Dissertations / Theses on the topic 'Mathematics and numeracy curriculum and pedagogy'

This thesis reports on a multiple case study of the actions of three Queensland secondary schools in the context of Year 9 NAPLAN numeracy testing, focusing on their administrative practices, curriculum, pedagogy and assessment. It was established that schools have found it both challenging and costly to operate in an environment of educational reform generally, and NAPLAN testing in particular. The lack of a common understanding of numeracy and the substantial demands of implementing the Australian Curriculum have impacted on schools' ability to prepare students appropriately for NAPLAN numeracy tests. It was concluded that there is scope for schools to improve their approaches to NAPLAN numeracy testing in a way that maximises learning as well as test outcomes.

This study explored the cognitive functioning of Year 6 students in the domain of decimal-number numeration, particularly with the intention of: (a) comparing the knowledge structure of proficient and semiproficient students with respect to tenths and hundredths knowledge; (b) constructing frameworks and models which explain the structural knowledge differences of proficient and semiproficient students with respect to tenths and hundredths; and (c) drawing implications for instruction. Forty- five students (12 high proficient, 12 semiproficient, 8 medium proficient, 8 medium semiproficient, 5 low proficient) were identified for semistructured individual interviews (Burns, 1994). The interview was informed by the numeration model and, as a consequence, incorporated tasks relating to position and order, to multiplicativity, and to the unitisation and reunitisation of decimal fractions. The interview results revealed that: (a) knowledge of position and order differentiated between high- performing (high proficient, high semiproficient, medium proficient) and low-performing (medium semiproficient, low proficient) students; and (b) availability and accessibility of multiplicativity tasks were the major factors which differentiated performance amongst the high-performing students. As a result of analyses of students' interview responses and the knowledge subcomponents of the decimal-number taxonomy, structural models that represented the cognitions and connections held by the composite performance categories for position/order, multiplicativity, and unitisation/reunitisation were constructed. From a comparison of the structural models, cumulative models that combined findings for each performance category across position/ order, multiplicativity, and unitisation/reunitisation were constructed. The cumulative models represented the two domains involved in decimal-number numeration understanding, namely, whole numbers and fractions, with multiplicativity represented as the structural knowledge that unifies and integrates the structural knowledge of position/order and unitisation/reunitisation. The models were used to draw implications for instruction in decimal numbers and mathematics generally.

Thesis (Ph.D.)--Indiana University, School of Education, 2008.
Title from PDF t.p. (viewed on Jul 21, 2009). Source: Dissertation Abstracts International, Volume: 69-10, Section: A, page: 3849. Adviser: Signe Kastberg.

