Orientador: José Marcos Lopes / Banca: Edison Righetto / Banca: Regina Litz Lamblém / Resumo: Este trabalho apresenta o resultado qualitativo de quatro atividades aplicadas no 6º ao 9º Ano do Ensino Fundamental e teve como objetivo principal elaborar, implementar e analisar uma sequência didática envolvendo robótica educacional e matemática (com enfoque aos números racionais). Essas atividades foram aplicadas em dezembro de 2014 na escola SESI de Andradina no estado de São Paulo. A escolha para o mês de dezembro foi intencional justamente para que os alunos utilizassem seus conhecimentos e habilidades adquiridos no decorrer desse ano letivo. A importância de se realizar tal temática, em conjunto, vem da necessidade crescente da utilização da tecnologia, que permeia o meio social no qual o aluno está inserido, a favor da educação e pelo fato das frações ainda serem um paradigma de difícil assimilação por parte dos alunos, de acordo com Silva (2006) e Demartini (2009). Com base na metodologia LEGO®, sintetizada em quatro verbos na ordem: contextualizar, construir, analisar e continuar, utilizamos três montagens de robôs dos fascículos da LEGO® Zoom para servir de suporte às resoluções das situações-problema desenvolvidas especificamente para a idealização deste estudo. O resultado desta pesquisa mostrou que além da diversão proporcionada, foi instigada a curiosidade dos alunos ao perpassarem por todas as quatro ações mencionadas anteriormente, pois consonante às situações-problema contextualizadas, os alunos, em grupo, assimilaram facilmente o objetivo de cada atividade / Abstract: This paper presents the qualitative result of four activities applied in the 6th to 9th grades of Elementary School and intend to design, implement and analyze a didactic sequence involving educational robotics and mathematics (with a focus on rational numbers). These activities were implemented in December 2014 in SESI school in Andradina, São Paulo state. The choice for the month of December was intended precisely so that students would use their knowledge and skills acquired during that school year. The importance of conducting this theme, together, comes the growing need of using technology that pervades the social environment in which the student is in; for education, and because the fractions are still a difficult paradigm to be assimilated by students, according to Silva (2006) and Demartini (2009). Based on LEGO® methodology, summarized in four words in order: Connect, Construct, Contemplate, and Continue, we used three assembly robots LEGO® Zoom to provide support to the resolutions of problem situations developed specifically for the idealization of this study. The research result showed that beyond that provided fun, it was instigated the curiosity of students to go through all four aforementioned actions, as consonant to problem situations contextualized, students, in group, easily assimilated the purpose of each activity / Mestre

This study concentrated on word problems in Grades Kindergarten-3 and the application of the Standards for Mathematical Practice and the Content Standards. The study also included an analysis of focus, coherence, and rigor in the materials. The textbooks used were among the first editions to be published after the acceptance of the Common Core State Standards in more than 40 states. The study analyzed the presence of the Common Core Standards in each series and how the three textbook series compared to each other in their word problem solving. The correlation of materials in the three textbook series relied on publishers’ descriptions in the Lesson Openers where the usages of the Standards for Mathematical Practice and the Content Standards and the principles of focus, coherence, and rigor are listed. The publishers’ descriptions were analyzed and compared to the individual evaluation criteria. Using an evaluation criterion, the study examined how Standards for Mathematical Practice were implemented in the textbooks. With the exception of a few grades in two textbook series, the texts displayed low percentages in their adherence to the Standards. The textbook series were similar in their development of word problems labeled with Standards for Mathematical Practice and word problems not labeled with the Standards. In this comparison, the only difference between the two types of word problems was in the verbiage. The Content Standards were used to determine the textbook series alignment with the Standards. The three textbook series showed low implementation of word problem Content Standards when compared to the total number of Standards. In two series, only one Content Standard was listed multiple times rather than a combination of comparable Standards. Relying on the publishers’ descriptions, the study showed how publishers implemented focus, coherence, and rigor in their materials. Of the three publishers, one publisher did not list coherence and rigor in its materials. The other two publishers adhered to focus and coherence in most or all of their materials. All of the publishers fell short in the application of rigor in their textbook series.

