The study was undertaken to identify the factors that influence standard seven pupils when they choose whether to continue with mathematics at senior secondary level or not. The relative importance of the factors was also determined. The literature study identified the following factors: attitude towards mathematics, utility of mathematics, family members' influence, mathematics teacher's influence, peer group influence, achievement and gender. The empirical study dealt with the following: * A 77 item questionnaire was completed by 201 standard seven pupils. * The statistical analysis revealed significant differences between pupils who chose mathematics and those who did not, with regard to all variables except gender. * A regression analysis identified the most influential factors as achievement, family members' influence, attitude and the mathematics teacher. * The overall implications were: - Pupils be made to experience success so that their attitudes may change. - Parents must be involved in their children's education. / Psychology of Education / M. Ed. (Psychology of Education)

Thesis (PhD (Curriculum Studies))--University of Stellenbosch, 2007. / This action research study was aimed at establishing the importance and role of communication, and determining to what extent it impacts on formative assessment in the mathematics classroom with particular reference to feedback. During the first cycle of research it was evident that conditions within the mathematics classroom were preventing this from being realised. If we as researchers were to assess the nature of communication patterns within the classroom situation, then those communication patterns should have existed. Our findings reflect that teachers were generally in control of all aspects of communication of their learners, and that communication was usually a type of monologue, with very limited response from learners to closed questions, (characterised by “yes” and “no” responses), which were frequently posed. The feedback from learners (perhaps inadvertently ignored), was not optimally utilised to enhance learning. Through observation it was determined that teachers’ ability to engage learners meaningfully for longer periods, or to consciously reflect upon their actions, needed to be developed. Praxis as research paradigm, which is based on reflection and appropriate response or action geared towards improving the circumstances or conditions of the people concerned (in this case teachers), underlies this study. This research is furthermore based on the following learning theories: enactivism, constructivism, facilitation theory, action learning, andragogy, reification, and situated learning...

Thesis (PhD (Curriculum Studies))--University of Stellenbosch, 2010. / Bibliography / The implementation of OBE has significant implications for teachers’ work; adopting an OBE approach entails reconstruction of professional knowledge and a redefinition of planning procedures, teaching approaches and assessment practices. A teacher attempting to make sense of OBE, learning outcomes, assessment standards, band levels, NQF, etc. will inevitably bring his/her worldviews, past experiences and beliefs into the process of teaching and learning, and would also need to engage with new concepts to keep track of the changes in meaning and priorities. Within this changing education scenario OBE, as an initiative, offers opportunities for new pedagogies to flourish, marking a departure from the safe haven of traditional pedagogy. Therefore a perspective on teachers’ beliefs regarding OBE can provide an alternative interpretive lens for researchers through understanding teachers’ actions and thoughts. Purpose: The aim was to examine strategies teachers employ in their classrooms in response to their beliefs about OBE. Teachers’ epistemological beliefs were explored and linked to OBE pedagogical frameworks and classroom management practices. Their belief systems were divided into three categories – the teachers’ views about OBE, mathematics knowledge, and the teaching and learning of mathematics. This study was based on the belief that conceptions are specific meanings given to phenomena, derived from different experiences involved in helping individuals make sense of their world. Furthermore, those worldviews in turn influence how new information is perceived. Methodology: The researcher adopted a qualitative exploratory design. The method of choice for this study was a combination of elements of phenomenology and ethnography. Nineteen teachers were interviewed and observed. The sample was drawn from two former Model C schools and three township schools. Data were analysed qualitatively. Findings: The findings confirmed that there are multiple beliefs that constitute a personal epistemology. Therefore, to investigate some unique entities of the belief system such as OBE requires examining the broader belief system. The majority of teachers responded to OBE implementation with uncertainty, anger, frustration and anxiety. In the absence of certainty about OBE and faced with a myriad of classroom iv challenges, teachers relied on their experience to make decisions regarding what was important to know, they drew on their own personal teaching theories more than what they thought about OBE to make judgments of learning processes. This study concludes that the link between teachers’ beliefs, conceptualisation of OBE and teaching practice is weak. Their beliefs about the nature of mathematics knowledge, teaching and learning mathematics had stronger connections with, and represented the basis for teachers’ pedagogical purpose behind their preferred teaching practice.