In Western Australia (WA), all secondary students are required to demonstrate their readiness to leave school and enter further studies or the workplace by achieving a minimum standard of numeracy and literacy. This minimum standard can be demonstrated by passing one of two assessments, the National Assessment Program – Literacy and Numeracy (NAPLAN), an annual national assessment for all students in Years 3, 5, 7, and 9; or, if not having reached a high enough standard on the NAPLAN Year 9 test, the Online Literacy and Numeracy Assessment (OLNA). The latter is high stakes test unique to WA which can be attempted in Years 10 through to 12. These two assessments are similar in that they both assess literacy and numeracy and share a common guiding set of standards, derived from the Australian Core Skills Framework (ACSF) (McLean, Perkins, Tout, & Wyse, 2012). This study investigated some ways that some mathematics teachers prepared their Year 10 students for the numeracy component of the OLNA. While the OLNA assesses numeracy skills rather than more conceptually oriented mathematical skills, the preparation of students for this assessment is the sole responsibility of mathematics teachers. The numeracy component of the OLNA comprises multiple-choice and short-answer worded questions that relate to real-life contexts. Students have 50 minutes to complete 45 questions, and the use of calculators is not permitted. Of importance, whilst previous NAPLAN papers are freely available to support NAPLAN preparation, mathematics teachers do not have access to previous OLNA assessments. They are however provided with an example test and a practice test through the School Curriculum and Standards Authority (SCSA) website. This limited transparency in assessment presents challenges for teachers seeking to prepare students for the OLNA. The study into how the teachers in the study prepared their Year 10 students for the numeracy component of the OLNA was guided by the following two research questions: 1. When preparing students for the mandated OLNA numeracy component in their Year 10 classrooms, does the pedagogy of mathematics teachers change? And if so, in what ways? 2. As calculators are freely used in Western Australian mathematics classrooms, how do these teachers accommodate the calculator free nature of the OLNA assessment? Peter Sullivan’s (2011) Six Key Principles for effective teaching of mathematics were used as the theoretical framework to inform data collection and analysis. These Principles, examined in detail, may be summarised by their headings as: 1. Articulating goals 2. Making connections 3. Fostering engagement 4. Differentiating challenges 5. Structuring lessons 6. Promoting fluency and transfer The study used a case study methodology involving an educational assistant and four teachers across two school sites who were all directly involved in preparing students to take the OLNA. Documentary research, in-depth semi-structured interviews, and observations were used to generate data in a 2-week period that coincided with preparation for the OLNA. The study’s findings suggest that pedagogies for preparing students for the OLNA are distinct in that much of the preparatory work is repetitive, completed independently, based on what the final assessment is expected to look like, and does not allow for the use of a calculator. Three of Sullivan’s Principles (1 and 6) – Articulating goals and Promoting fluency and transfer – were observed to be well represented in most OLNA preparation classes where there was a particular focus on independent work and repetitive exercises that attempted to mimic the OLNA assessment. In contrast, Principles 3 and 5 – Fostering engagement and Structuring lessons – were poorly represented in the data. These principles involved engagement in learning through collaboration, communication, and varied representation of mathematical content. The remaining two Principles, 2 and 5 - Making connections and Differentiating challenges, were present in varying degrees. A key finding was that most of the participants said they felt ill-equipped to prepare their students for the OLNA. They struggled with not having access to the actual assessment, the support resources were perceived as unreliable, and feedback from past results was minimal. As classroom time needed to be divided between curriculum work and OLNA preparation, the teachers’ contact time was not equitably distributed between all the students, with “OLNA students” often receiving less curriculum instruction than “non-OLNA students.” In some instances, students preparing for the OLNA received no curriculum-focused teaching during that time. It is of concern if the pedagogical principles that mathematics education researchers indicate should be present in a classroom for the effective teaching of mathematics, are not evident in OLNA preparation classes. The current research is limited in scope and duration due to the small sample size and the data collection time period, with only two sites studied immediately prior to a single round of OLNA testing. Nevertheless, this study has generated important agendas for future research in Western Australia and nationally into numeracy and mathematics teaching. Future research into the impacts of this high-stakes test on teacher and student wellbeing and on mathematics curriculum progression is recommended.

The aim of the study is to examine high school mathematics teachers' lesson plan development and implementation practices used in the border region of Mexico and USA. The study also attempts to determine how a transition from Mexico (Ciudad Juarez, Chihuahua) to the U.S. (El Paso, TX) impacts high school mathematics teacher’s lesson plan development practices incorporating the Borderland Pedagogy. The Borderland Pedagogy theoretical framework (Cline & Necochea, 2006; Romo & Chavez 2006; Fiume, 2005) was developed to explore educational experiences of teachers situated within border regions. The framework highlights key characteristics of Borderland Pedagogy that influence lesson plan development and implementation practices. The framework was used to design multiple case studies research to examine and understand teaching practices on both sides of the border in general, and pedagogical experiences of transitioning teachers in particular. Elbaz-Luwish (2007) and Sabar (2004) defined teacher transition as an adaptation of a teacher to a new language, culture, and new educational system. Scholars (Shimizu, 2008; Diazgranados et al., 2008; Lit and Lit, 2009) suggest that lesson plans are designed according to teachers’ experiences, knowledge about the subject matter, and beliefs about teaching, and learning. The study is built on understanding that teaching on the border impose unique requirements on lesson plan development practices reflecting flexibility, cultural and linguistic diversity. The research sample included two Mexican teachers, two US teachers, and one transitioning teacher. The design of the study is operationalized based on the following data sources: (1) teacher-developed lesson plans, (2) classroom observations, and (3) structured interviews. Data was analyzed using frequency-based initial and focus coding scheme. The key observation in lesson plan development among participating Mexican and US teachers revealed complexity and uniqueness of borderland teachers’ practices in recognizing, addressing, and implementing national/ state standards and curriculum (Secretaría de Educación Pública, Texas Education Agency). Results of the study suggest that the Borderland Pedagogy could serve not only as a framework but also as an instrument to document and interpret transformative pedagogical practices of teachers teaching on the border.

