The development and standardisation of a mathematics proficiency test for learners in the foundation phase

English: Learning problems, during childhood, manifest in the form of learning restraints, learning disabilities and learning disorders. The concepts can be classified separately but in this research, the three concepts are viewed under the umbrella term of learning problems. There are three main causes of learning problems in children namely: cognitive factors; non-cognitive factors; and socio-environmental factors. In this study emphasis shifted from general learning problems to one specific learning area, namely; -rnathematics. Mathematics is a construction of knowledge that deals with qualitative and quantitative relationships in space and time. For a child to become competent in mathematics, the child must go through various processes, namely, cognitive, personal and social developmental processes. The child in the foundation phase must go through mathematical processes to comprehend certain mathematical tasks. The comprehension of specific mathematical concepts is operationalised by the successful execution of related mathematical tasks. These tasks are universal, yet in this study emphasis was placed on the tasks required of a child in the foundation phase in the Free State. If the child is not able to complete a task, problems in mathematical achievement can occur. Mathematical learning problems can be classified in terms of mathematical learning restraints, disabilities or Mathematics Disorder. The problems manifest in the form of various mathematical errors and the most common sources of these problems include the child, the teacher and the task. An assessment must be done to identify a child with a mathematics problem and provide information about prevention and treatment. In this research the VASSI Mathematics Proficiency Test was developed and standardised, for the Free State Department of Education, to serve as an assessment tool, to identify learners in the foundation phase with problems in mathematical achievement. The sample consisted of learners in grade one, two and three whose home language was English. Four phases were carried out while compiling the test. The first phase consisted of the construction of the preliminary questionnaire. In this phase seven schools compiled preliminary questionnaires for grade one, two and three learners and from these items a preliminary questionnaire consisting of 40 items was compiled. In phase two, the 40 item tests of grade one, two and three were given to 13 schools to administer. These results were analysed and the final 20 items were selected. The items were selected according to the Classical Test Theory with respect to their difficulty value, discrimination value, item variance, test variance, item-test correlation, item-criterion correlation, criterion-related validity and the coefficient-alpha. In phase three norms were determined by administering the test during the first and fourth terms of2000. Inter polarisation was carried out to determine the second and third term norms. Various statistical properties were investigated, these included the size of the sample; the number of items in each test; means with respect to sex, age, and the first and fourth administrations; standard deviations of the tests; reliability of the tests and skewness and kurtosis. The validity of the test was also investigated with regard to the content and prediction validity. The reliability and validity correlation coefficients varied from good to excellent. The obtained results suggest that the test can be administered in practice with confidence. The VASSI Mathematics Proficiency Test complies to the following criteria: • the test is applicable to grade one, two and three learners; • the norms are available per term so that the test can be carried out at any time of the year; • the test consists of universal mathematics concepts: • the test can be administered to groups or individuals: • the test can be used diagnostically; and • the test should be of value to future generations of learners.