Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

Equal representation as a social issue is about the participation of one social group, in a particular context, in proportion to the numbers in the group within the total population. The proportion of women in parliament, and of the participation rate of students of lower socioeconomic status in higher education, are examples. The aims of this…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item…

The three purposes of this study were to (a) describe fraction ordering errors among at-risk fourth grade students, (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors, and (c) examine the effect of students' ability to explain comparing problems on the probability…

A critical numeracy examination of Benford's Law suggests that our understanding of the integers is faulty. We think of them as equally likely to turn up as the first digit of a random real world number. For many real world data sets this is not true. In many cases, ranging from eBay auction prices to six digit numbers in Google to the…

In this article, Derek Hurrell, points out that while it's easy to fall into the impression that the proficiency strand "Fluency" is all about knowing basic number facts in all its many and splendid ways. He add it is easy to overlook, that within Fluency there are requirements that are based in Algebra; Measurement and Geometry; and…

In this proposal, I introduce a method for modeling the dynamics of a sixth-grade student's accommodation of his fractions scheme to include a disembedding operation (Steffe & Olive, 2010). I will describe a three-part approach consisting of a constructivist teaching experiment, retrospective analysis, and stochastic modeling of the student's…

This compendium organizes information on the math and science projects sponsored by NCER and NCSER into two main sections: Mathematics and Science. Within each section, projects are sorted into chapters based on content area, grade level, and intended outcome. In determining the chapters, we considered the emerging college- and career-readiness…

Simple experiences with probability can extend third graders' understanding of the need for fractions. Three activities are given which build on language-arts experiences and incorporate concepts in multiplication, graphs, and fractions. (MNS)

This book is written to answer commonly asked homework questions of fourth, fifth, and sixth graders. Included are facts, charts, definitions, explanations, examples, and illustrations. Topics include ancient number systems; decimal system; math symbols; addition; subtraction; multiplication; division; fractions; estimation; averages; properties;…

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics curriculum. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…

This is an experimental SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include why study mathematics, decimal and non-decimal numeration, the…

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics program. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics curriculum. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…