Recently, in an attempt to promote globalization and internationalization, the Chinese government has introduced AP (Advanced Placement) and IB (International Baccalaureate) programs in Chinese high school. Although it is one of the biggest countries to introduce international programs to its secondary education in an effort to prepare more students to go overseas to pursue their higher education, China does not have much research focusing on introduced foreign academic programs. The purpose of this study is to fill in some gaps in the research while providing a better understanding of the depth behind the phenomenon of introducing the AP program and the IB diploma program in China and that introduction’s impact on the existing general Chinese high school program in mathematics. Multiple sources of data were collected and used to make various kinds of analysis such as contextual analysis, cross-curricula comparisons and statistical analysis. The findings illustrated the differences and similarities between the AP program and the IB program in their respective schools in Ningbo, China. It further examined the differences and similarities between the AP program/ IB program and the intended Chinese high school program in mathematics education. It also explored mathematics instructors’ perceptions of the imported AP and IB programs in China. Limitations of this study include the absence of some test scores, the relatively small sample size and the circumscribed selection of interviewees. This study provides a guide to help Chinese students and their parents decide on a learning program based on individual preferences. Also, the results of this study indicate that a considerable gap exists between secondary education and higher education in Chinese mathematics, and also points to possible limitations for individualized learning. The findings imply the need to consider curricular reform and suggest that local teachers and non-local teachers who teach in the imported programs consider reinforcing their teaching by learning from each other. Policymakers need to make adjustments to consider local conditions when introducing international programs so as to offer the most suitable program possible to native students.

National and international studies show that the standard of mathematics teaching and learning in South Africa is very low compared to other countries. These statistics are worrying because mathematics is one of the ‘gatekeeper’ subjects that determine learners’ access to higher learning and a better future. My study, aimed at exploring two Foundation Phase teachers’ selection and use of examples and representations when teaching number, forms part of a longitudinal study currently underway within the Wits Maths Connect Primary (WMC-P) Project. One of the broad aims of the WMC-P Project is to improve primary teachers’ mathematics content knowledge and also to see this translated into improved pedagogy on the ground. This qualitative study was carried out within the WMC-P Project’s 20-Day in-service training course and one of the ten government schools participating in the broader study. My study aimed to build on research that has been carried out on teachers’ use of examples and representations with a focus on the South African terrain. The dataset comprised of two Foundation Phase teacher’s pre-tests, course-work tasks, field notes, and transcripts of observed lessons. Data was analysed using an analytical framework based on current literature related to examples and representations within mathematics teaching. Findings from my study show possible associations between a higher content knowledge score and the extent of a teacher’s example space and more coherent connections between different representational forms. More studies around this topic are needed because research shows that teachers’ examples and representations in mathematics teaching are important for good teaching and conceptual understanding.

Research Project in Education for: Masters in Education / This study analyzed the pedagogical practices of three Grade 10 Mathematical Literacy (ML) educators. The rationale behind the study was to add information and insight into the very new and under researched Further Education and Training secondary school subject of ML. Botha (2011) discussed how one of the main concerns with ML integration into the South African national curriculum was that the educators being asked to teach ML were moved into it from other subjects without any real education or training, and so when teaching, relied on previously learned pedagogical practices from other subjects. It is the contention of this study that this is a real issue in terms of the teaching of ML in classrooms and in terms of damaging its perceived academic status. In order to offer insight into how ML is its own distinct subject and not simply a lesser version of Mathematics, this study analyzed three lessons of each of the three educators through the lens of Pedagogical Link Making (PLM) (Scott, Mortimer, & Ametller, 2011). PLM was the conceptual framework that guided the observations and post observation interviews, and through analysis of the educators’ pedagogical practices as well as a thematic analysis of discussion points during the interviews, this study came to five major findings. The findings suggested that the ML educators were not properly educated in ML pedagogy and that the educators made the majority of pedagogical decisions in the classroom based on generating learner interest and motivation for work. It also found that the educators used many of the links outlined by PLM, but also admitted to holding a lower academic expectation of ML and ML learners. A call is made to increase research into the relatively new subject of ML along the lines of pedagogical practices in order to assist new ML educators to translate and transmit the goals and content of ML provided for by the Curriculum and Assessment Policy Statement (CAPS

No description available.

A research report submitted to the Wits School of Education and the Faculty of Science, University of the Witwatersrand in partial fulfilment of the requirements for the degree of Master of Science by combination of coursework and research. Johannesburg, 5 June 2017 / This research report focussed on the teaching of the function concept directed at the errors the learners make as well as the misconceptions which could be associated with those errors. The study was conducted at a secondary school in Johannesburg, South Africa. This was a qualitative error analysis study which also had a form of interventional or remedial teaching. The research was driven by the following research questions: (1) What errors and misconceptions do grade 11 learners show on functions?, (2) What learning affordances and constraints can be created if teaching is directed at learners’ errors and misconceptions? and, (3) To what extent can the learners’ achievement on the topic functions be boosted if teaching is directed at learners’ errors and misconceptions? The study used a purposive sample of six grade 11 mathematics learners from a group of 34 learners. To answer these questions, I structured the study to encompass numerous phases of data collection using different instruments. Firstly, I constructed a test instrument and used it on this group of grade 11 learners. These learners had been taught functions earlier in the year, so the test was diagnostic to measure the cognitive levels of the learner on the concept and also to establish the errors made and misconceptions they carried onto the section from other sections or picked up from the function concept. The study was mainly based on the constructivism theory of learning and teaching, but also had other theories to link to it such at the socio-cultural theory, the APOS (actions, process, object and schema) theory, the concept image and concept definition as well as the variation theory. The errors I picked up from the pre-test I classified and analysed using the conceptual framework grounded on the abovementioned theories. It was this analysis which enabled me to structure the desired intervention program together with the teacher after which I conducted a post-test with the subjects. Other forms of data collection such as the interview and observation were employed during the study. I used the interview to get clarity from the learners’ pre-test questions responses, whilst the observation I used during the intervention lessons the teacher had with the learners. Indeed the findings were that, while there was a substantial improvement on learner performance on the post-test, it appeared clearly that cognitive levels of the learners on the function concept had been enhanced. This improvement of performance was a result of the teaching that was directed at the errors, which also interprets to having created a favourable environment which could be interpreted as learning affordances to boost the learners’ understanding of the function concept. / LG2017

