Notes strong and widespread pressures for middle school teachers to teach fractions. Discusses experimental and empirical evidence that traditional fractions instruction is highly vulnerable to criticism from a number of angles. (SR)

Comparison of pre- and posttest scores in mathematics computation of 2 classes of (n=91) ninth-grade students, 1 class emphasizing drill and practice and the other focusing on learning concepts, found the mean grade equivalent score for computation of the concept class increased more than 2 years and these students attempted to answer more…

Provides an overview of research on transfer, highlighting its main tenets. Looks at interviews of two grade 5 students learning about mathematical concepts regarding operations on positive and negative quantities. Focuses on how their learning is influenced by prior knowledge and experience. (Author/MM)

Describes a classroom-based model for professional development that allows teachers to gain further insight into matching learning experiences with a child's potential. (ASK)

The unpacking of the mathematical knowledge necessary for teaching division is examined. A core task for surfacing and unpacking one's division knowledge is presented and the understandings that might comprise a package of teacher knowledge for division is discussed.

This article focuses on a form of instructional design that is deemed fitting for reform mathematics education. Reform mathematics education requires instruction that helps students in developing their current ways of reasoning into more sophisticated ways of mathematical reasoning. This implies that there has to be ample room for teachers to…

"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…

This study investigated ability-related differences in strategy use and development in the domain of simple arithmetic, in terms of the model of strategic change, using the choice/no-choice method and the chronological-age/ability-level-match design. Twenty-six second-graders with strong mathematical abilities (MA), 25 second-graders with weak MA,…

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

This investigation involves first assessing and then designing instruction to resolve student difficulties with addition facts. The ultimate goal was improving students' computational fluency.

The aim of this study was to ascertain the nature of the interaction between the affective value of musical distraction, personality type and performance on the cognitive tasks of reading comprehension, free recall, mental arithmetic and verbal reasoning in children aged 11-12 years. It was hypothesized that the cognitive performance of extraverts…

Many people believe that the 1989 National Council for Teachers of Mathematics (NCTM) standards heralded the biggest mathematics reform of the 20th century. Despite all reform efforts, recent studies indicate that mathematics taught in primary and middle school mainly consists of basic arithmetic tasks that use memorization and repetition. Today…

This article discusses a comparative study, funded by the European Union, of the teaching of mathematics in five European countries, (Flanders, England, Finland, Hungary and Spain) to students in the upper primary (ages 10-12) and lower secondary (12-14) years. These ages were chosen as they represent a time when many students' experiences of…

In this study, we examine whether preventive enrichment of pre-math skills has an influence on number knowledge in preschool children from low income families. Our data analyses use two methods to examine the influence of two independent programs implemented during junior kindergarten and kindergarten. The first implies the traditional approach…

Teachers who believe "practice makes perfect" may engage students in repetitive, perhaps timed, computational exercises. If educators teach students to understand the procedures they practice, however, they will not need as much drill and they will have more flexible use of the computations they perform. Three-quarters of a century ago,…