Validation of learning hierarchy in senior secondary school mathematics

Abstract

Facing sequencing of instructional content is one of the major problems mathematics teachers are encountering in schools. Attempt was made to review literature on the identified problem. Sufficient research findings revealed that there are substantial evidences to support the general thoery of the hierarchical structure of knowledge. A learning hierarchy for teaching bearing and distances in senior secondary school was constructed. Based on the hypothesized ordering of the nine subunits (eight cognitive entry characteristics and one criterion task), a diagnostic test was constructed to assess mastery of each of the eight units in the hierarchy and summative test. (Mathematics Achievement Test-MAT) was constructed to assess the mastery of the criterion task. The reliability coeffient (r) and difficult level (p) of MAT are 0.80 and 0.4 respectiviely. The nine instrument were administered to four hundred and ninety two SS 3 students selected through multi-stage random sampling technique from public co-educational secondary schools in three of the five local government areas in Ibadan metropolis. The hierarchical orderings of the nine subtask (eight CEC and one Criterion task) were generated in flow-chart. Task analysis was basically used to establish links among units and criterion task. A correlation analysis each unit with criterion task. All the indices (r) were significant at 0.05 alpha level, hence all the subunits in the hierarchy were retained. It is sufficient to recommend for the entire practcing mathematics teachers that adequate sequencing of instructional objectives to reveal the prerequisite subtasks is an adequate procedure for enhancing better achievement in any mathematics topic