Little change has resulted from decades of attempts at reforming the teaching of mathematics (Davis et al., 1990). This study involved approximately 43 teachers who had completed an inquiry-based professional development program prior to being provided with a new mathematics curriculum designed to support inquiry-based teaching. It analyzed the relationships between their implementation of the inquiry-based teaching and their use of the curriculum materials. A series of bivariate correlations were run to investigate the relationships between the professional development and aspects related to the implementation of the new curriculum. The factors being so inter-related, it was hypothesized that relationships would exist between all of the factors, but only some of the expected relationships materialized. Like others before, this study supports the idea that merely providing professional development and new curriculum will not always result in a change in teaching. While the teachers in this study were not necessarily resistant to change, a lack of time to implement new teaching does seem to have affected the level of change in teaching. Future research is needed related to methods and timing related to the implementation of new teaching practices and curriculum and their relationship to teacher change.

This dissertation is a currere study of how five students and their teacher understand their mathematical learning inside a Grade 10 classroom in Quebec. More closely, this research examines how recollections of past, present, and future mathematizing are tied to one’s sense of identity. Through analysing the entries in a teacher journal and the autobiographical stories of former students, identifications with and against common tropes of what it means to be “good” at mathematics were examined. This dissertation thus asks, how do participants in mathematics teaching and learning read their experiences, and why does a study like this matter to the future of the subject or to education overall? Using the autobiographical Curriculum Studies method of currere, a psychoanalytic stylistic analysis, and a cultural studies component whereby participants were encouraged to respond to the characters in the popular sitcom The Big Bang Theory, responses were gathered through individual interviews. Insights were derived from psychoanalytic readings of both transference and countertransference taking place in the learning space and beyond. The researcher’s and participants’ responses were understood through the ways in which the teacher’s emotional world is transferred onto the act of teaching and how, reciprocally, the teacher is addressed through feelings, phantasies, defences, and anxieties. The former students were interviewed with the stages of currere in mind in order to elicit free associative responses that lent insight to the regressive, progressive, and analytic stages. The final, synthetical, stage of currere took place to unpack my identificatory work as a researcher and teacher in the mathematics classroom. The methodological considerations in this dissertation included outlining the significance of repetitions of language in interviewees’ responses, both individually and collectively. Participants’ responses began to indicate a complex emotional world whereby their categorization in a “lower” mathematics course in high school nevertheless did not trap their identities into common tropes of of negativity, difficulty, and anxiety. Rather, the types of language and frequency of word use signal how the emotional landscape of students’ mathematical lives is shaped by how students perceive teachers to see them as mathematical or not. This research reveals how mathematics concepts, but more often, pedagogical dynamics, lead to complicated psychological terrain traversed by both teachers and students. I argue that using currere as a methodology readily employable with high school students helps to uncover the complex worlds of mathematical identity formation including the role of societal stereotypes. Furthermore, if educators understand their own dynamics of love and hate in relation to mathematical competence, performance, and pedagogy, they might better foster mutuality between students and teachers overall.

What do the Honda Civic, the Mazda 626, and the Boeing 747 have in common? What about Weird Al's song Bob, the first name of Miley Cyrus' alter ego, and the 70s sensation Abba? What do all these things have in common? They all contain palindromes. While some people recognise a palindrome when they see one, fewer realise that a palindrome is a special case of a pattern and that these patterns are all around. Palindromes frequently occur in names, both of vehicles and people, and in music.

This study outlines the development and initial validation of an abbreviated instrument intended to measure motivation for mathematics of university students in developmental algebra courses. I look across many of the predominant theories on motivation with the aim of representing several of these theories as latent constructs in a single instrument that is short enough to be administered in a reasonable amount of time, but inclusive enough that it could incorporate subscales representing multiple distinct latent factors. This study answers a call by researchers expressing a need to investigate relationships between disparate theories on motivation and is a response to recent studies that have used several subscales from many published instruments in whole or in part as lengthy combined instruments to measure motivation across theories. The practice of utilizing many separate instruments to measure across theoretical frameworks may be unwieldy leading to validity concerns based on response processes, and the practice of taking individual items from separate instruments may potentially be incomplete leading to validity concerns based on the internal structure of the instrument and underrepresentation of the intended construct.

