musolino, and Gelman, and one that remains highly controversial, is where number…

Weiss, Keith, Zhu, and Chen (2013a) and Weiss, Keith, Zhu, and Chen (2013b), this issue, report examinations of the factor structure of the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV) and Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV), respectively; comparing Wechsler Hierarchical Model (W-HM) and…

This discussion article addresses issues related to expansion of the Wechsler model from four to five factors; multiple broad CHC abilities measured by the Arithmetic subtest; advantages and disadvantages of including complex tasks requiring integration of multiple broad abilities when measuring intelligence; limitations of factor analysis, which…

The Organization for Economic Cooperation and Development [OECD] is a global policy organization that includes the United States and about half of the Western Europe countries. It administers international comparison tests, called Programme for International Student Assessment (PISA), for 15 year-old students in Mathematics and other subjects. I…

As a result of his review of 52 sets of K-12 mathematics standards--for the 50 U.S. states, the District of Columbia, and the Common Core State Standards Initiative--the author finds that the majority of U.S. states fail to focus on the mathematics that elementary school children need to learn to be successful in college math. Arithmetic is the…

This article focuses on the first school for indigenous girls in Algeria that opened in Algiers in 1845. The founder, Eugenie Luce, taught girls the rudiments--French language and grammar, reading, arithmetic, and Arabic, while the afternoon hours were devoted to sewing. This early focus on teaching French in order to achieve the "fusion of…

In the last three decades there have been a variety of studies of what is often referred to as "everyday" or "street" mathematics. These studies have documented a rich variety of arithmetic practices involved in activities such as tailoring, carpet laying, dieting, or grocery shopping. More importantly, these studies have helped to rectify…

The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses…

This paper illustrates a different conception of arithmetic, an arithmetic with reasons as well as rules. This arithmetic includes making connections between different representations and making sense of rules as well as using them. It provides a foundation for "Algebra the Web of Knowledge and Skill" in the sense that algebra can be…

Discusses flaws in the reasoning behind a "new system" proposed for rounding numbers that was published in a previous issue of this journal. Concludes that the new system should be used only for numbers in which the nonzero digits following a dropped 5 have some significance. (JRH)

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

"Children's Choices," a project of a joint committee supported by the International Reading Association (IRA) and the Children's Book Council, is published annually in "The Reading Teacher." Books recommended by children are grouped by levels: Beginning Reader (ages 5-7); Young Readers (ages 8-10); and Advanced Readers (ages…