A study of the problem of teaching the concept of integers as directed distance in grades three through five and its relationship to level of left-right conceptualization, age level and sex

The study investigated the problem of teaching the concept of integers as a directed distance in grades three through five of the elementary school. Data was analyzed to determine if a significant difference existed in achievement between grade levels, age levels, levels of left-right conceptualization and sex. The subjects used in the study consisted to 49 third grade students, 56 fourth grade students and 52 fifth grade students. The elementary school from which the study sample was drawn is located in a suburb of Houston and consists of families from the low-middle to the middle-middle economic range. The racial origin of the school's student body is classified as predominately Anglo. The Instruction on the concept of integers as a directed distance was conducted by the classroom teachers for a period of nine days. Following the instructional period, using a written and an oral achievement test designed by the investigator, two measures of achievement were collected on each subject. The data was analyzed using the following independent variables: 1. Grade Levels—grades three through five. 2. Age Levels—using six months intervals of the age range in the study. 3. Levels of Left-Right Conceptualization—subjects were classified according to their level of left-right conceptualization (three developmental levels in left-right conceptualization have been identified by Piaget (1928)). 4. Sex Classification. The dependent variables in the study were the scores on the written and oral integer achievement tests. The data was analyzed using two different experimental arrangements and their associated cell structures: 1. Using an experimental arrangement containing the independent variables grade, left-right conceptualization and sex, the vector of means for the integer achievement test scores were tested for significant difference over the levels of the independent variables and the interaction of the independent variables. 2. Using an experimental arrangement containing the independent variables age, left-right conceptualization and sex, the vector of means for the integer achievement test scores were tested for significant difference over the levels of age and the interaction of age with the other Independent variables in the arrangement. From the analysis of the data it was concluded that there was no difference in achievement on the concept of integers as a directed distance due to age, and sex. It was also determined that the achievement was not affected by the interaction of any of the independent variables tested for interaction. A difference in achievement on the concept of integers as a directed distance was found between the grade levels and levels of left-right conceptualization. Post hoc probes of the dependent variables over the levels of grade and left-right conceptualization led to the following conclusions: 1. There was no difference in achievement on the oral achievement test, after removing the effects of the written achievement test, due to level of left-right conceptualization. 2. Moving from one developmental level to the next in the three levels of left-right conceptualization resulted in an increased performance on the written achievement test on the conceptualization of integers as a directed distance. 3. Performance increased on the written achievement test between grades three and four but appeared to level off between grades four and five forming an asymtotic curve. 4. The performance on the oral achievement test, after removing the effects of the written achievement test, increased between grades three and four but decreased between grades four and five; however, since the observed means appeared to increase from one grade to the next, it would appear that the removal of the effects of the written achievement test created the decrease between grades four and five. Summarizing the conclusions, it would appear that teaching the concept of integers as a directed distance in the third grade would not be as advisable as in the fourth and fifth grades. Also, if the achievement on the concept is to be evaluated utilizing a written test, students with higher left-right developmental level would have an advantage over those with lower left-right developmental level.Education, College o