To answer these concerns and develop a tool for future research, I conducted a three phase study. Phase one of this study asked experts in motivation to comment on and pick the best items from a pool of 122 items sourced from several popular previously published instruments that contained factors associated with self-determination, self-efficacy, achievement goals, and expectancy-value. The commentary by experts gave insight into item alignment with theory, and all items with at least 40% endorsement by experts proceeded to phase two.

In phase two, cognitive interviews of students and instructors provided insight into the cognitive processes employed in responding to the 53 items endorsed in phase one. Two researchers coded these qualitative interview data with a grounded theory approach and quantified the data using intra-respondent matrices. Effect sizes of each code provided evidence of content validity of preferred items, and concerns over social dynamics, misrepresentation of factors associated with poor wording, and the use of words like “very much” that forced students to quantify their cognitive processes provided evidence against non-preferred items.

During phase three I administered an instrument containing the surviving 34 items from phase two to 186 participants from twelve developmental algebra courses. Concerns over the broadness of the domain of mathematics led to the removal of self-efficacy and task-value items, and concerns over the abbreviated nature of the instrument led to the removal of items associated with extrinsic motivation. Concerns over the multilevel nature of achievement structured items led to their removal. Thus an exploratory and confirmatory factor analyses of the remaining 16 items representing intrinsic motivation, mastery orientations, performance orientations, and expectancy led to a four factor model that discriminated along theoretical lines and was a good fit for the data. A regression of achievement on the four latent factors from this model revealed expectancy to be the only significant predictor of achievement. With gender included as a moderating variable, performance and expectancy were both significant indicators of achievement for females, but expectancy was the only significant indicator for males. The latent factors from the instrument developed for this study had strong bivariate correlations to subscales from previously published instruments that represented similar constructs.

Several sources provided evidence of content validity. Qualitative data provided evidence in the form of commentary from experts and cognitive interview data from students and instructors. A structural equation model provided evidence of validity based on relationships to other variables. For this model the dependent variable achievement was regressed upon the latent motivation variables with gender included as a moderating variable. Exploratory and confirmatory factor analyses provided validity evidence based on the internal structure. Validity based on consequences and response processes was controlled by using an anonymous process where participation was blind to instructors and researchers, and the administration of an abbreviated measure in a familiar paper and pencil face-to-face format reduced construct irrelevant variance.

This process produced a four factor 16 item Motivation for Mathematics Abbreviated Instrument measuring intrinsic motivation, mastery orientation, performance orientation, and expectancy while accumulating validity evidence for three out of five sources of validity. The result of this inquiry was a psychometric instrument that may be used by researchers, practitioners, and grant writers who desire a tool to measure motivation for mathematics across several of the predominant theories on motivation.

This study surveyed Teachers of the Deaf in New Zealand who worked with a year 4 or year 8 student in 2006. The aim was to establish which assessments these teachers used and the extent to which the assessments influenced the IEP process and the teacher’s daily practice. The question was raised as to which assessments might provide reliable valid data to track the development of deaf and hearing-impaired students in New Zealand. The key findings from the study included that Teachers of the Deaf use assessments commonly used in deaf education more often than classroom assessments, but do make significant use of running records as well. There were differences between the two Deaf Education Centres use of assessment, and also disparity in the ways teachers arrive at assessment decisions such as allocating a curriculum level to a learning area. There was variance between the assessments used by a Teacher of the Deaf working in a satellite classroom, and the assessments completed by itinerant Resource Teachers of the Deaf. There appeared to be deaf students on Resource Teacher of the Deaf caseloads who were not assessed in mathematics by either the class teacher or the Teacher of the Deaf and the level of support by Teachers of the Deaf in mathematics is low. From within the complex picture of the assessment landscape for deaf students there are a number of signposts for future direction suggested by this study. These are: the need for a national assessment policy for deaf students; the need for data to be gathered nationally about the achievement of deaf students; sustained professional development around Teacher of the Deaf, common classroom assessments and national assessment tools; a closer look at the marking guidelines for Formal Retells and the need for student self-assessment practices to be further encouraged.

