Specific suggestions for teaching young children (ages 5-7) mathematical principles are offered, covering such concepts as addition, subtraction, multiplication, division, arithmetical laws, and utilizing a story to teach various mathematical concepts and skills. (DB)

Describes four easy-to-construct board games and puzzles that teachers can use to strengthen their students' mathematical problem-solving skills in both the classroom and the real world. (MDM)

Discusses the role of conjectures in learning mathematics, how conjectures demonstrate mathematical power, and how conjectures build understanding and encourage connections. (ASK)

Provides an overview of the conceptual analysis of the unit fraction that provided the framework for developing a comprehensive array of fraction activities for fourth-grade students. Reveals the students' difficulties in learning the unit-fraction concept and discusses the didactical implications of these difficulties. Contains 15 references.…

Dependence on algorithms is as insidious as dependence on technology. States that many children and adults lack the facility to recognize and work with relationships in and between numbers and number operations. (ASK)

Examines students' understanding of the quantitative relationships, operations, and properties of relationships and operations that are introduced in arithmetic and beginning algebra courses. Develops alternative approaches to the teaching of structure such as the structural-to-computational model and the procedural-to-structural model. Concludes…

Interviews with 12 adults in General Educational Development classes, four adults in basic math, and 22 preservice teachers assessed their understanding of the part-whole concept, a key element in math success. Gaps in understanding were found in all three groups. (SK)

Presents a problem introducing pupils to the ideas of consecutive and integer while practicing addition. Investigates the overall pattern of results with regard to formulating some general results, considers the algebra of the problem, and suggests proofs of why some numbers can and others cannot be formulated in this way. (ASK)

Suggests scales as alternative representations of numerical concepts and operations that can be used as arithmetic-mean machines, adding machines, multiplication machines, and geometric-mean machines. (ASK)

Presents solutions for a problem concerning doubling a recipe from a previous article on number concepts in the October 1997 issue. (ASK)

Presents research on students' use and understanding of algorithms in Poland. Concludes that there are detrimental side effects that stem from the teaching and learning of standard written algorithms. (ASK)

Discusses the role of play in the learning of mathematics. Describes a play for the third grade mathematics classroom that focuses on negative numbers and number concepts, and revisits Vygotsky from this point of view. Concludes that mathematically imaginative play can contribute greatly to mathematics learning in elementary school. (Contains 20…

Giving children time and encouragement to explain methods of calculation is a useful strategy. Uses this strategy with a group of children and discovers surprising thinking by one child on number facts. (ASK)

Discusses ways to improve the understanding of problems involving combination and complementation. Analyzes three children's initial mental representations, procedures, and reflections when presented with four different situations. Concludes with the impacts of the logico-mathematical relation of inclusion in these processes. Contains 31…

Presents a lesson that provides students in the early primary grades with the opportunity to explore counting techniques and develop an informal sense of permutations and combinations. (Author/CCM)