| Summary: | The study was designed in two parts. The purpose of the first part was to gather evidence to support a model hypothesizing relationships between the fraction algorithms, that is, specified algorithms for addition, subtraction, multiplication,
and division, and renaming skills, that is, specified skills for renaming for the algorithm (RAL) and renaming for the answer (RAN). The purpose of the second part was to investigate the effects in performance of the subtraction algorithm,
of reviewing the five RAL skills hypothesized as relating directly to the subtraction of fractions algorithm (treatment one); and to investigate the effects in performance of each of the four algorithms, of reviewing the purpose of the five RAL skills within the subtraction algorithm (treatment two).
A repeated measures, hierarchical design was employed in which six sixth-grade classes were assigned to one of three experimental groups, so that no treatment
was replicated in any one school. Group A received both treatment one and treatment two. Group B received treatment one. While Group A was receiving treatment two, Group B was instructed in geometry. Group C (control group) received
instruction in geometry and measurement during the treatment periods. Treatment
one was administered on each of five consecutive days. Treatment two was administered in one day. The regular mathematics teacher for each classroom participated in the experiment. Lesson plans and worksheets for the treatments were provided by the experimenter.
A pretest consisting of three parts: Part A on the seven RAL skills, Part B on the nine RAN skills, and Part C on the four algorithms, was administered
on two consecutive days before the treatments. Posttest one consisting of two parts: Part A on the five RAL skills, and Part B on subtraction, was administered
in one day following treatment one. Posttest two consisting of the same parts as the pretest, was administered on two consecutive days following treatment two. All tests were constructed by the experimenter.
For Bart One of the problem, two computer programs, an item analysis and a frequency tabulation, were used. Evidence was found to support the proposed
model. In other words, there appears to be a relationship between RAL skills and algorithm achievement, particularly for addition and subtraction; and between RAN skills and the ability to obtain a simplified answer for each of the four fraction algorithms.
For Part Two of the problem, a random effects model, multivariate analysis of covariance was used to test the effects of the two treatments. Pretest scores were used as the covariate in the analysis. No statistical significance was found in performance of the subtraction algorithm following treatment one. No statistical
significance was found in performance of the four algorithms following treatment two. === Education, Faculty of === Graduate
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