This dissertation examines elementary teacher candidates' perceptions of hip-hop culture and utilizing hip-hop pedagogy in a mathematics classroom. This study demonstrates how elements of hip-hop may be integrated into an elementary mathematics methods course to develop pedagogical knowledge that challenges teacher candidates to explore the benefits of utilizing hip-hop as a tool in the classroom. This study contributes to the growing body of research that investigates the use of hip-hop pedagogy in educator preparatory programs. Participants in this study were teacher candidates at a large university in Texas enrolled in the final year of their educator preparatory program. This research shows that as a result of integrating hip-hop pedagogy in the mathematics methods course, teacher candidates had increased knowledge and more positive perceptions of hip-hop culture, and they demonstrated a greater willingness to integrate hip-hop pedagogy in their future classrooms.

Thesis (MEd (Education))--Cape Peninsula University of Technology, 2020
This study investigates factors that affect the integration of Educational Technology (ET) by mathematics teachers for pedagogy in less affluent high schools in the Western Cape. ET has permeated the education system in the 21st century. It is now a norm for ET to be used in classrooms for educational purposes. Despite the prevalence of a variety of ETs, not all mathematics teachers are fully equipped to take advantage of the immense benefits posited by ET. This study reveals that a lot of mathematics teachers in public schools in the Western Cape still face critical challenges in their attempt to fully integrate ET for pedagogy.  The study employed a qualitative research design to explore the factors affecting the integration and use of ET for curriculum delivery by mathematics teachers in less affluent high schools in the Western Cape Province. The framework underpinning this study is the Technological Pedagogical Content Knowledge (TPACK) framework which guided the researcher in the analysis of the research findings. The researcher used two data collection instruments, namely, semi structured interviews and observations. Face to face semi-structured interviews were conducted with 9 participants and themes were used for analysing data. Participants were fully furnished with information regarding their rights when participating in the study. They were informed that they could withdraw at any given stage during the interview process. Despite the permeance of technology in the education sphere, the study’s findings show that teachers in less affluent schools in the Western Cape still experience mitigating factors that militates against effective integration of technology in classrooms for pedagogy. For effective integration of ET to take place, several factors needed to be critically addressed. They included the lack of training, limited access to ET, lack of technical support, lack of time and the theft of ET resources.

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.

Mathematics is an important skill that is taught to all children in the UK in a structured manner from a very early age. The purpose of this thesis was to examine how working memory (Baddeley & Hitch, 1974a; Baddeley & Hitch, 1994) and UK curricular mathematics are related, if specific components of working memory were more impactful upon performance in mathematics than others, and if we can predict mathematics outcomes using working memory measures. With reference to the influence of working memory on overall curricular mathematics performance, a cohort of 70 children from two primary schools in the North West of England was tested annually from their Reception year (mean age 5yrs 1m) at school to Year Two (mean age 6yrs 11m ). The study used a number of working memory tasks, a UK curricular mathematics test, and two Performance Measures. This allowed data to be analysed both in a cross-sectional manner and longitudinally (Chapter 5).The thesis also differentiates UK curricular mathematics into four separable “strands”, Number, Calculation, Measures, Shape and Space, and Problem Solving. These strands are described consistently throughout the UK mathematics curricular literature (DfEE, 1999; DfEE & QCA, 1999a; DfES, 2003a) and the cohort data was used to statistically analyse the relationships between working memory and each strand in turn using a correlational design in Chapters 6 to 9.Results indicated that working memory is a robust predictor of overall mathematics performance (Chapter 5), and of the Calculation Strand (Chapter 7). This finding was demonstrated in both the cross-sectional analyses and also in the longitudinal regression analyses. Of the working memory measures a distinct pattern of association was revealed. In particular the data imply that there is a strong role for the central executive at each age range, but in Year One verbal short-term memory emerges as an important predictor variable. Working memory also showed significant predictive influence over the remaining three curricular mathematics strands that were measured, particularly at the youngest age grouping, but working memory was not found to be a robust longitudinal predictor of Number, Problem Solving or Measures, Shape and Space. The overarching conclusion is that working memory, and in particular the central executive, may support the development of early curricular mathematical skills independent of the influence of age and Performance Measures. The practical and theoretical implications are considered.

