Discussed are the difficulties that entering college freshmen seem to have with mathematics, particularly with fractional forms. A success-oriented program is suggested in which all students are successful. To obtain this goal, a number of alternative routes are discussed such as presenting decimals before fractional forms and the use of the…

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

Examining how students reconstruct stories they've heard can give insights into why students often have difficulty understanding and retaining mathematics. Behavioral psychologists refer to the phenomenon of piecing together a series of events as "chaining." This paper argues that the cognitive capacity to reconstruct a whole contextual…

It is suggested that elementary school students find rational numbers troublesome because some teachers have an inadequate understanding of rational number concepts and poor facility with rational numbers skills. How to help them overcome difficulties, develop concepts, and know what topics to emphasize are discussed. (MNS)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Suggests that a superior way of teaching fractions is to assist learners to conceptualize fractions, especially to grasp the varied meaning of fractions. Advocates using hands-on procedures, gives three different meanings of the concept "fraction," and explains how to teach children the deeper meaning of numberline subunits, fractions as division,…

The mathematics concept of fractions was taught to a group of learning disabled, dyslexic, and multiply handicapped students (15-20 years old) by preparing a fruit salad. Enthusiastic student participation and enhanced knowledge illustrated the effectiveness of employing several sensory modes in learning activities. (CB)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

It is viewed understandable that many teachers consider fractions one of the most difficult mathematical topics to teach. School experiences need careful planning to include sequential activities which develop accurate concepts, and concepts are thought best developed by activities which move along the concrete-to-abstract continuum. (MP)

Learning to teach mathematics for understanding is not easy. First, practice itself is complex. Second, many teachers' traditional experiences with and orientations to mathematics and its pedagogy are additional hindrances. This paper examines teaching practices and reviews some of what is known about prospective and experienced elementary…

Proposes and describes four teachers' beliefs necessary in creating constructivist classroom environments. Presents the background, description, and analysis of seven teaching episodes that examine the mathematical understanding actions of pupils in classrooms in which teachers exhibit these beliefs in an effort to verify the necessity of the…

This report resulted from work with primary grade children and teachers in Kankakee, Illinois. Essays by four resource persons and two observers are included, each expressing insights and feelings in order to share ideas with resource persons for primary mathematics teaching in other schools. A main objective is to represent the ways elementary…