Wiskundeprestasie, verbale en nie-verbale redeneringsvermoë by swart standerd 5-leerlinge : 'n psigometriese ondersoek

Abstract

1. INTRODUCTION According to Van Staden (1975, p.viii) there is an urgent need for psychological and scholastic achievement tests for Black ethnic groups. The Department of Education and Training was aware of this need and approached the HSRC to standardize achievement tests in Mathematics to be used for initial evaluation in the various standards. This study makes a contribution towards meeting this need .by supplying such a test in Mathematics. 2. AIMS 2.1 ACHIEVEMENT TEST IN MATHEMATICS This investigation consists of two sections. The first section , which constitutes the greater part of this study, consists of the development of an achievement test in Mathematics which is used as a measuring instrument in the second part of the study. This implies that various hypotheses are not stated in the first section. 2.2 In the second section of the study the relationship between Verbal and Non-Verbal Reasoning on the one hand and achievement in Mathematics on the other is investigated. In this section the following hypotheses will be investigated: p1 = p2 The null hypothesis is stated that there is no difference in the predictive power of Verbal and Non-verbal Reasoning for achievement in Mathematics by Black pupils.

H 1 p1 f p2 The alternative hypothesis is stated that there is a difference in the predictive power of Verbal and Non-Verbal Reasoning for achievement in Mathematics by Black pupils. μ 1 = μ 2 A second null hypothesis is stated that there is no difference in the mean achievement in Mathematics by Black boys and girls in standard 5. H 1 μ1 f μ 2 The alternative hypothesis is stated that there is a difference in the mean achievement in Mathematics by Black boys and girls in standard 5. p = 0 p f 0 A third null hypothesis is stated that intelligence is not a predictor of achievement in Mathematics by Black pupils. The alternative hypothesis is stated that intelligence is a predictor of achievement in Mathematics by Black pupils. 3. RATIONALE OF THE MEASURING INSTRUMENTS 3.1 RATIONALE OF THE ACHIEVEMENT TEST IN MATHEMATICS The rationale of the test is based on the assumption that the ability of a Standard 5 pupil to manipulate numbers and to solve mathematical problems is a valid criterion of his achievement in Mathematics. 3.2 RATIONALE OF THE VERBAL REASONING TEST The test is based on the assumption that the ability to do basic operations and/or reach logical conclusions in connection with verbally stated analogies, classifications, ratios and computational problems is a valid indication of verbal reasoning ability .

3.3 RATIONALE OF THE NON-VERBAL REASONING TEST The test is based on the assumption that the ability to reason deductively, i.e. to arrive at a general principle from given data and to complete a series by applying the principle, is an indication of non-verbal reasoning ability . 4. DESCRIPTION OF THE MEASURING INSTRUMENTS 4 .1 MATHEMATICS ACHIEVEMENT TEST The test consists of Forms A and B. Each form consists of two tests: (i) Test 1: Ready Knowledge (ii) Test 2: Comprehension 4.2 VERBAL REASONING TEST In this test verbal subject-matter is used to measure the ability to form and logically manipulate verbal concepts. The content is heterogeneous and it includes tasks such as t he completion of analogies and number rows, classifications, logical conclusions and arithmetical problems. 4.3 NON-VERBAL REASONING TEST (Pattern Completion) The items consist of incomplete patterns to be completed by choosing one of five given options. 5. METHOD OF INVESTIGATION 5.1 METHOD USED IN THE FIRST PART OF THIS INVESTIGATION After a comprehensive literature study on aspects concerning this study had been done, the standardization of the Mathematics Achievement Test (chapter 3) was commenced. The Mathematics Achievement Test was compiled by the researcher

and submitted to the internal committee for Mathematics of the HSRC for comments and approval. After the test had been edited according to recommendations, it was applied to a representative sample of Standard 5 pupils in the Pretoria East area. The results were processed, item analysis and item selection were done and approved by the internal committee for Mathematics. The selected items for the establishment of norms were applied to a representative, stratified sample of Black Standard 5 pupils in March 1979. The results were processed and norms established. 5.2 METHOD USED IN THE SECOND PART OF THIS INVESTIGATION The investigation group was for purposes of economy limited to Standard 5 pupils in 38 schools in the Mamelodi residential area near Pretoria. After the application of the Mathematics test by the researcher, the Pattern Completion and Verbal Reasoning Tests were applied by two Black inspectors. The test instructions for Mathematics were in English and those of the other two tests in Northern Sotho and Zulu. The same answer sheet, which is scored mechanically, was used for both parts of this investigation. 6. DISCUSSION OF RESULTS The standardization of the Mathematics measuring instrument established that the Mathematics Achievement Test was valid and reliable measuring instrument as well as a good predictor of mathematics achievement at the end of the year. The following findings have also been made: a) There is no significant difference between the mathematical achievement of boys and girls. b) There is no significant difference between the mean mathematical achievement of urban and rural pupils. c) However, certain Bl~ck language groups achieve significantly higher (on the 5%-level) in Mathematics. According to the means, the Xhosas were the best achievers in Mathematics. The second objective of this investigation was to establish whether Verbal Reasoning, Non-Verbal Reasoning and Intelligence are predictors of mathematics achievement and to establish which of the two, Verbal Reasoning and Non-Verbal Reasoning, is the better predictor. The role of sex in mathematics achievement was also investigated. The latter has already been reported in (a). It has been found that Verbal Reasoning is a better predictor of mathematics achievement than Non-Verbal Reasoning and that Intelligence, as jointly measured by the Verbal Reasoning Test and Non-Verbal Reasoning Test, is a good predictor of mathematics achievement. It seems from this investigation that Verbal Reasoning, Non-Verbal Reasoning and Intelligence are all predictors of mathematics achievement, with Verbal Reasoning as the best predictor, followed by Intelligence and then Non-Verbal Reasoning.