The thesis argues that measurement learning, when adjusted to reflect the cultural and linguistic needs of the student cohort, can be culturally inclusive. The study emphasises the importance of contextualising measurement curriculum and pedagogic practice to students’ interests to promote student agency in their learning. The local knowledge, understanding, and perspectives of Utopia Eastern Anmatyerr and Alyawarr participants were privileged to determine the appropriate ways to contextualise concepts related to Akatyerr (desert raisin) with concepts of measurement. The thesis explains the changes made to hear students’ voices to enable their interests to inform pedagogical decision-making and their measurement learning.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico
Our research aims to identify and analyze the different meanings that the terms Literacy and Mathematics Literacy appear in the Mathematics Education literature. From these notions, we aimed to: identify their presence in prescribed curricula and curricular materials presented; identify competences related to the use of numerical concepts and skills focusing on some critical capacity regarding its use; characterizing content and basic procedures that have involved the ability to use mathematical knowledge and procedures in real contexts. This study is guided by the following question-guideline: What are the skills numerical concepts presented by the graduating students of Basic Education? Seeking to answer it, we have organized our research in two complementary phases. At first we have conducted an exploratory study involving literature review and document analysis. The documents analyzed were from the National Curriculum Parameters II Elementary Education and Secondary Education, as well as two collections of textbooks referring to these two levels of education. In the second phase, we have developed a semi-structured interview guide. The subjects in this phase consisted of High School students from São Paulo district. For the understanding of the terms Literacy and Mathematics Literacy and their presence in the curriculum for Primary and Secondary Education, we have taken as reference the work of researchers such as: D'Ambrosio, Ole Skovsmose, Merrilyn Goos, Vince Geiger and Shelley Dole, João Pedro da Ponte, Lynn Arthur Steen and Joaquín Giménez. From these studies, we have concluded that although the approaches of different authors have specific nuances, they have common elements in order to translate into skills to be developed/enhanced by humans. Upon review of the documents, we have noticed that, when proposing and defending proposals titled as Mathematics literacy, numeracy, literacy, among others, the authors of textbooks have addressed learning situations that little have converged with the concepts presented. We have identified through interviews that most students can perceive the presence of Mathematics and some of its concepts in their daily lives. In relation to the numerical competence situations, it was found that generally students solve problems using mathematical operations but concerning the critical capacity of students, we have observed some uncertainty on making process decision in solving the proposed situations
Nesta pesquisa tivemos por objetivo identificar e analisar as diferentes acepções com que os termos Literacia e Alfabetização Matemática aparecem na literatura em Educação Matemática. A partir dessas concepções, objetivamos: identificar sua presença em currículos prescritos e apresentados em materiais curriculares; identificar competências relacionadas ao uso de conceitos numéricos e focalizar a utilização desses conceitos envolvendo também a capacidade crítica relativamente ao seu uso; caracterizar conhecimentos e procedimentos básicos que envolvem a capacidade de usar conhecimentos e procedimentos em contextos reais. Este estudo pauta-se pela seguinte questão-diretriz: Quais competências relacionadas ao uso de conceitos numéricos apresentam os alunos egressos da Educação Básica? Em busca de respondê-la, organizamos nossa pesquisa em duas fases complementares. Na primeira, realizamos um estudo exploratório envolvendo levantamento bibliográfico e análise documental. Os documentos analisados foram os Parâmetros Curriculares Nacionais do Ensino Fundamental II e do Ensino Médio, além de duas coleções de livros didáticos referentes a esses dois níveis de ensino. Na segunda fase, elaboramos um roteiro de entrevista semiestruturada. Os sujeitos da pesquisa nessa fase foram constituídos por alunos egressos do Ensino Médio de escolas paulistanas. Para a compreensão dos termos Literacia e Alfabetização Matemática, e sua presença nos currículos do Ensino Fundamental e do Ensino Médio, tomamos como referência os trabalhos dos pesquisadores Ubiratan D Ambrosio, Ole Skovsmose, Merrilyn Goos, Vince Geiger e Shelley Dole, João Pedro da Ponte, Lynn Arthur Steen e Joaquín Giménez. A partir desses estudos, concluímos que, embora as abordagens de diferentes autores tenham nuances específicas, elas possuem elementos comuns no sentido de se traduzirem em competências a serem desenvolvidas/potencializadas pelo ser humano. Mediante análise dos documentos, percebemos que, ao proporem e defenderem propostas intituladas como de alfabetização matemática, numeracia, literacia, entre outras, os autores de livros didáticos abordam situações de aprendizagem que pouco convergem com as concepções apresentadas. Foi possível identificar com as entrevistas que a maioria dos alunos consegue perceber a presença da Matemática e algumas de suas ideias presentes em seu cotidiano. Com a proposição das situações relacionadas às competências numéricas, foi possível constatar que geralmente os alunos resolvem os problemas recorrendo a técnicas operatórias, e, no que diz respeito à capacidade crítica dos alunos, observamos certa insegurança por parte deles na tomada de decisões no processo de resolução das situações propostas

