The purpose of this study is to compare the differences of four essential aspects (i.e., representational forms, contextual features, cognitive demand levels, and response types) embedded in mathematical problems within the topics of numbers and operations in mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This…

Problems are discussed in which addition facts are presented using words instead of numbers. The letters are then replaced by numbers that will make the addition problems correct. (MP)

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of…

The author gives a method for involving students in developing and verifying elementary number theory hypotheses by studying areas and perimeters of primitive pythagorean triangles. (MN)

The derivation of a method to drive the general term of a sequence is presented. The difference sequences and binomial coefficents are used in the derivation. An application of this method is made to solve Polya's problems concerned with dividing space in regions by a given number of planes. (JP)

Six mathematics problems are posed; details are given of the solutions for six other problems. (DT)

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

This study looked at student difficulties with fractions by focusing on understanding of part/whole relationships. The sample consisted of two sixth-grade and two eighth-grade classes. A lack of substantial improvement from sixth to eighth grade on many fraction tasks was noted and viewed as cause for concern. (MP)

This study investigated whether there was a difference in achievement by first graders between their ability to solve open sentences presented in vertical form and in horizontal form. It was recommended that the horizontal form be avoided in grades one and two. (MP)

Instructional techniques are given for the use of calculators in (1) finding prime numbers, (2) solving trigonometric equations, and (3) solving polynomial equations. (CP)

Gifted students attending a week's summer mathematics program completed problems involving elementary number theory ideas and extensions. The sequence of these problems and strategies used are presented to help teachers looking for topics to enrich the mathematical experiences of students in middle grades or older. (JN)

Presents activities utilized with primary teachers to alleviate instructional concerns about using calculators and provide reasons for using calculators in their mathematics instruction. Activities address the topics of estimation, number sense, numeration, whole number and fraction operations, probability, and problem solving. (MDH)

Presents results of 46 randomly selected children's performance measurement and partitive division problems when remainders are zero, nonzero but not used in the solution, and nonzero and used in the solution. Results indicate that children demonstrate an understanding of division prior to formal instruction. (MDH)