Fractions Skill Research Articles

Toward Making Representation Count in Children's Conceptions of Fractions

As children's experience with numbers is usually based on the discrete integers used for counting, their theory of number may become increasingly resistant with age to accepting fractions as numbers that represent the continuous nature of measurable points in space. In this article, we report the results of studies that involved introducing children to fraction skills at an early age. In Study 1, children in Grades 2 and 3 were trained to order fractions along a number line using stimuli that are amenable to linear measurement. They were significantly more successful at ordering fractions and integers than children trained with circular stimuli. In Study 2, although many children had persistent difficulties, a subgroup trained on linear stimuli who could order fractions and represent fractional increments often succeeded on computation problems. Some displayed their understanding in a longitudinal study.

Influence of peer-model attributes on children's beliefs and learning.

Schunk, Hanson, and Cox (1987) investigated the effects of peer-model attributes on children's self-efficacy (i.e., perceived capabilities) and skill. Children enrolled in below-grade-level classes for mathematics instruction observed either one or three same-sex peers demonstrating rapid ( mastery model ) or gradual ( coping model ) acquisition of fraction skills, after which they received instruction. Observing a single coping model, multiple coping models, or multiple mastery models led to higher self-efficacy for learning, more rapid problem-solving during the instructional sessions, and higher posttest self-efficacy and skill than did observing a single mastery model. Children who observed coping models (single or multiple) judged themselves similar in competence to the models; children who observed mastery-models judged themselves less competent than the models.

An Evaluation of a Level-One Instructional Videodisc Program

In this project, a Level 1 videodisc program called “Mastering Fractions” was evaluated. The evaluation was conducted in two parts. Part 1 was a controlled study that compared the “Mastering Fractions” program to a more traditional fractions curriculum while controlling for any novelty effect of the videodisc medium. Part 2 of the evaluation was a descriptive study that examined the use of “Mastering Fractions” in non-experimentally controlled classroom environments. The results of the evaluation indicated that the use of the “Mastering Fractions” program resulted in significant gains in fraction skills and computations. Further, it was concluded that the achievement gains found in the study were attributed to the instructional content of the “Mastering Fractions” program and not to the novelty of the videodisc medium. Finally, it was found that even though the program had a positive effect on student achievement, the effectiveness of “Mastering Fractions,” like other instructional programs, is somewhat dependent upon the commitment and quality of the teacher using the materials.

Peer-model attributes and children's achievement behaviors.

In two experiments, we investigated how attributed of peer models influenced achievement behaviors among children who had experienced difficulties learning mathematical skills in school. In Experiment 1, children (M = 10.6 years) observed either a same- or opposite-sex peer model demonstrating rapid (mastery model) or gradual (coping model) acquisition of fraction skills. Observing a coping model led to higher self-efficacy, skill, and training performance. In Experiment 2, children (M = 10.9 years) observed either one or three same-sex peer models demonstrating mastery or coping behaviors while solving fractions. Children in the single-coping model, multiple-coping-model, and multiple-mastery-model conditions demonstrated higher self-efficacy, skill, and training performance, compared with subjects who observed a single mastery model. In both studies, children who observed coping models judged themselves more similar in competence to the models than did subjects who observed mastery models.

The Effectiveness of Videodisc Instruction in Teaching Fractions to Learning-Disabled and Remedial High School Students

This study compares the effectiveness of a videodisc curriculum that incorporates principles of instructional design (including discrimination practice and cumulative review) with a traditional basal program designed to teach basic fractions skills. Twenty-eight high school students, including 17 mildly handicapped students, qualified for the study by showing (a) mastery of whole number operations and (b) less than 50 percent mastery of the fractions skills to be taught. The students were matched in pairs based on a pretest score and math scores from the California Achievement Test, and then randomly assigned to one of the treatments. During the ten-day intervention, observers collected data on levels of treatment implementation and student on-task behavior. A criterion-referenced posttest and two-week maintenance test were administered. The videodisc curriculum resulted in significantly higher posttest and maintenance test scores. Levels of on-task behavior were significantly higher in the videodisc sessions, although levels in both conditions were above 80 percent. An analysis of student error patterns indicated that differences in instructional design features contributed to the relative effectiveness of the two curricula.

Let's Do It: Fractions with Counters

The wrong kind at the wrong time may be an apt description of the instruction with fractions usually provided children in the upper grades, a period in which fraction skills and concepts seem to be developed all at once.

Square Roots From Anywhere

A novel approach to roots, building algebra, fraction, and intuitive limit skills.