Suggestions are given for activities to use to introduce common and decimal fractions. Models are used initially and symbols are introduced slowly. Decimals are related to common fractions. (MP)

Argues the importance of teaching fractions and discusses examples of fundamental problems in students' conceptualization of common fractions and decimal fractions. (SS)

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…

This manual contains individual learning activity sheets on "Prenumbers", "Whole Numbers", and "Fractions." Each activity sheet and its accompanying instructional recommendations focus on a single concept or skill. The program presented is not intended to comprise a complete mathematics program for children who have difficulty in mathematics and…

Interview and questionnaire responses of students in grades K-10 completing common and decimal fraction tasks suggested the existence of 2 sequential unistructural-multistructural-relational learning cycles within the concrete symbolic mode. (46 references) (MKR)

We compared alternative instructional strategies for integrating knowledge of decimal place value and regrouping concepts with procedures for adding and subtracting decimals. The first condition was based on recent research suggesting that conceptual and procedural knowledge develop in an iterative, hand over hand fashion. In this iterative…

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

A study interviewed 6 grade-6 students after participation in 21 lessons on basic concepts of fractions and decimals to determine how different children construct rational number concepts. Discussed the formation of the key concept of equivalent fractions based on student responses to interview questions. (MDH)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)

Describes the constructs of referents, relationships, and modes and illustrates how these constructs may be reflected in students' written responses to a decimal task that requests an explanation. Examines sets of responses from two classrooms using the proposed framework to illustrate the type of information that teachers may acquire through the…

Describes common misconceptions with decimals and suggests activities that can strengthen connections between decimal concepts and fractions, place value, and physical models, such as the number line. Encourages reasoning, communicating, and problem solving. (TO)

This paper reports on a teaching experiment involving decimal instruction conducted with a class of elementary students (n=20) in a public school of a small city. After doing extensive work with multiplication, division, ratio, and fractions through an innovative mathematics curriculum, fifth grade students were introduced to decimal numbers. To…

Presents an activity investigating what happens when a decimal point is in the wrong position or used at all. (YDS)

What research says about the learning and teaching of decimal fractions is summarized, with some instructional strategies and activities to improve learning suggested. (MNS)