Investigates the problem-posing abilities of third-grade children who displayed different profiles of achievement in number sense and novel problem solving. Concludes that children had difficulties in posing a range of problems in formal contexts in contrast to informal contexts, and children of different achievement profiles displayed different…

How can a chain with 63 links be cut in 3 places so that you could hand a person any number of links from 1 to 63? Considers variations on the problem and derives a general formula. (TO)

Describes five basic understandings involved in rational counting: (1) groupings of same or different items may be counted; (2) there is a stable order of the counting numbers; (3) one-to-one correspondence; (4) it does not matter which item is counted first; and (5) the cardinal principle. Discusses the importance of rational counting ability and…

Presents activities that can be helpful in establishing a conceptual basis for dividing rational numbers. Some activities involve metric units while others are appropriate for small-group work with calculators. (AIM)

Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…

Identifies big ideas for the informal study of algebra-related topics in the middle grades including notation, variable, function, and properties of number. Suggests meaningful ways to accomplish them. (YDS)

Describes a lesson plan in which students apply their mathematical intuition to determine win-loss possibilities of teams in a sports league and develop a formula for calculating the magic number for clinching first place. (YDS)

Describes how the human body can be used to make sense of various number patterns and relationships. (YDS)

Presents a mathematics game appropriate for middle school or high school students that aids in the teaching and understanding of closure properties. (Author/NB)

Presents the Perfect-Square Geometry Partners problem to teach students about patterns. (Author/NB)

Investigates how mathematics is used in various careers. Students explore number sense and operations, logical reasoning, data analysis, and algebra. (Author/NB)

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)

The study compared two methods of teaching an initial place value skill: a concrete, semiconcrete, abstract teaching sequence and an abstract-only presentation. Learning-disabled elementary and middle school students (N=24) using the concrete to abstract teaching sequence performed significantly better on three posttests than students taught the…

Two experiments involving a total of 40 three and 39 four year olds were undertaken to determine subjects' ability to sort and compare numbers according to magnitude. Results indicate that readiness skills for early childhood mathematics education should include development of appropriate concepts of number magnitude. (TJH)

Investigates the relationship between the home experiences of six children aged five years and their level of numerical understanding. High scorers were characterized by exposure to a wide range of number experiences, a strong family orientation towards numeracy, and the opportunity to observe their mothers using numbers to solve everyday…