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)

Smartphone technology can be integrated in mathematics education, since most learners immerse in this technology. Teachers should be facilitators of confined learning in traditional classrooms, including digital facilitators. The aim of the study was to determine the effect of integrating smartphone technology on Grade 10 learners’ achievement in algebra. The study focused on two Grade 10 classes from different township schools in the Gauteng Province. The study was conducted during the first term of 2016. A quasi-quantitative experimental research design was used. Smartphones were integrated in algebra teaching and learning, using the Microsoft Math online application: https://www.math.microsoft.com. Despite challenges encountered during the study, the results indicated a positive impact on learners’ achievements in algebra, amongst experimental group learners. A need exists for future research in integrating smartphone technology in mathematics education. / Mathematics Education / M. Ed. (Mathematics Education)

The study investigated errors made by Grade 9 learners when simplifying algebraic expressions. Eighty-two (82) Grade 9 learners from a rural secondary school in Limpopo Province, South Africa participated in the study. The sequential explanatory design method which uses both quantitative and qualitative approaches was used to analyse errors in basic algebra. In the quantitative phase, a 20-item test was administered to the 82 participants. Learners’ common errors were identified and grouped according to error type. The qualitative phase involved interviews with selected participants. The interviews focused on each identified common error in order to establish the reasons why learners made the identified errors. The study identified six (6) common errors in relation to simplifying algebraic expressions. The causes of these errors were attributed to poor arithmetic background; interference from new learning; failure to deal with direction and operation signs; problems with algebraic notation and misapplication of rules. / Mathematics Education / M. Ed. (Mathematics Education)

The aim of this study was to explore the effects of a problem-solving heuristic instructional method on Grade 6 learners’ achievements in algebra. Two main theories inspired the design of this teaching method, namely the modelling and modelling perspective, and action, process, object, schema (APOS) theory. Modelling and modelling perspectives guided the development of modelling-eliciting activities used in the teaching method and the APOS theory guided the sequence of activities used to develop Grade 6 learners’ conceptions in algebra. The impact of the problem-solving heuristic instructional method was investigated with 198 Grade 6 learners from four different primary schools in the Zululand district of Kwazulu-Natal that were conveniently sampled. A mixed-method approach was used in this study and a hypothesis was formulated to investigate the effects of the teaching method on the learners’ achievements in algebra. The qualitative component consisted of a pre-intervention class observation of mathematics lessons of all four mathematics educators in the schools used for this study. The design and implementation of the problem-solving heuristic instructional method and the quantitative component employed non-equivalent control group design with pre-test and post-test measure. The main instruments for data collection were an observation schedule to document sequence of events in the classroom during the class observation, a standardized achievement test in algebra used to measure effects of the problem-solving heuristic instructional method and modelling-eliciting activities used as a medium of interaction between learners and the researcher during the implementation of the problem-solving heuristic instructional method. Findings from the class observation indicated all four schools made use of comparable traditional methods of instruction. The implementation of the problem-solving instructional method gave insights into how a problem-solving heuristic instructional method can be developed and used in Grade 6 algebra lessons, and the factors that could influence learners’ conceptual development in algebra. The findings from the quantitative component supported the initial hypothesis that improved scores in algebra are achieved through participation in the problem-solving heuristic instructional method. Quantitative data was analysed using the t-test, analysis of covariance, Johnson-Neyman (J-N) technique and the effect size. / Mathematics Education / D. Phil. (Mathematics Education)

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.