Antecedentes a la aprobación de la Constitución 2008

The foundation of the NSC curriculum in South Africa is explicitly identified as outcomes-based education, which promotes a learner-centred, and activity based approach to education. It “serves to enable all learners to reach their maximum potential by setting the Learning Outcomes to be achieved by the end of the education process” (DoE, 2003 p. 2). The National Senior Certificate (NSC) in Mathematics focuses on learners who intend to continue with studies in Mathematics or who intend to enter into careers in which Mathematics is a requirement.

Parker (2006) describes the Mathematics curriculum as a “hybrid curriculum, one that

exhibits features of a competence model as well as a performance model” (p. 12). On

the general level as seen in the introduction and aims of the curriculum, the focus seems to be politically motivated and expresses the need for social justice for all and democratic access to Mathematics. However, the strong framing of the assessment standards and the contents indicate a need for explicit and visible criteria which are features of a performance-based pedagogy (Parker, 2006).

Parker (2006), in her analysis of the NCS, also found that the idea of empowerment as a purpose of Mathematics learning is visible in the curriculum document and that the focus seems to be on a structured form of applied Mathematics, including problem solving and mathematical modelling within different contexts and including real life. However, she argues that the idea of transferability of everyday knowledge into

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Mathematics is absent. There is also an added focus on the historical aspects of the development and use of Mathematics in different cultures.

(b) Alignment

Any national school examination that is used for selection of learners for admission to further study or to measure a nation’s mathematical competence needs a set of criteria that can be used to align the examination with the written curriculum and to determine its cognitive level (Berger, Bowie & Nyaumwe, 2010). The foundation of the new curriculum in South Africa is explicitly identified as OBE, which promotes a learner- centred and activity-based approach to education. A positive feature of this curriculum is that the Department of Education (DoE) published Subject Assessment Guidelines for Mathematics (SAGM) that outline the criteria and expected weightings of learning outcomes stated in the National Curriculum Statements (NCS) (DoE, 2008). Attention is therefore given to how things will unfold in practice; this is essential in a developing country such as South Africa (Rogan, 2007).

The DoE also published a SAGM taxonomy (based on the 1999 Trends in International Mathematics and Science Study [TIMSS] mathematics survey), designed for use in constructing and assessing the final examination (DoE, 2008). This taxonomy uses the categories of knowledge, routine procedures, complex procedures and problem solving. This is only one of many possible approaches when analysing the cognitive level of examination items, most of which are based on Bloom’s taxonomy – the well-known hierarchy of six different levels of cognitive objectives (Bloom, 1956).

Berger, Bowie and Nyaumwe (2010) point out two difficulties in applying the SAGM taxonomy. They argue that the SAGM assumes that cognitive levels increase with the type of mathematical activity, which means that memorisation has the lowest cognitive level, then routine procedures, then complex procedures and then problem solving. This could lead to problems when assessing the cognitive levels of the examination items, and leaves no space for important mathematical activities such as justification, conjecturing, and communicating mathematical ideas, although these are important elements of the written curriculum. This could lead to a weak alignment of the examinations and the NCS. Secondly, the SAGM taxonomy cannot distinguish between

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a complex procedure with high complexity and a complex procedure with moderate complexity.

(c) The signalling ability of the NSC Mathematics curriculum

The research of Engelbrecht, Harding and Phiri (2010) indicates a weak correlation between certain prior knowledge in areas required to pass university Mathematics and Grade 12 results. Jacobs (2010) emphasises that this could be because the students were unprepared for the level of cognitive skills required at university, or it could indicate that they did not put in sufficient effort. Volmink (2010), chair of UMALUSI, however, made it clear that the NCS serves as the end of a school phase and that the principles stated in the NCS make no mention of preparing learners for higher education.

Engelbrecht and others, (2010) determined that students coming from the OBE system had confidence in their abilities, were willing to try, were not prepared to follow the lecturer blindly, and wanted to experiment and do things their way. On the negative side, they also showed lack of mathematical rigour and had a unique way of writing unfamiliar to lecturers, and there was deterioration in their specific skills of factual knowledge, algebraic manipulation and mathematical formulation. It appears that the self-confidence they started out with in the courses was not justified because it was not supported by the necessary mathematical skills. There was a particular concern regarding the poor ability of students to ‘write’ Mathematics using the correct notation. It seems that the students were underprepared for those topics that had been removed from the previous curriculum, such as absolute values and trigonometric functions. Although exponents and logarithms were taught in the school syllabus, the students’ knowledge of these topics was insufficient and they could not keep up with the pace at university. The level of knowledge of functions was too low and the performance in the applications of differentiation was not promising for the follow–up topic of integration. It appears that in some university Mathematics courses the emphasis had shifted to a more theoretical approach, for which OBE students were not prepared. The overall conclusion of Engelbrecht and others (2010) was that the OBE curriculum widened rather than narrowed the gap between school and university Mathematics.

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Kriek and Basson (2008), when reflecting on the content of the NCS, states that the inclusion of financial and statistics problem-solving skills enhances the curriculum and should create open-minded learners who are less method-bound than in the past. The fact that the learners are no longer required to learn formal proofs in either Algebra of Geometry has a negative impact on first-year Mathematics. The third paper (Probability and Geometry) requires real problem-solving skills and computational methodology, but not many schools write the paper or have staff who are trained to teach it (Jacobs, 2010).

The fact that the NSC Mathematics papers enforce lower time constraints (150 marks written in three hours, as opposed to the previous 200 marks in three hours) has an impact on the preparation of students for higher education (Jacobs, 2010). Green and Rollnick (2007) claim that time constraints are one of the reasons for testing at lower cognitive levels. Higher-order cognitive skills are unsuitable for limited time examinations because critical thinking takes time and testing in itself is a stressful event for students (Felder & Brent, 2001; Green & Rollnick, 2007).

In 2010, the UK’s National Recognition Information Centre (UK NARIC) did a benchmarking analysis of the National Senior Certificate and comparisons with its international counterpart, the General Certificate of Education (GCE) A level. They acknowledged the social, political and cultural contexts that have influenced the NSC and still influence its evolution, and found that the NCS and NSC had developed extensively since 2005. Although the NCS Grades 10-12 had initially been criticised for a lack of subject specificity (Mhlolo, 2011) the development of the SAG have been universally welcomed by all stakeholders, especially teachers and examiners. The UK NARIC report found that the current problem of learners being unprepared in Mathematics cannot be laid at the door of the curriculum, but is rather a reflection of the uneven quality of the delivery of the curriculum. Evidence suggests that ”candidates are increasingly more adept at taking initiative and displaying independent research and study skills. It is believed that this contributes to a gradual improvement in the all-round abilities of South African undergraduates” (UK NARIC, 2014, p. 106).

61 (d) Pedagogy

Although it is not within the scope of this study to discuss the acted curriculum in the South African classroom, the opinions of two scholars, Parker and Ndlovu can be mentioned. Parker finds that the words “learner-centred” and “activity –based” are used exactly once in the NCS Mathematics document (in the rationale) and that the meanings thereof are never explained. This has led to many different interpretations of the concepts by teachers in the classroom (Parker, 2006).

Ndlovu (2013) writes that it appears that the teaching and learning methods used in OBE Mathematics classrooms are increasingly being questioned for their effectiveness, and therefore there is a need for rethinking the efficacy of the underpinning constructivist learning theory.

3.3.3 Thinking skills required in the transition from school to university