In August 2008, the National Council of Teachers of Mathematics (NCTM) brought together approximately 60 mathematics education researchers and practitioners for a 4-day working conference. During this working conference, the participants analyzed over 350 mathematics education practitioner-generated questions in seven areas: assessment,…

Research findings related to the development of language, abstract reasoning, and problem solving-skills by children from three to eight years old are integrated by consideration of classroom implications. Individual differences, the teacher-child relationship, and other topics are also discussed in this context. (SD)

Several issues concerning mathematics curriculum for the primary grades are discussed. Five considerations necessary for building a balanced curriculum are defined and discussed: broadening content, providing variety in learning and thinking strategies, balancing emphasis on skills, concepts and applications, discretion in use of manipulative…

Research on mathematics learning is integrated and organized around groups of questions emerging from the primary classroom. Subjects covered include attitudes, diagnosis, readiness, effective use of concrete and manipulative materials, the role of language and vocabulary, presentation of specific content and techniques, selection of algorithms…

Characteristics of good problems for primary school children are described and illustrated in discussions of sample problems. A collection of problems meeting these criteria is presented and annotated, and the organization of the classroom for problem-solving activities is discussed. (SD)

After a discussion on planning instruction, a series of activities designed to develop pre-number and number concepts are presented. Activities are arranged by difficulty within sections devoted to classifying, comparing, ordering, measuring, organizing data, distinguishing shape and size, recognizing patterns, number awareness, and counting. (SD)

The development of number concepts from conservation through order and place value notation is discussed in the context of applications to classroom instruction. Activities designed to motivate, build, and reinforce these concepts are described, and a list of objectives is presented in the form of a suggested progress record. (SD)

Instruction on properties of whole numbers, the meanings of operations on whole numbers, symbolic representation and algorithms for completing these operations is discussed. Many activities appropriate to each of these topics, and suitable for primary school children, are presented. (SD)

A series of activities designed to help primary school children understand the meaning of the term "fraction," the symbolization, and equivalence of fractions are presented. Identification of units and pictorial representation are stressed, as is the uses of concrete materials. (SD)

The value and technique of pre-geometry and geometry instruction in the primary grades are discussed. Geometric concepts such as open and closed figures, connectedness, similarity, congruence, straightness, and angle are presented through suggested activities, lesson plans, and evaluation procedures. (SD)

The nature of measurement, the standard measurement concepts are discussed in terms of children's preconceptions and activities for building measurement concepts through primary school instruction. A broad range of activities including counting, computation, calibration, and relating measure to size is presented. The metric system is briefly…

Activities related to content areas important to the primary mathematics program, but outside the scope of arithmetic, geometry and measurement, are presented. Topics include relations, number sentences, solving sentences, logic, probability, statistics, number theory, and the system of integers, Inclusion of these topics is justified and…

Citing a number of instances in which measurement is an important part of everyday life and of scientific procedures. The author argues that measurement is necessary to modern society. (SD)

After considering the mathematical system common to various types of measure, the author argues that instruction needs to reflect the common aspects of measure systems as well as the distinctive attributes of different systems. (SD)

Research findings related to children's concepts of length, area, volume, weight and time are reviewed. Implications for instruction in measurement of these qualities are discussed. (SD)