El estatus laboral

Since the sample consisted of learners whose ages range from 16 years to 20 years, consent letters were given to the parents of the learners and as well as consent letters given to the learners. These are available in appendices A and B. The parents were given the liberty to choose whether they allowed their children to participate in the research or not. It was explained to the learners and their parents that the research results would not affect the

learners’ academic marks. Learners’ anonymity would be respected. Learners’ confidentiality would also be guaranteed by using coding of learners in order to guarantee learners’

anonymity and confidentiality (Creswell, 2012; Opie, 2004).

The consent letters contained the explanation that the aim of the research was to find ways and means of improving the teaching and learning of functions in Mathematics in Grade 11 in the school and particularly to enhance learner participation and performance regarding this topic. The consent letters also gave the learners and their parents’ information about exactly what the process of the research would involve. This includes that the researcher, who is their teacher and registered with the University of the Witwatersrand, would require the learners to take a Mathematics test on functions, conduct the lesson in their classes and audio record the lessons and to video record a lesson on functions in the classes. The process also includes an interview the learner if selected and an audio recording of the interview if the learner was chosen for the interview.

The letters also gave the parents and the learners the information that the results from the learners’ tests and the videotape will be used to study the teacher’s teaching and to study and improve on the teacher’s teaching ability. The researcher, her supervisor and the teachers involved with the observation of the lessons and the videotapes would see the learners’ tests and the videotaped lessons. The teachers who would be involved with the planning and analysis of the lessons and tests would be given letters to pledge their willingness to keep the

anonymity and confidentiality of this information as seen in Appendix C. The researcher was would write a report which would be discussed at conferences and in journal articles. The learners’ results, videotapes and, if they were selected, the learners’ interview information, would be used for the duration of the project and stored for a further five years. Thereafter the content would be destroyed.

The letters explained that the videotape would be used to provide a full record of the lessons. The researcher would use the videotapes to ensure that she had an accurate record of the classes she teaches and thereafter observes. The researcher and observers were going to use the videotapes together with the notes they made during their observation of the lessons to analyse the lessons and to recommend the changes that could be made to the lessons for the classes that followed each lesson. The videotape would focus on the teacher who is also the researcher in this case. The camera person would, however possible, focus the video away from learners’ faces, to help secure confidentiality. The videotape would only be used for the purposes of the research project.

The consent letters informed the parents and the learners that the names of the learners would not appear in any reports or articles. Pseudonyms were to be used instead and also that the research was completely separate from the learner’s school work. All information obtained for research purposes would not affect the learners’ assessment in school. There would also be no problem if the learners do not want to take part in the research. If they chose not to participate, this would not affect them in any way and if they decided that they no longer wanted to continue participating in the study, they were free to withdraw at any time. They learners could simply inform the researcher who would then make the necessary changes to her research process. Learners who decided not to be part of the research would not be victimised or excluded from the process, but the video camera would be directed away from them as they would be put in a position in the class where this could be done.

4.6

METHODS USED IN THE STUDY.

The study uses the mixed methods research design. Mixed methods design research is a procedure used in collecting and “mixing” both qualitative and quantitative methods of analysing data in a single study or a series of studies to understand a research problem (Creswell & Clark, 2011, p.179). In this study, the mixed methods research design is used to analyse the data quantitatively in order to best highlight and compare the different

achievement levels of the learners in both the pre-test and post-test. The qualitative analysis of the data is used to ascertain the object of learning that informed the intervention process. Both the quantitative and qualitative data provide a better understanding of the research problem (Miles & Huberman, 1994).

Quantitative and qualitative methods of data analysis are used in this study. Quantitative methods of data analysis are used to see the bigger picture of the aspects of functions that the learners find most problematic. Quantitative analysis of data involves “summed scores of individuals added over several questions that measure the same variable where individual items are added to compute an overall score for a variable” (Creswell, 2012, p.178). Qualitative methods of data collection are used to provide a more detailed and much richer description of the aspects of functions that the learners encountered and found most

problematic (Dayer, 1995).

A “table of specifications” of the learning area objectives are drawn, “identifying” the different levels of “understanding, application, analysis and synthesis” (Popham, 1991, p. 13). The table of specifications for the pre- test appear in Table 3 after the appendices. The learners’ skills in manipulating the given information in order to arrive at the required responses are also the focus of the diagnostic tests. Short answer items are included in order to give the researcher information about learners’ thinking processes in producing the answers (Greeno, 1978).

The table of specification for the observation schedule includes the types of examples used by the teacher and the representations used at the start of the lesson. This is used for further explanation by the teacher and for further work by the learners. It also includes the kind of words that were used in explaining the key concepts of the lesson and the aids used in

explaining these key concepts. The types of activities the learners were engaged in during the lesson include whether they were listening, asking questions, answering questions, copying from the board, solving the problems and writing their solutions, discussing their thinking with other learners in groups and explaining their thinking to the class or doing exercises. The time spent on each of these activities was also recorded.