El cero y el vacío

This study focuses on the researcher’s practice with learners in one particular educational institution. Therefore, there is a lack of generalisability in that it is applicable only in this case. For example, there is a limitation associated with sampling. Most of the BEd students who participated in this study did Mathematical Literacy in Grade 12. Unlike in Mathematics, the topic of transformation geometry is not dealt with in depth in the subject Mathematical Literacy. An implication of this might be that most of the participants were not exposed before to some of the deep concepts and calculation procedures involved in transformation geometry,

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which were part of the pre-test they had to write as part of this study. This gap in their previous knowledge and skills might have led to the occurrence of more errors or the presence of more misconceptions that one would get in another group of students doing a similar BEd programme in some other university in the country. This would thus contribute more towards the lack of generalisability of the study. However, the findings and recommendations from this study are useful, to some extent, in other similar contexts.

There was a lapse of time between the period when the pre-test was given and the time when interviews were conducted with selected participants, because the researcher had to first analyse the content of the written tests and then decide which participants to conduct interviews with. This lapse of time could have an influence in the kind of responses or explanations given by participants during the interviews. This is because students might have discussed the test after writing it, realised some of the errors they have made, and then given an explanation that is influenced by the opinion of others by the time they gave explanations on how they came up with the answers they gave in the test. Some participants might, therefore, have given ‘contaminated’ responses, yet the researcher was interested particularly in their own individual opinions and the reasoning behind the answers they wrote in the test. Furthermore, the lapse of time between the pre-test and the post-test could influence the interpretation of the finding.

There was a limit of time during which participants could be involved with the research. The participants involved in this research were second-year BEd students, who had various other commitments in terms of both their own studies, involving other modules in the BEd programme, as well as in other topics that they had to learn and master within their second- year BEd mathematics curriculum. Therefore, the number of cycles in the action research approach used in this study was limited to the amount of time that the researcher could manage to engage with the participants on the topic of transformation geometry. Although the periods used to do the research with the participants were outside their normal lecture periods, the researcher had to be aware of their other commitments and leave enough room for them to engage with such commitments. However, the rigour with which the research was conducted, in terms of validity issues and deep analysis of data, compensated for any insufficient time that might have been a limitation to the study. Furthermore, the recommendations given by the researcher in connection with changes that could be effected for subsequent actions research cycles, would contribute more towards strengthening the significance of this study.

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The researcher was actively involved in the design and implementation of the intervention programme following the analysis of the written pre-tests and the interviews. Consequently, the researcher had a vested interest in the success of the intervention programme for both her students’ sake as well as for the sake of the research study as a whole. Thus, the fact that there was no outside opinion in terms of evaluating an intervention programme that was designed by the researcher, implemented by the researcher with her own students and evaluated by the researcher, might be a limitation in terms of researcher bias towards the need to see the programme being a success. That being said, the researcher acknowledges that action research, as the method used to conduct this research, is subjective in nature and the researcher has more control of how to conduct the research. What is more important is that the researcher has to explain what she is doing and why she is doing it. The researcher in this current study did provide explanations in support of the activities developed for, and actions taken during, the implementation of the intervention programme. Therefore, there is a possible reduction in the bias that might be caused if decisions were taken and actions carried out without explanation.

Few studies have been conducted within the South African context on the use of Van Hiele theory with pre-service student teachers. For example, it would have helped if there was a good deal of literature on the Van Hiele levels at which BEd Foundation Phase students in South Africa were reasoning in transformation geometry (this was not part of the objectives of this current study). Then the researcher would base some of the arguments, before conducting this current study, on such literature, as well as relate the errors displayed by students in this current study, to such literature from a South African perspective. However, as much as the lack of such studies as mentioned above is a limitation, it is also a strength in terms of the study’s contribution to the limited research in the South African context, thus increasing the significance of this present study.