Thesis (MEd)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: Traditionally the success of learners in South Africa was based on one examination. The education depended on memorization, at the expense of other important skills such as critical thinking, problem solving and analysis. The modern working situation requires learners with critical thinking skills who can solve problems. Traditionally learners were seen as ‘empty vessels’ and their existing knowledge was not considered. The traditional assessment methods were not good enough to give teachers the information they needed to know about the learner. The education therefore requires reconstruction. In 1997, education in South Africa experienced a paradigm shift with the introduction of Curriculum 2005 and Outcomes-Based Education (OBE). The education system has been systematically reconstructed since then. In 2001, Curriculum 2005 was implemented in the senior phase. Along with this paradigm shift came a change in learner assessment. The Further Education and Training band will only be influenced by the curriculum in 2004, but since 1996, teachers have been instructed to assess learners continuously. The Institute for Mathematics and Science Teaching of the University of Stellenbosch (IMSTUS) was contracted in 2000 to implement continuous assessment (CASS) in Mathematics in Grade 10 – 12 in the Northern Cape. The project is known as the CASS project. One of the aims of this project is to motivate teachers to implement the new guidelines of the Northern Cape Education department for continuous assessment. The research is firstly an empirical investigation of the perceptions of teachers in the IMSTUS project being conducted in the Northern Cape on continuous assessment. Secondly, it is an investigation to determine whether teachers are convinced that alternative/formative assessment can improve teaching and learning. It focuses on whether continuous assessment is regarded by teachers as an educational tool or a bureaucratic process. A questionnaire was given to teachers who participated in this project. The questionnaire consisted of questions on teachers’ perceptions on continuous assessment, the rationale for assessment, how assessment and feedback can be done, and the equity in the assessment of Mathematics. There were 34 questionnaires of which 31 (91%) were returned. Twenty-three of the responses were from schools in the Kimberley district, while the other 8 were from the De Aar district. The participating schools were from traditional advantaged, as well as disadvantaged communities. The conclusions of the research are that the participating teachers have the following perceptions on continuous assessment: 1. Continuous assessment is used for: • grading purposes and for year marks, in other words for bureaucratic purposes; • the improvement of teaching, learning, and for diagnostic purposes, to identify learners’ misconceptions and strengths -in other words, it can also be used for educational purposes. 2. The process of continuous assessment does not reflect learners’ real mathematical potential. 3. Some respondents were of the opinion that the process of continuous assessment does however reflect learners’ real mathematical potential. 4. Continuous assessment is time-consuming. 5. Continuous assessment must be systematical. The way in which teachers implement continuous assessment testifies to a summative process, although they in a way learners formative assess. This does not improve formative assessment and therefore is it exclusively a bureaucratic process. / AFRIKAANSE OPSOMMING: Die sukses van leerders in Suid-Afrika het tradisioneel op ’n eenmalige eksamen berus. Die onderwys was te lank op memorisering geskoei, ten koste van ander belangrike vaardighede soos kritiese denke, probleemoplossing en analisering. Die hedendaagse werksomstandighede vereis leerders wat krities kan dink en wat probleemoplossings kan hanteer. Tradisioneel is leerders se bestaande kennis nie in ag geneem nie en die tradisionele assesseringmetodes het onderwysers nie genoeg informasie gegee wat hulle van die leerders moet weet nie. Die onderwys verg dus rekonstruksie. In 1997 het onderwys in Suid-Afrika ’n paradigmaverskuiwing ondergaan met die invoering van Kurrikulum 2005 en Uitkomsgebaseerde Onderwys (UGO). Die onderwys is stelselmatig gerekonstrueer en Kurrikulum 2005 is in 2001 in die senior fase geïmplementeer. Hierdie kurrikulumverandering bring ook ’n verandering in assessering mee. Die Voortgesette Onderwys en Opleidingbaan sal eers in 2004 deur die Kurrikulum beïnvloed word, maar onderwysers moet reeds sedert 1996 leerders deurlopend assesseer. Die Instituut vir Wiskunde en Wetenskaponderwys van die Universiteit van Stellenbosch (IWWOUS) is in 2000 gekontrakteer om deurlopende assessering (DASS) in Wiskunde in Graad 10 - 12 in die Noord-Kaap te implementeer. Die projek staan bekend as die DASS-projek. Een van die doelstellings van hierdie projek was om onderwysers te motiveer om die Noord-Kaap Onderwysdepartement se nuwe riglyne vir deurlopende assessering te implementeer. Die navorsing is eerstens ’n empiriese ondersoek na die persepsies wat die onderwysers in die IWWOUS-projek in die Noord-Kaap oor deurlopende assessering het. Tweedens is dit ’n ondersoek of onderwysers oortuig is dat alternatiewe/formatiewe assesssering onderrig en leer kan bevorder. Dit fokus of deurlopende assessering ’n opvoedkundige of burokratiese proses vir hierdie onderwysers is. ’n Vraelys is aan onderwysers, betrokke by die projek, gegee. Die vraelys het vrae bevat oor onderwysers se persepsies oor deurlopende assessering, die rasionaal vir assessering, hoe assessering en terugvoering gedoen word en gelykberegtiging in die assessering van Wiskunde. Daar is 34 vraelyste versprei waarvan 31 (91%) terugbesorg was. 23 van die vraelyste was van skole in die Kimberley-streek, terwyl die ander 8 vraelyste in die De Aar-streek was. Die deelnemende skole kom uit die tradisioneel bevoordeelde sowel as benadeelde gemeenskappe. Onderhoude is met 10 onderwysers in die Kimberley-streek en 2 onderwysers in die De Aar-streek gevoer. Die bevindinge van die navorsing is dat die deelnemende onderwysers die volgende persepsies oor deurlopende assessering het : 1. Deurlopende assessering word gebruik vir • bevorderingsdoeleindes en vir jaarpunte, met ander woorde vir burokratiese doeleindes; • die verbetering van onderrig en leer en diagnostiese doeleindes om leerders se wankonsepte en sterkpunte te identifiseer. Deurlopende assessering word dus ook vir opvoedkundige doeleindes gebruik. 2. Die proses van deurlopende assessering weerspieël nie leerders se werklike wiskundige vermoëns nie. 3. Die proses van deurlopende assessering weerspieël ook leerders se wiskundige vermoëns. 4. Deurlopende assessering is tydrowend. 5. Deurlopende assessering moet sistematies wees. Deurlopende assessering soos deur hierdie onderwysers geïmplementeer, is ’n summatiewe proses, alhoewel hulle tog in ’n mate hulle leerders formatief assesseer. Dit verbeter egter nie formatiewe assessering nie en daarom is dit uitsluitlik ’n burokratiese proses.

