The overarching purpose of this document is to define a new vision for mathematics instruction that explicitly attends to the needs of English Language Learners (ELLs), addressing the interdependence of language and mathematics. The sections in this report are devoted to (1) making clear that the grade-level college- and career-readiness…

This paper describes a model of student attainment of mathematical concepts and its development. In this model three types of activities (developmental, connecting, and abstract) are considered as an overlay on the three ways of representing mathematical concepts (physical/visual, oral, and symbolic). Each activity type involves some means of…

Discussed is research on children's understanding of zero and infinity and teaching suggestions for improving understanding. (RH)

Interviews with fourth, fifth, and sixth graders found that they thought about the concept of average as mode, median, and/or a procedure. Presents approaches to develop the concept of average. (MKR)

Considered are three different types of paper-and-pencil items: labeled word statements, symbolizations, and portrayals. The items are used for testing understanding of mathematical concepts. Limitations of pencil-and-paper items are noted. (RH)

Describes common misconceptions with decimals and suggests activities that can strengthen connections between decimal concepts and fractions, place value, and physical models, such as the number line. Encourages reasoning, communicating, and problem solving. (TO)

Explores the concept worksheet, which can help students identify and analyze important mathematical concepts and is a simple assignment that can be completed by students overnight. Four types of exercises are included: definition, web of attributes, examples, and nonexamples. (MKR)

Too many approaches to mathematics instruction at the elementary level focus only on the production of correct answers rather than on the development of mathematical thinking skills. Author urges encouragement of children's own thought processes. (Author/PGD)

Both good art teaching and good mathematics teaching are based on shared language, problem solving, and planned experiences with many materials to develop concepts and practice skills. This book provides a framework of activities by year level that integrate mathematics and art to enrich the elementary classroom. Each activity lists mathematics…

The authors suggest a few games for which programmable pocket calculators are used to create an environment in which mathematical concepts can be experienced more easily by students. (Author/MK)

Concepts of fractions from an adult perspective as well as from a child's perspective are examined. Types of students' schemes for some terms related to fractions are reported. (YP)

Describes the use of a graphic organizer--webs--to help students learn to connect concepts in mathematics. (MKR)

Included are brief articles on a laboratory approach for teaching basic geometry, having students give examples, and trigonometry and design. (MNS)

The importance of teaching mathematical concepts is stressed. How they can be taught and how preservice teachers can be trained to teach them are delineated. (MNS)

Ways are presented to help students develop precomputational fraction concepts and skills using a circular-region or "pie" model. (MK)