Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

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,…

Beyond Crossroads recognizes that success in the modern world demands higher-level thinking across the mathematical sciences. Broad quantitative literacy skills are essential for the college graduates of today and tomorrow if they are to be informed citizens and productive workers. Such skills include the quantitative aspects of daily life and…

The No Child Left Behind Act has brought great attention to the effectiveness of math and literacy program in U.S. Schools. Literacy instruction was the hot topic of the 1990s, but numeracy has taken center stage in current education debates. Although the importance of literacy skills in other subject areas is quite obvious, the connection between…

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…

Why is it that some schools are more successful that others in improving achievement in literacy and numeracy for those pupils who have barriers to their learning? What is it that makes the difference for the lowest achieving 20% of pupils? Her Majesty's Inspectors visited a number of schools that were making a significant difference for…

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…

This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…

The Eisenhower National Clearinghouse for Mathematics and Science Education (ENC) helps teachers by offering a broad assortment of services to enable them to quickly locate educational resources. This theme issue of the serial "ENC Focus" is designed to give educators information on curriculum resources available for teaching math and science in…

Presents a problem of triangular tiles that involves counting and probability. Includes instructor guiding questions. (KHR)

Two experiments compared 6-month-olds' numerosity discrimination performance on both large numbers and small numbers with both total filled area and total contour length controlled. Results showed that infants succeeded in discriminating 4 from 8 elements, but failed to discriminate 2 from 4 elements, providing evidence for the existence of two…

Argues that adults' relationship with mathematics has three components: cognitive, affective, and social. Focuses on the affective and social components and suggests that the differences between informal mathematics and formal school mathematics lead to the former not being recognized as mathematics. Believes this situation should be analyzed from…

Describes how students can compute and estimate, mentally and rapidly, by using appropriate number relationships. (YDS)