Thesis (MEd)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: According to Prins(1995), readability factors in Mathematics text do not only influence the comprehension of questions, but also have a marked influence on learner achievement levels. Extending on Prins (op cit), this study sought to investigate whether there are any differences in the quality of interpretation and choice of algo-heuristic methods when isiXhosa-speaking learners respond to mathematical word problems set in English and isiXhosa. The study was located within an ethnographic framework, with all of the 109 participants speaking isiXhosa as LI. The participants were in grades 8 (44), Grade 9 (29) and grade 10(36) and all took Mathematics as one of their school subjects. Learners were divided into four groups based on achievement levels in English in June examinations. The study was cross-sectional, with each of the four groups comprising learners who were good achievers, average achievers and under achievers in English second language. A unique methodological and data collection design was undertaken in such a way that each of the participants responded to word problems set in both English and isiXhosa. Two questions were administered to all learners (one in each of the two languages). The two questions were written in two sessions. If a learner responded in English during the first session, s/he will respond in isiXhosa during the second session and vice versa. There was a 5-minute break in between the sessions. Data was analysed both quantitatively and qualitatively. The broad focus of the analyses was on learners' quality of interpretation of the given word problems and the choice of computational methods they employed when they responded to the word problems. Three categories were investigated under each of the focus areas. Categories investigated under the quality of interpretation were: [J Totally false interpretation [J Partially correct interpretation and [J Totally correct interpretation Categories investigated under the choice of computational methods were: [J Standard methods [J Non-standard methods [J Unidentifiable methods The evidence gathered suggested that isiXhosa-speaking learners interpret word problems better when they are set in isiXhosa rather than English. Another important finding was that isiXhosa-speaking learners prefer to use standard methods when they respond to word problems set in English and also prefer to use non-standard methods when they respond to word problems set in siXhosa. / AFRIKAANSE OPSOMMING: Volgens Prins (1995) beïnvloed leesbaarheidfaktore in Wiskundetekste nie net die verstaan van vrae nie, maar het dit ook 'n merkbare invloed op leerders se prestasievlakke. Ter uitbreiding op Prins (op cit) het hierdie studie gepoog om ondersoek in te stelof daar enige verskille in die kwaliteit van interpretasie en keuse van algo-heuristiese metodes is wanneer isiXhosasprekende leerders op wiskundige woordprobleme reageer wat in Engels en isiXhosa gestel is. Die studie is binne 'n etnografiese raamwerk geplaas. Al 109 deelnemers het isiXhosa as eerste taal gepraat. Die deelnemers was in Graad 8 (44), Graad 9 (29) en Graad 10 (36) en het Wiskunde as een van hul skoolvakke geneem. Leerders is in vier groepe verdeel, en die indeling is op prestasievlakke in Engels in die Junieeksamen gebaseer. In hierdie deursneestudie het elk van die vier groepe uit leerders bestaan wat goeie presteerders, gemiddelde presteerders en onderpresteerders in Engels tweede taal was. 'n Unieke metodologiese en data-insamelingsontwerp is op so 'n wyse toegepas dat elkeen van die deelnemers op woordprobleme gereageer het wat in beide Engels en isiXhosa gestel is. Twee vrae is aan elke leerder gestel, een in elk van die twee tale. Die twee vrae is in twee sessies beantwoord. As 'n leerder tydens die eerste sessie in Engels reageer het, sou sy/hy tydens die tweede sessie in isiXhosa beantwoord, en omgekeerd. Daar was 'n pouse van vyf minute tussen die sessies. Data is beide kwantitatief en kwalitatief ontleed. Die breë fokus van die analises was op die kwaliteit van die leerders se interpretasie van die woordprobleme en die keuse van bewerkingsmetodes wat hulle aangewend het wanneer hulle op die woordprobleme reageer het. Drie kategorieë is in elk van die fokusareas ondersoek. Die kategorieë wat onder die kwaliteit van interpretasie ondersoek is, was: Cl 'n Algeheel verkeerde interpretasie Cl 'n Gedeeltelik korrekte interpretasie en Cl 'n Algeheel korrekte interpretasie Kategorieë wat onder die keuse van bewerkingsmetodes ondersoek is, was: u Standaardmetodes u Nie-standaardmetodes en o Onidentifiseerbare metodes Die gegewens wat ingewin is, het daarop gedui dat isiXhosasprekende leerders woordprobleme beter interpreteer wanneer die probleme in isiXhosa eerder as in Engels gestel is. 'n Ander belangrike bevinding was dat isiXhosasprekende leerders verkies om standaardmetodes aan te wend wanneer hulle op woordprobleme wat in Engels gestel is, reageer, en dat hulle ook verkies om nie-standaardmetodes te gebruik wanneer hulle op woordprobleme reageer wat in isiXhosa gestel is.

