Notes how literature has a powerful role to play in fostering children's understanding of mathematical ideas. Discusses 19 books focusing on mathematics. Concludes that children's literature can help restore the story that has often been missing in traditional mathematics instruction. (SG)

Two studies addressed the role of representation ability and control of attention on solutions to an appearance-reality task based on two types of objects, real and representational. In Study 1, 67 preschool children (3-, 4-, and 5-year-olds) solved appearancereality problems and executive processing tasks. There was an interaction between object…

This article examines the classroom value of assigning good mathematical problems and especially of encouraging many different approaches to their solutions. (Contains 6 figures.)

An attempt to implement problem solving as a teacher of ninth grade algebra is described. The problems selected were not general ones, they involved combinations and represented various situations and were more complex which lead to the discovery of Steiner triple systems.

Different representations of rational numbers are considered and students are lead through activities that explore patterns in base ten and other bases. With this students are encouraged to solve problems and investigate situations designed to foster flexible thinking about rational numbers.

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.

Strategies that children used to solve a fraction problem are presented, and an insight into how students think about divisions and fractions is described. Teachers can use these strategies to help students establish connections related to fractions.

This article presents a brief biography of Paul Erdos, who focused on problem-solving, particularly in the areas of number theory, combinatorics and graph theory. During his life he had no property, no family and no fixed address. He buttered his first piece of bread at age 21. He never cooked, nor ever drove a car. Another mathematician, Ron…

A special but common type of scenario is one in which a company has a promotion that is designed to make the customer purchase more of their product than they otherwise might. Although this can be aimed specifically at children, it really applies to all persons. The basic premise is that the company issues a "set" of different items or…

The unified approximations reduce the conceptual complexity by combining solutions for a relatively large number of different situations into just two similar sets of processes. Processes used to solve problems by either the unified or classical approximations require similar degrees of understanding of the underlying chemical processes.

There has been a long-standing debate in the fields of philosophy and cognitive science surrounding the relationship of language to cognition, but the exact nature of this relationship is still unclear (Sokolov, 1968/1972). In the current study, we explored the role of language in one aspect of cognition, namely problem solving, by administering…

Given a set of urns, each filled with a mix of black chips and white chips, what is the probability of drawing a black chip from the last urn after some sequential random shifts of chips among the urns? The Total Probability Formula (TPF) is the common tool to solve such a problem. However, when the number of urns is more than two and the number…

Providing families with information about infant sleep can positively impact parents' well-being and infants' sleep habits. Few parents receive professionally based information about sleep, perhaps due to contradictory information found in the literature. This review summarizes: (1) normative sleep patterns for infants; (2) factors that affect…

While waiting for his meal to arrive, a truck driver was using his straw to move water from one glass to another when he was struck by this question: If I keep doing this, will the two glasses ever have exactly the same amount of water? This article looks at various problems related to that question.

A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…