South African learners struggle to achieve in both international and national Mathematics assessments. This has inevitably become a serious concern to many South Africans and people in the education arena. An algebraic word problem holds high preference among the topics and determines success in Mathematics, yet it remains a challenge to learners. Previous studies show there is a connection between learners’ low performance in Mathematics and errors they commit. In addition, others relate this low performance to English language inproficiency. This has encouraged the researcher to investigate the errors Grade 11 learners make when they solve algebraic word problems. The researcher used a sequential explanatory mixed approach to investigate Grade 11 learners from Gauteng, South Africa when they solve algebraic word problems. Accordingly, a convenient sampling helped to select three schools, and purposive sampling to choose the learners. In this study, the researcher employed a quantitative analysis by conducting a test named MSWPT with 150 learners. In addition, the researcher used qualitative analyses by conducting the Newman (1977) interview format with 8 learners to find out areas where errors are made and what kind of errors they are. Findings discovered that 90 learners demonstrated unfitness due to poor linguistic proficiency, while the remaining 60 learners fall into three main categories, namely those who benefitted from researcher unpacking of meaning; those who lack transition skills from arithmetic to algebra; and those who lack comprehension and calculation knowledge. Conclusively, the researcher found linguistic, comprehension, semantic and calculation errors. The reasons learners make these errors are due to (i) a lack of sufficient proficiency in English and algebraic terminology (ii) the gap between arithmetic and algebra. / Institute for Science and Technology Education (ISTE) / M. Sc. (Mathematic Science Education)

The aim of this study was to investigate the comparative effects of Constructivist-Based Teaching Method (CBTM) and the Traditional Teaching Method (TTM) on Grade 11 Mathematics learners’ errors in algebra. The constructivist learning theory (CLT) was used to frame this study. Mainly, CLT was used to influence the design of CBTI to hone participants’ errors in algebra that militate against their performance in Mathematics. The study was conducted in the Mpumalanga Province of South Africa with a four-week intervention programme in each of the two participating secondary schools. Participants consisted of n=78 Grade 11 Mathematics learners and one Grade 11 Mathematics teacher. A non-equivalent control group design consisting of a pre-test and post-test measure was employed. The Grade 11 teacher in the control school employed the TTM while the researcher implemented CBTM in the experimental school. The main aspects of CBTM entailed participants’ construction of their own knowledge from the base of prior knowledge and through group learning approach and exploratory talk in which discussions included argumentation, verbalising explanations, justifications and reflections. Participants in experimental school became familiar with the basic principles of CBTI such as group work, which enhanced the construction of conceptual understanding of algebraic concepts. This reduced most of the errors they commit in algebra and elevated their performance in Mathematics. The principal instruments for data collection consisted of a standardised Algebra Concept Achievement Test and lesson observations. The pre-test was used to determine participants’ initial errors in algebra before the intervention. A post-test was given at the end of intervention to ascertain change in participants’ errors in algebra over a four-week intervention period. Using descriptive and inferential statistical techniques, the study found that participants in experimental school significantly reduced their errors in algebra than those in control school. The study showed that CBTM was a more effective pedagogy that improved the errors Grade 11 learners commit in algebra than the TTM. / College of Education / M. Ed. (Mathematics Education)

The purpose of this study determined if a significant relationship existed between the amount of professional development that teachers participated in and the impact on the classroom instruction that followed. The goal was to study the effect that this had on student achievement in the State of Texas Assessment of Academic Readiness (STAAR) for English 1 and Algebra 1 for students at a large north Texas high school. Testing years for the study included the school years 2013-14, 2014-15, and 2015-16. Additional variables included the work in three areas of teacher professional development over the three-year period. Fourteen teachers, in two subjects, were studied in their implementation of classroom instruction. Particular attention was given to the instructional changes, and the number of hours of professional development in the areas of instruction, technology, and differentiation. Teachers were given opportunities to participate in 18 hours of professional development in all three areas in each of the three years. Teachers were then asked to incorporate the work that they completed each year into their day to day classroom instruction. The goal of the implementation of the professional development in addition to the curricular specifics regarding instruction of state standards was expected to produce increased state scale score marks for the students in the classes. Results of the study indicated success for students in the area of English 1 end-of-course assessment. From the beginning of the study, where student success rates in English state assessment was calculated at 47% overall passing rate, to the completion of the study, where student success was charted at 70% overall passing rate, significant changes were noted. In addition to the improvements made in English I, there were also significant changes made in the approaches to the Algebra 1 assessment. Classroom instructional practices were noted as much improved, and professional learning community collaboration produced significant classroom instructional improvements.