published_or_final_version / abstract / Education / Master / Master of Education

Research has shown that academic under-performance in higher education can be attributed inter alia to psychosocial difficulties arising from students’ under-preparedness for the rigours of university life, the struggle to accommodate diverse cultural worldviews and poor proficiency in the language of learning and teaching (Chang 1999). As internationalisation of higher education institutions has became more common worldwide, the need for support systems to deal with problems of a multicultural student body has become essential if students are to have equitable opportunities for success. In this regard, Monash South Africa (MSA), an international multicultural higher education institution, introduced a tutor-mentor programme to improve academic outcomes among mathematics students in the Foundation Programme (FP). The impact of this programme was investigated by means of an empirical investigation and framed by a bricolage of learning theories which served as a conceptual framework for the study under the metaphors of acquisition and participation. The literature study showed that tutoring and mentoring programmes tend to be successful pedagogical supports. The empirical inquiry took the form of a mixed-method case study which explored the impact of participation in the tutor-mentor programme on mathematical performance among FP mathematics students at MSA. The participants in the study, which was carried out in two phases, were mathematics students, tutor-mentors and lecturers in the FP. Phase 1 quantitatively explored the extent of effectiveness of the tutor-mentor intervention, using a quasi-experimental non-equivalent control group design. Two formal tests were used to gather data, which were analysed by an analysis of covariance and the Johnson-Neyman technique. Quantitative findings supported the initial assumption of the study: that participation in the tutor-mentor programme as an intervention strategy improved the mathematics scores of FP students at MSA. Phase 2, a qualitative study, used purposive sampling. Data was gathered through focus group and individual interviews, observation, spontaneous conversations and photographs. Interpretation of the quantitative and qualitative data was presented according to the phases and thereafter integrated. Qualitative findings provided information about the dynamics of the tutor-mentor programme in providing academic and psychosocial support to students. Finally, a situation-producing theory was developed from the integrated findings, and recommendations made for improvement of practice. / Educational Studies / D. Ed. (Comparative Education)