This thesis explored how six teachers of mathematics embedded Aboriginal and Torres Strait Islander Peoples’ Histories and Cultures into the core mathematics curriculum. Semi-structured interviews were conducted, then written transcripts were analysed through the use of Bernstein’s Theory of Pedagogic Discourse. Teachers shared their perspectives on how they have developed their cultural capabilities, and how this has informed culturally responsive teaching of mathematics. Recommendations are made for how to support in-service teachers with their personal cultural capabilities to authentically embed Aboriginal and Torres Strait Islander Peoples’ Histories and Cultures in mathematics curriculum.

The present study examined the effectiveness of a shared storybook reading intervention in increasing children’s early numeracy and early literacy skills through a multiple baseline single case design. Four parent-child dyads were included in the study, and children’s early numeracy and early literacy skills were measured using the eNumeracy Early Math Assessments and the Preschool Early Literacy Indicators, respectively. The study also measured mathematical dialogue to determine if an increase in children’s early numeracy skills is due to the intervention and not other confounding variables. Finally, the study measured intervention integrity, and parent ratings of social validity. Results of the study indicated that parent-child mathematical dialogue increased for three participants and could not be calculated for the fourth participant due to attrition. Visual analysis and hierarchical linear modeling results indicated no statistically significant early numeracy or literacy outcomes across participants. A masked visual analysis indicated that there was an observable difference in children’s scores on the eNumeracy Ordinal Position measures, but none of the other outcome measures. Additionally, the majority of parents were able to implement the intervention with integrity and all parents reported high levels of social validity. The findings of this study show that the parent directed shared mathematical storybook reading intervention was effective in increasing mathematical dialogue between parents and children. Future studies should examine the impact of shared mathematical storybook reading interventions on discrete early numeracy and literacy skills specifically targeted during the book reading interventions.

Providing access to a post-secondary education for a diverse population of learners with varied levels of academic preparation continues to be a challenge for California community colleges. One response has been to establish partnerships. Each partnership incorporates different scopes, instructional patterns, and outcomes to impact students. The literature supports the construction of academic pathways that provide evidence of persistence and student success. Research legitimizes connections that link students to student support services and academic skill development. California community colleges are implementing partnerships designed to achieve this end.

This study examined the impact of a noncredit to credit partnership. It explored the factors that contributed to student success in community college credit entry-level mathematics courses. The findings of the study revealed the impact of alternative course structures that integrate subject competency with preparation for the rigor of credit math courses. The study findings revealed the benefit of in-class tutoring and counseling that connects students to support services and reduces transitional barriers. This study will add to the volume of research regarding student success as it examines a noncredit program utilizing untapped resources to support student success in a community college district setting.

Improving mathematics instruction is an essential issue many school leaders are encountering as they feel increased pressure to ensure high-quality learning for all students. Key responsibilities of school leaders in leading mathematics improvement include observing instruction and providing teachers with feedback. If school leaders fulfill these responsibilities effectively and help teachers become better practitioners in the classroom, they can have a substantial impact on raising student achievement. As a result of minimal research and contradictory recommendations guiding school leaders towards mathematics leadership, many school leaders are not effectively fostering growth in mathematics instruction. The purpose of this study was to provide clarity to school leaders by pinpointing what elementary school leaders need to know in order to effectively observe mathematics instruction and provide teachers with feedback. More specifically, the study examined the necessity of a school leader's mathematics content knowledge, student pedagogical knowledge, and knowledge of how teachers learn to teach mathematics. The study was conducted using a three-round Delphi method completed by an expert panel composed of 15 stakeholders with diverse perspectives in the area of mathematics leadership. The study yielded guidelines regarding what school leaders need to know in order to effectively observe elementary mathematics instruction and provide informed feedback to teachers. The experts unanimously concluded that school leaders must understand elementary mathematics as a process of reasoning rather than merely rules, facts, and procedures. One-hundred percent of the panel also strongly agreed that mathematics instruction must occur in student-centered classrooms where teachers act as a facilitator of learning and use effective questioning to engage students in developing mathematical understandings and connections. The study concluded with 11 additional critical findings.
Ed. D.

