Introductory (graphical) linear programming in the senior secondary school : an action research study of some cognitive obstacles to its learning and an evaluation of a teaching approach designed to reduce the effect of these cognitive obstacles

This action research study, in two parts, investigates the difficulties experienced by senior secondary (Year 12) students in learning to solve by graphical means linear programming problems involving two decision variables. Herscovics' (1989) term "cognitive obstacle" is introduced as describing either a mental structure which prevents the learning of new material or the structure of the material itself which prevents it from being readily assimilated. The aim of the first part of the study is to determine possible cognitive obstacles to the learning of linear programming. The aim of the second part is to evaluate a teaching programme designed to alleviate these cognitive obstacles. It is found that the teaching programme used, based around a set of specific heuristics, is partially successful. It is suggested that key factors in solving linear programming problems include: the ability to comprehend problem statements, the ability to express variables and constraints on variables in mathematical terms and the ability to conceive of literal symbols as representing numbers, rather than as objects. Various ideas for teaching and research are recommended