This qualitative case study investigated how six National Board Certified secondary mathematics teachers integrate knowledge of students into their practice to create socio- academic spaces for learning. Individual audiotaped interviews were utilized to generate data about what knowledge these teachers had of their students, how they gathered this knowledge, and how this knowledge of students influenced their decisions related to curriculum and instruction. The data were used to form an understanding of the nature and function of the socio- academic spaces that teachers create in planning for and delivering instruction. The study revealed that as teachers interact independently with the curriculum, they create spaces for analysis and reflection. In addition, as they interact with their students around the curriculum, they create spaces for their students to practice, to make connections, to communicate, and to apply and experience math. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection

This study compared data related to National Board Certification (NBC) of mathematics teachers in a South Florida school district. Data included 1,162 student scores on the 2014 AP Calculus AB exam, student gender, student grade level, and eligibility for free or reduced price lunch (FRL) status. Teachers completed the Standards' Beliefs Instrument (SBI) (Zollman & Mason, 1992) to determine alignment of their beliefs with the National Council of Teachers of Mathematics (NCTM) standards. Interviews were conducted with five NBC mathematics teachers to understand how they incorporate best mathematics teaching practices in their daily instruction. A t-test analysis revealed that students taught by NBC teachers scored significantly higher (M = 3.70) on the AP Calculus AB Exam than those taught by non-NBCTs (M = 2.74); Cohen's d (.6429) indicated a moderately large effect size. No causation is to be implied; various confounding factors may also contribute to the variance in student scores. Three factorial ANOVA tests were performed to test interaction effects. Two significant interaction effects were detected: (1) NBCT status and student grade level; and (2) NBCT status and student FRL (free and reduced price lunch) status. No significant interaction was found between NBCT status and student gender. With a reliability estimate using Cronbach's alpha, a second t-test was conducted. A statistically significant difference was found regarding the mean scores of NBCTs and non-NBCTs regarding their beliefs according to the vision of the NCTM. NBCTs generally have practices that align more with the NCTM mathematics teaching standards. Interviews with five NBC teachers of AP Calculus provided rich qualitative descriptions of their teaching philosophies, approaches, and best practices contributing to student success. The results of this study reinforce evidence from previous research that the process of obtaining the NBC contributes to a teacher's professional expertise and is related to student success; however, since there may be other confounding factors related to teachers, students, and their schools, the NBC cannot be considered the sole factor contributing to student success in AP coursework and exams. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection

Gender inequalities perpetuated by educational and occupational segregation may be exacerbated in part by socialization processes that occur in the years leading up to when high school students typically begin considering postsecondary options. Students’ feelings of self-efficacy in certain subjects can be an important factor that informs their decisions to pursue coursework and programs. This study used stereotype theory to understand how students' perceptions of their 9th grade math teacher's fairness affected their 11th grade math efficacy and how this relationship was moderated by the gender of the student and their math teacher. Using the High School Longitudinal Study of 2009, linear regression models predicting students’ math efficacy in 2012 indicated that students have higher levels of math efficacy when they perceive their math teachers as more fair, though this relationship was explained away by controls. An additional interaction term between student gender and math teacher gender revealed that girls’ efficacy is more strongly affected by perceptions of their male math teachers than perceptions of their female math teachers. This finding may be explained by the persistence of stereotypes around math that assume male superiority in the subject, which leads students to see their male math teachers as true authorities in math as opposed to their female math teachers.