Initiatives in many countries to improve learner performances in mathematics in poor communities have been described as largely unsuccessful mainly due to their cursory treatment of curriculum alignment. Empirical evidence has shown that in high achieving countries the notion of coherence was strongly anchored in cognitively demanding mathematics programs. The view that underpins this study is that a cognitively demanding and coherent mathematics curriculum has potential to level the playing field for the poor and less privileged learners. In South Africa beyond 1994, little has been done to understand the potential of such coherent curriculum in the context of the NCSM. This study examined the levels of cognitive demand and alignment between the written, tested and taught NCSM. The study adopted Critical Theory as its underlying paradigm and used a multiple case study approach. Wilson and Bertenthal’s (2005) dimensions of curriculum coherence provided the theoretical framework while Webb’s (2002) categorical coherence criterion together with Porter’s (2004) Cognitive Demand tools were used to analyse curriculum and assessment documents. Classroom observations of lesson sequences were analysed following Businskas’ (2008) model of forms of mathematical connections since connections of different types form the bases for high cognitive demand (Porter, 2002). The results indicated that higher order cognitive skills and processes are emphasized consistently in the new curriculum documents. However, in the 2008 examination papers the first examinations of the new FET curriculum, lower order cognitive skills and processes appeared to be emphasized, a finding supported by Umalusi (2009) and Edwards (2010). Classroom observations pointed to teachers focusing more on rote learning of both concepts and procedures and less on procedural and conceptual understanding. Given the widespread evidence of the tested curriculum impacting on the taught curriculum, this study suggests that this lack of alignment between the advocated curriculum on one hand, the tested and the taught curricula on the other, needs to be investigated further for it endangers the teaching and learning of higher order cognitive skills and processes in the FET mathematics classrooms for the poor and less privileged. Broader evidence suggests that this would work against efforts towards supporting the upward mobility of poor children in the labour market.

Thesis (Ph.D. (Mathematics Education)) -- University of Limpopo, 2018 / The purpose of the study is to explore the effectiveness of Annual National Assessment (ANA) in monitoring the standard of mathematics education and to assess the mathematical proficiencies tested and exhibited by Grade 9 learners in South Africa. The research problem was premised on the dearth of data that justifies ANA as an evaluative assessment. As such, the study utilised five strands which were; procedural fluency, conceptual understanding, strategic competence, adaptive reasoning and productive dispositions as a theoretical framework to assess mathematics that was tested and exhibited by learners. To explore the research problem, the study used mixed methods in the context of exploratory sequential design. Document analysis was used first to capture mathematics content and cognitive levels examined by ANA. Second, learner responses were explored using four variables of achievement levels; no response, correctly answered, incorrectly answered and partially answered. First, the results from the analysis of ANA questions indicated that ANA mostly tested questions of low complexity. Second, the results from the learners’ responses revealed that the majority of learners were not proficient to ANA irrespective of low complexity testing. Third, the Porter’s alignment index for ANA and TIMSS was between moderate and perfect. Subsequently, content and cognitive levels were misaligned in the three consecutive years of ANA testing. It implies that learners were most likely to show a deficit of higher order problems solving skills which are a prerequisite of courses in advanced mathematics. Additionally, the results suggest that ANA had challenges of reliability and validity as an evaluative assessment due to inconsistency in the testing. As such, it is recommended that the complexity of ANA be addressed, the content areas where learners are not proficient be addressed and the alignment of ANA must be frequently calculated to monitor the standard of mathematics education in South Africa effectively. Keywords Alignment index, mean deviation, strands of mathematical proficiency, systemic assessment.

The Department of Basic Education (DBE) has associated the poor pass rate in the National Senior Certificate (NSC) Grade 12 Physical Sciences examinations to the learners’ lack of practical skills and the inability of learners to solve problems by integrating knowledge from the different topics in Physical Sciences. The CAPS (Curriculum and Assessment Policy Statement) is central to the planning, organising and teaching of Physical Sciences. Even though more than a third of the learners achieved below 30% in the NSC Grade 12 Physical Sciences: Physics (P1) November 2017 examination, there was a lack of references made to the CAPS, rationalising the poor performance. A disjointed alignment between the CAPS and the P1 is a possible cause for the poor performance. Since there have been no previous studies that investigated the alignment between the CAPS and the P1, this study aims to fill that gap. This study used a positivist research paradigm and a case study research strategy. A purposive sampling procedure selected the CAPS Grades 10 – 12 Physical Sciences document; the Physical Sciences Examination Guidelines Grade 12 documents and the final and supplementary P1 examinations in the period starting November 2014 to March 2018 as the documents for analysis. A summative content analysis research technique was conducted using the Surveys of Enacted Curriculum (SEC) research method. The SEC method employed the use of the four topics of Grade 12 Physics and the four non-hierarchical levels of cognitive demand as described in the modified version of Bloom’s taxonomy. The physics topics included mechanics; waves, sound and light; electricity and magnetism; and optical phenomena. The cognitive demand levels included recall; comprehension; application and analysis; and synthesis and evaluation. This study found a 100 percent categorical coherence, a 67.3 percent balance of representation, a 79.4 percent cognitive complexity and an average Porter’s alignment index of 0.77 between the CAPS and the P1. The overall Cohen’s kappa for all the documents analysed was 0.88. The findings of this study indicate that the mechanics topic was under-emphasised whilst the application and analysis cognitive demand was over-emphasised in the P1. The CAPS and the P1 did not utilise the highest cognitive demand, synthesis and evaluation which may be interpreted as an environment that fosters lower order thinking. To change this environment of lower order thinking and simultaneously increase the alignment between the CAPS and the P1 this study recommends that firstly, the CAPS decreases the recall based content of the mechanics topic. Secondly, the CAPS and the P1 increase the synthesis and evaluation cognitive demand-based content at the expense of the recall cognitive demand-based content. Thirdly, the CAPS must include the content of the school-based physics practical assessments while decreasing the focus on physics definitions. The ultimate aim is an improvement in the pass rates of the NSC Grade 12 Physical Sciences examinations. / Science and Technology Education / M. Sc. (Mathematics, Science and Technology Education (Physics Education))