Some aspects of objective testing in mathematics for the purpose of diagnosis and selection

The project investigates the feasibility of using objective tests for diagnostic purposes and of using certain items from these tests in the construction of selection/ attainment tests. The possibility of using the information gained from both types of test to form the basis of a mathematical record for a child is also discussed. The tests are devised to reveal the algorithmic difficulties encountered by children in the four computational skills of addition, subtraction, multiplication and division. To show the various sub-stages required for mastery of a particular skill, each of the four computational skills was divided into its component sub-stages. Ideally each of these sub-stages would have been tested at the appropriate point in the child's school career but due to the shortage of time for the project all the sub-stages for a particular computational skill were tested in a single test. To ensure that the tests were not too long three items were set to represent each sub-stage and five tests were given; these being Addition, Subtraction, Multiplication (Part 1), Multiplication (Part 2) and Division. A major problem arose when constructing the distractors for the items of the Objective Diagnostic Tests because these had to be constructed from algorithmic considerations and no books could be found which, contained these in enough detail. Thus it was necessary for the writer to construct his own tests which would be analysed to reveal the necessary information. The investigation into the feasibility of employing certain items used in the diagnostic tests for selection/attainment purposes arose out of practical considerations. If it were possible that the diagnostic tests could generate certain items for the selection/attainment tests then the teacher would be saved much time and effort by not having to write (at least) two sets of items. Finally the information gained from both types of tests is briefly discussed as the basis for a Mathematical Record of each child.