Research Report submitted to the Wits School of Education, Faculty of Science, University of the Witwatersrand, Johannesburg In partial fulfilment of the requirements For the degree of Master of Science (Mathematics Education) Johannesburg, 2017 / South Africa’s performance in mathematics education is ranked amongst the world’s worst. This performance is not only alarming at an international level, but also nationally. Annual National Assessments (ANA) conducted by the Department of Education have showed that the level of mathematics across the foundation and intermediate phase is poor with a pronounced dip in performance at a Grade 4 level (Department of Basic Education, 2014). Multiplication and division are common challenging areas that contribute to this poor performance. This is concerning as mathematics is globally recognised as a key competence for providing access to higher education and developing a country’s society and economy. My study, aimed at exploring multiplicative reasoning with Grade 4 learners through structured problem solving, is focused on the learning of multiplication and division within the context of an intervention concentrated on developing learners’ ability to model multiplicative situations. Shifts in the use of models were investigated following a smallscale intervention in which different modelling approaches (particularly ratio modelling) were introduced and developed. A control group was used to determine the usefulness of the intervention. Questions which I sought to answer were: (a) what kinds of multiplicative reasoning (models) are Grade 4 learners using prior to intervention, (b) what changes, if any, are seen in overall performance, across the intervention and control group, in the post-test, and, (c) what kinds of differences in model use were associated with the shifts in performance? The main dataset comprised of 61 pre- and post-test scripts across three Grade 4 classes in a former Model C school in a Johannesburg district. A sample of 15 interviews were also conducted across the classes. Document analysis and transcription notes were used to analyse data with a Realistic Mathematics Education (RME) framework informing my analysis. Findings from my study reveal that prior to intervention, Grade 4 learners presented limited multiplicative models which were predominantly confined to traditional algorithms. After the small-scale intervention, learners used a broader range of models with an emerging take up of ratio models. The success rate associated with the models presented by learners also improved. Limited and/or no changes in model use and their respective success rates were seen in the control group suggesting that the intervention program was useful. These findings suggest that, as a future recommendation, it would be worthwhile to investigate the outcomes of running a similar intervention in less privileged settings. / MT 2018

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Signed on 10 September 2016 in Austin, Texas, USA. / This dissertation investigated the possible connection between the two constructs of metacognition and the strands of mathematical proficiency. Using a small convenience sample of Grade 12 learners at a public all-girls high school in Johannesburg, South Africa, the teacher/researcher examined if training in metacognitive knowledge influenced the learners’ conceptual understanding, procedural fluency, strategic competence and heuristic strategy use. Two instruments (pre-test and post-test) developed by the researcher and completed by the students were on-line assessments of metacognition utilising written self-reports of strategy use that occurred simultaneously with mathematical problem solving. Qualitative analyses were applied to the data and learners demonstrated declarative, procedural and conditional metacognitive knowledge in their explicit heuristic and content-specific strategies. The learners also demonstrated strategies which could be inferred from their working. The study showed evidence of mixed transferability of metacognitive training to mathematical proficiency. Questions for further research are provided. / LG2017

Master of Science in Mathematics Education 2017 / This study focused on mathematical teachers’ beliefs about teaching critical thinking and how these beliefs informed teaching mathematics in practice. Two sets of interviews were conducted that investigated what conceptions of critical thinking, teaching strategies and tasks, and assessment methods, teachers believed promoted critical thinking in their mathematical classroom. Qualitative methods of inductive analysis were used to analyse teachers’ responses based on grounded theory where categories were constructed and re- organised into themes. The study found that teachers had a limited understanding of critical thinking and their beliefs about teaching critical thinking skills in mathematics did not appear to be reflected in practice. These newly qualified teachers demonstrated that they need assistance in developing and using teaching strategies and tasks that promote critical thinking skills in mathematics. / MT 2018