Análisis cualitativo de peptidomas y marcajes isotópicos: MSHandler.

It was indicated that the course outcomes for Module 1, Introduction to Mathematical Literacy of the ACE course, included a critical analysis of national and international literature on Mathematical Literacy and the NCS curriculum documents and guidelines (DoE, 2003a; DoE, 2005; DoE, 2006; DoE, 2008). It appears that the two ACE teachers might have had the perception that regurgitating of the curriculum documents and course literature was expected from them in the situated context of assessment of the ACE Mathematical Literacy course. Their understanding and interpretation of the course outcomes might have been that they would obtain maximum marks for the course if they restated curriculum documents and other course literature. This analysis suggests that the teachers did not engage in critical analysis of course literature and largely did not develop their own voice with respect to the course literature as was expected.

This suggested that questions for formal assignments and examinations should focus on the application of theory learned and not merely on the reproduction of theory and facts. The cognitive level expected for an ACE course should not be restatement of course material, but should involve critical engagement with course material. The internalizing of knowledge and the construction of new ideas and meanings should be based on the course material and linked to experience.

6.2.2.2 Contextual nature of course assessment tasks

Following the advice in the Teacher Guide (DoE, 2006) and in Steen (2001), all the tasks that I set on the ACE course were located within an everyday context. The ACE Mathematical Literacy teachers were always given contextual data for the Mathematical Literacy lessons that they had to design as part of the course. Since the context was given, the teachers did not have a choice as whether to integrate the context in the planned lessons or not. The choice opened for the teacher was related to how to he/she should relate context and mathematical contents within the lesson structure. Of interest here is the fact that neither Teacher A nor Teacher B appeared to mention that all the tasks they had met in the ACE Mathematical Literacy programme were problem-solving tasks set in context. The

notion that all the tasks for the ACE Mathematical Literacy course were context-based could be critiqued since Mathematical Literacy tasks are not always context-based; tasks could also begin with content and then focus on applying the mathematics in different contexts. Evidence of this practice was apparent in the content-led Mathematical Literacy teaching agendas as described by Graven and Venkat (2007).

6.2.2.3 Development of the cognitive level of questions used in tasks

Evidence from the analysis of assessment tasks suggested that Teacher A and Teacher B did not include enough questions on a higher cognitive level, namely ‘applying multistep procedures in a variety of contexts’ (level 3) and ‘reasoning and reflecting’ questions (level 4). As mentioned previously, the tasks would largely not prepare learners for Paper 2 of the National Senior Certificate examination (DoE, 2008; Venkat and Phungula, 2008) since the overall cognitive level of the analysed questions was not high enough. This suggests that the ACE Mathematical Literacy course should emphasize ‘learning’ in relation to the design of tasks and the cognitive level of questions as advocated by the Subject Assessment Guidelines for Mathematical Literacy (DoE, 2008).

6.2.2.4 A spectrum of Mathematical Literacy teaching practices

My intention, as course developer and presenter, was that each ACE Mathematical Literacy teacher would lead to the development of a teaching practice (Wenger, 1998) envisaged by the Department of Education (DoE, 2003a). Both teachers did not, in practice, integrate the components of context and mathematical content into a dialectical relationship (DoE, 2003a; Graven and Venkat, 2007) in the ways I expected, but developed unique Mathematical Literacy teaching practices which connected to the empirically based spectrum of teaching agendas (Graven and Venkat, 2007).

The empirical data from this study suggested that the ACE Mathematical Literacy course material should include the spectrum of agendas (Graven and Venkat, 2007) which includes different nuances for Mathematical Literacy teaching practice with regards to the relationship between context and content.

6.2.2.5 Development of meaning and Mathematical Literacy teaching practice

Although this study was based on only two teachers in the ACE Mathematical Literacy course and only one lesson of each was observed (which was a limitation of both the course and the research design), the empirical data demonstrated that the theoretical meaning which the two teachers gained on the ACE Mathematical Literacy course did not fully translate into their Mathematical Literacy teaching practice. The suggestion is that the course should include a practical component where teachers are expected to teach Mathematical Literacy as part of the ACE Mathematical Literacy course assessment. This component should include lesson planning, the set of classroom assessment tasks and lesson presentation. The purpose of the classroom practice would be diagnostic with respect to teaching practice of the teacher involved. The teacher, fellow-ACE Mathematical Literacy teachers

and the course facilitator would be required to reflect on his/her teaching practice in order to scaffold the development of a meaningful Mathematical Literacy teaching practice. In doing this the learning components of meaning and practice (Wenger, 1998) might successfully be integrated and might it be possible for the two components to ‘mutually define’ each other (Wenger, 1998, p5).