Creswell and Plano Clark (2011:223-232) give three options for merging quantitative results and qualitative findings: side-by-side comparisons in a discussion or summary table; joint display comparisons in the results; or interpretation or data transformation in the results. Side-by-side comparison for merged data analysis was employed for this study and the researcher presented quantitative results and qualitative findings in a discussion. The discussion was used as a vehicle for merging and conveying the merged results.
The results from learner journal entries, semi-structured interviews and learner observation and questioning evidenced that learners were developing mathematical problem solving skills as the intervention progressed and had developed them by the end of the intervention. Learners could formulate the question in a given problem, understand the conditions and variables in the problem, select or find the data needed to solve the problem, formulate sub- problems and select appropriate solution strategies to pursue, correctly implement the solution strategy or strategies and solve sub-problems, give an answer in terms of the data in the problem and evaluate the reasonableness
of their solutions. The researcher observed that learners frequently checked and monitored their understanding during the problem solving sessions. The transcribed data from the semi-structured interview audio-recordings revealed that learners had become conscious of how and why they were solving a given problem.
The data from the MPSSI indicated that learners in the experimental group perceived themselves as having developed mathematical problem solving skills by the end of the intervention. This confirmed what the researcher concluded from the journal entries, semi-structured interviews and learner observation and questioning, that is, that grade 8 learners in the experimental group had developed mathematical problem solving skills at the end of the intervention. However, the MPSSI indicates that learners in the control group did not perceive any change in their mathematical problem solving skills at the end of the intervention. Learners in the experimental group achieved better results in their mathematical tasks and written work as the intervention progressed and demonstrated tremendous improvement in their post- word- problem and multiple-choice tests. Learners in the control group did not show any significant improvement in their post-tests. It seemed reasonable for the researcher to conclude that learners in the experimental group had developed mathematical problem solving skills and this had a positive impact on their performance and achievement in mathematics.
The F-test results for the questionnaire in table 4.4 indicate that there were significant changes in the experimental group compared to the control group. Learners in the experimental group improved their attitude towards mathematics, became more willing to engage in problem solving activities, persevered during the problem solving process and had developed self- confidence with respect to problem solving. It was reasonable for the researcher to conclude that learners in the experimental group had indeed overcome “obstacles” before they could benefit from the PCTLA and be in a position to develop mathematical problem solving skills.
From the above discussion the researcher concluded that the quantitative results and qualitative findings converged. The learners had indeed
developed mathematical problem solving skills by being exposed to the PCTLA and this had a major positive impact on their performance and achievements in mathematics.
4.5
Conclusion
This chapter presented the data analysis and the discussion of the results. The aim of the empirical study was to explore the development of mathematical problem solving skills of grade 8 learners in a PCTL environment and to investigate its effect on these learners’ performance and achievement in mathematics. The empirical study was in the form of a mixed methods research design. The purpose of the qualitative research was to explore the development of mathematical problem solving skills of grade 8 learners in a problem-centred teaching and learning environment. The quantitative strand’s purpose was to test the effect of the development of mathematical problem solving skills on grade 8 learners’ performance and achievement in mathematics. From the results and findings of the study the researcher confidently concluded that the grade 8 learners had indeed developed mathematical problem solving skills at the end of the intervention and this had a positive impact on their performance and achievement in mathematics.
The next chapter, which is the final chapter of this study, summarises the research, reviews the research questions and discusses the researcher’s recommendations, the limitations of the study and possibilities for further research.
CHAPTER 5
SUMMARY OF THE
RESEARCH, CONCLUSIONS
AND RECOMMENDATIONS
5.1
Introduction
The purpose of this study was to explore the development of mathematical problem solving skills of grade 8 learners in a problem-centred teaching and learning environment at a secondary school in Gauteng. Furthermore, the study aimed at investigating the effect of mathematical problem solving skills on grade 8 learners’ performance and achievement in mathematics. This chapter provides an overview to demonstrate that the research question, research sub-questions and aims originally stated in the first chapter were addressed and achieved. This is the final chapter of this study and the summary of the research, a review of the research questions, the limitations of the study, areas for possible further research, recommendations and conclusions are presented.