# Open Collections

## UBC Theses and Dissertations

### A study of the relationship between the ability to compute with decimal fractions and the understanding of the basic processes involved in the use of decimal fractions Farquhar, Hugh Ernest

#### Abstract

Modern theory of arithmetic instruction supports the idea that the development of understandings of basic mathematical principles produces a desirable type of learning. This is a reaction against the traditional method of instruction which places emphasis upon mechanical drill procedures, devoid of meanings. This study is an attempt to deter-mine what relationship, if any, exists between computational ability and understanding of fundamental processes. The investigation has been limited to the area of decimal fractions. Two tests -were developed for the purpose of the investigation. The test in computation was constructed and validated using pupils of the junior high school level as testees. Student-teachers constituted the personnel for the construction and validation of the test in understandings. The investigation, of relationship was performed using 236 Normal School students as testees. The tests, which had been constructed for use in the study, were administered at the beginning of the school term. The data obtained from the investigation were analyzed and the following conclusions were formulated: 1. There is a positive correlation of considerable magnitude between the scores on the test in computation and the scores on the test in understandings. ( r = .640 ). This is an indication that there is a tendency for the scores to vary in the same direction. 2. When the factor of intelligence is held constant, there is a net correlation of marked magnitude -which is somewhat less than, the apparent coefficient. This indicates that the common factor of intelligence has an influence upon the relationship between the two variables. 3. The magnitude of the relationship between scores in understanding and intelligence test scores is an indication of common elements in both these tests. 4. The relationship between, the scores in computation and the intelligence test scores is not high. A high intelligence does not appear to be a prerequisite for high achievement in computation. 5. There is evidence that ability in computation is not essential for high achievement in understandings and vice versa, nor do high scores in one of these factors guarantee high scores in the other. 6. Although a study of the scatter diagram suggests that success in computation is more probable if it is accompanied by a high degree of understanding, it cannot be inferred from the data that one variable is the cause or the effect of the other.