Thirty-six Korean first graders were interviewed to study their ability solving addition problems with sums of 10, single-digit sums between 10 and 18, and subtraction problems with minuends between 10 and 18. Finger methods to show sums over 10 and the regular named-10 Korean number words supported their learning of 3 efficient recomposition…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article describes how the story of Alice in Wonderland helps students understand the operation of multiplying by a rational number less than 1 and related aspects of ratio and proportion. Included with this article is a "How Tall Is Alice?" Worksheet. (Contains 1 table and 6 figures.)

This article explores how counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. It is suggested that the teacher's role is one of noticing, questioning,…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

Children's literature can play a significant role in integrating math and science concepts into real-world applications. One particularly delightful selection is "Cucumber Soup" (Krudwig, 1998). This book can create a context--making cucumber soup--for weighing and for a real-life on adding fractions. This kind of learning context takes children…

Although many studies have examined the alignment of state standards with large-scale assessment and instruction, fewer have attended to alignment concerning alternate assessments for students with significant disabilities. This study was designed to (1) compare expectations in one state's alternate assessment (AA) with curricular priorities…

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…

This article describes a recent and successful initiative on teaching place value and the decomposition method of subtraction to pupils having difficulty with this technique in the 9-12-year age range. The aim of the research was to explore whether using the metaphor of selling chews (i.e., sweets) in a tuck shop and developing this into an iconic…

In 2 experiments, the efficacy of motor imagery for learning to type number sequences was examined. Adults practiced typing 4-digit numbers. Then, during subsequent training, they either typed in the same or a different location, imagined typing, merely looked at each number, or performed an irrelevant task. Repetition priming (faster responses…

Piagetian tasks have more to do with the child's ability to inhibit interference than they do with the ability to grasp their underlying logic. Here we used a chronometric paradigm with 11-year-olds, who succeed in Piaget's conservation-of-weight task, to test the role of cognitive inhibition in a priming version of this classical task. The…

"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

Few studies investigating the impacts of teacher characteristics and beliefs about the importance of early skill learning have included measures of children's learning outcomes. This study investigated how teachers' educational attainment, experience, and beliefs impact the development of letter identification and number concepts (enumeration,…

Noting that many parents who might teach their young children are often discouraged by a lack of information or fear of being labeled "pushy," this book provides parents with a step-by-step program for teaching preschoolers letters and numbers as a way of giving children a head start on formal education. The handbook consists of a…