Students recognized as less successful individuals in mathematics are tested for their understanding of fractions. The data reveals that most were only able to apply remembered rules to problems without actually knowing if the rule worked for the given situation. (MP)

A thirty-four item criterion referenced multiple choice mathematics placement examination was administered to 383 freshmen entering Chicago State University in the Fall, 1974. Each item of the test was constructed to measure a specific computational behavioral objective. The proportion of students demonstrating each desired behavior is reported.…

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

Activities geared to reinforcing the skills involved in solving linear equations are given. The material is prepared on worksheets designed for duplication. Student use of calculators is suggested, and the material can aid in promoting mental computation and estimation. (MP)

The use of folding paper strips as a mathematical model in the instruction of operations with fractions is presented. (MP)

Practical tips on the teaching of subtraction, addition and subtraction of fractions, and finding the vertex of a parabola are given. (MK)

Ways are presented to help students develop precomputational fraction concepts and skills using a circular-region or "pie" model. (MK)

This discussion of decimals covers topics such as place-value, zero, the decimal indicator, grouping, the metric prefixer, and rules for interpreting dimensions. (MP)

The author argues that students do poorly with problems involving percent because they do not adequately understand ratio and proportion. Described is an instructional sequence designed to build these concepts. (SD)

Summarizes solutions submitted for a problem posed in a previous issue of Mathematics Teaching in the Middle School. The problem pertains to making a fraction equivalent to one-third that uses all the numbers, zero through nine, exactly once. Includes actual student solutions. (DDR)

Describes a method for teaching multiplication of fractions based on Piaget's constructivism. Instead of teaching the algorithm of multiplying the numerators and denominators, students are presented with many problems and ask to invent their own ways of solving them. (DDR)

Describes an action research project aiming to improve student understanding of decimal numbers through an instrument. (YDS)

Approximately half of a group of 12-year-old students were taught fraction and ratio topics by a concrete process-oriented method. The others were taught in the regular way. The concrete, process-oriented approach resulted in significantly improved achievement in, and attitude toward, fractions and ratios. (Author/DC)

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)

Research findings on decimals and money are briefly summarized, followed by suggestions for classroom use. (MNS)