The development of a mathematics proficiency test for English-, Afrikaans- and Sesotho-speaking learners

English: Mathematical Literacy, Mathematics and Mathematical Sciences is a learning area in the intermediate phase, which forms part of the General Education and Training band. This learning band is level one of the National Qualifications Framework and is overseen by the South African Qualifications Authority. The curriculum of this learning area consists of various learning strands, namely numbers and operations, fractions, patterns, shapes and space, measurement, and data. When learners fail to meet the expectations of the curriculum, mathematics becomes a major assessment concern. If this problem is not identified it could hinder the acquisition of more advanced mathematical skills. The first task in helping a learner who is struggling with mathematics is to identify the problem. For learners to succeed at mathematics they need to go through various developmental phases. Various cognitive processes form part of these phases. Often in a young child’s functioning, cognitive problems arise such as the inability to perform various mathematical tasks. For this reason a cognitive model for mathematics was used to reflect upon six key concepts that influence learning and teaching in the Mathematical Literacy, Mathematics and Mathematical Sciences learning area. These concepts include the categories of representing experience; motivation; individual differences; cognitive categories and cognitive processes; instructional procedures; and conceptual learning. Learners need to make sense out of what is going on during a mathematics lesson. To help learners develop meaning, a teacher provides experiences that foster mental manipulations. Psychologists refer to these mental manipulations as cognitive processes. When a learner is unable to carry out the cognitive processes necessary for task completion, mathematics becomes a major assessment concern. If a learner fails to meet the expectations of the curriculum or fails to carry out the cognitive processes necessary for successful task completion, then, in accordance with the aim of this study, the Intermediate Phase Mathematics Proficiency Test can be used to identify and address this problem. During the construction of this test, care was taken to ensure that the test was cross-culturally adapted. Differential Item Functioning was used to limit the possibility of cultural bias. The Item Response Theory and the Classical Test Theory were also used for item analysis and selection. The test was standardised for English-, Afrikaans- and Sesotho-speaking grade four, five and six learners. During standardisation, separate norms for each term were calculated. These norms are available in both stanines and percentile ranks. The test can also be used qualitatively to determine not only the learning strand in which the learner may be experiencing problems, but also the specific cognitive process, such as receiving, interpreting, organising, applying, remembering and problem solving, which might be preventing the learner from reaching his or her full mathematical potential. The Intermediate Phase Mathematics Proficiency Test is also a reliable and valid measuring instrument since the bias of the assessment measure has been decreased. This was done by eliminating any item that was biased towards a specific cultural group. The test can therefore be used in practice with confidence. In a multicultural society like South Africa, the adaptation of assessment measures and the elimination of bias from psychometric tools forms a vital part of the transformation process. The Intermediate Phase Mathematics Proficiency Test is a multicultural test with South African norms.