A Computer Approach to Mathematics Curriculum Developments Debugging

Abstract

Background:Sequencing contents is of great importance for instructional design within the teaching planning processes. We believe that it is key for a meaningful learning.Material and methods:Therefore, we propose to formally establish a partial order relation among the contents: the relation: “to be a prerequisite”. We have applied this approach to the mathematical contents of the compulsory Secondary Education of the Spanish educational system. This information has been modeled as a graph. The amount of contents considered (814) and the number of ordered pairs in the order relation considered (17,782) has produced a big graph. In order to work effectively with that amount of data, we have used software specialized in network analysis. More precisely, we have used the software packages Pajek and Gephi.Results:This software, together with the use of techniques borrowed from graph theory, has allowed providing a tool for debugging curriculum developments (similar to rule based expert systems verification).Conclusions:This is a contribution to the processes of sequencing contents and, therefore, to the processes of planning teaching and instructional design.