The purpose of this study was to explore the ways in which educators address climate change and the impacts of human activity on the environment in conjunction with the Next Generation Science Standards. This study utilized qualitative methods, a phenomenological methodology informed by Moustakas, and a Systems Theory and Ecojustice Education conceptual framework. The central research questions was: in what ways do educators who are implementing the Next Generation Science Standards address climate change and the impacts of human activity on the environment? The supporting research questions were: in what ways do educators who are implementing the Next Generation Science Standards perceive their roles and responsibilities in addressing climate change and the impacts of human activity on the environment? in what ways do educators who are implementing the Next Generation Science Standards interpret the associated Earth and Human Activity standards prior to enactment? and, how do educators who are implementing the Next Generation Science Standards teach climate change and the impacts of human activity on the environment?Eight participants were purposely selected using criterion sampling. All participants taught in grades six-twelve, had at least five years teaching experience, and worked in the Sacramento Valley region of California. Data collection consisted of interviews, observations, and document analyses. During the data analysis, horizontalization was utilized which led to the illumination of the following themes: Climate change is an existential crisis, Examination and refinement of pedagogy, Perceptions on Next Generation Science Standards pedagogy, Inquiry-based pedagogical methods, Pedagogical resources, Fostering relevancy to students, and Steps toward an eco-ethical consciousness. The conclusions drawn are: context is key, confusion persists and teachers need guidance and support, adopted curricula and content standards are inadequate, systems thinking and eco-ethical mindsets are vital, teachers are essential for survivability, and more needs to happen. The recommendations from this study are of relevance to policy makers, administrators, curricula and standard developers, teachers, and anyone else interested in mitigating the impacts of human activity on the environment.

Thesis (MEd)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: This study explored the number sense of 47 final year primary school pre-service teachers in Namibia and was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests. The literature review revealed that learner performance is linked to teacher subject knowledge (Ball, 1990, Ma, 1999) and that teachers’ confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics (Ball, 1990; Graven 2004). Number sense studies of pre-service teachers (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) have indicated that the development of number sense should be a focus of primary pre-service teacher education. The data in this mixed method research design were obtained from a Number Sense Questionnaire, a Written Computations Questionnaire and a Mental Calculations Questionnaire. These questionnaires were adapted from instruments developed by Professor Der-Ching Yang for 6th and 8th grade learners in Taiwan. Teacher confidence was measured by the McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Six randomly selected pre-service teachers were interviewed to determine their use of number-sensible strategies. The correlation analysis shows a strong relationship between number sense and mental calculations; between number sense and confidence in both the ability to do and the ability to teach mathematics and between mental and written calculations. The overall results of this study reveal that the final year primary pre-service teachers demonstrate limited number sense and possess very few of the indicators of number sense that were described by Kalchman, Moss and Case (2001). The findings expose a lack of conceptual understanding of the domain numbers and operations, particularly in the domain of rational numbers and the operations of multiplication and division. The pre-service teachers have little or no access to a variety of flexible number-sensible strategies to solve problems and calculate mentally. They lack the fluency in basic facts and procedures to perform written calculations efficiently and correctly. Unexpectedly, the analysis of the confidence survey shows that they are confident in both their ability to do mathematics and their ability to teach mathematics. It is recommended that mental calculations and computational estimation should become a focus of primary school mathematics education. Institutions responsible for teacher training should develop the number sense of pre-service teachers and research effective and long-term professional development programmes. The confidence and willingness of the teachers to learn can be used as an important resource.
AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die getalbegrip van 47 finale jaar primêre skool voordiens-onderwysers in Namibië en is gemotiveer deur die swak prestasie van die Namibiese primêre skool leerlinge in beide nasionale en internasionale gestandaardiseerde assesseringstoetse. Die literatuurstudie het aan die lig gebring dat leerlinge se prestasie gekoppel is aan onderwyservakkennis (Ball, 1990, Ma, 1999) en dat onderwysers se vertroue in hulle vermoë om wiskunde te doen en te onderrig, die manier waarop hulle onderrig en hul bereidwilligheid om wiskunde te leer beïnvloed (Ball, 1990, Graven 2004 ). Studies van voordiens primêre onderwysers se getalbegrip (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) toon dat die ontwikkeling van getalbegrip 'n fokus van primêre voordiensonderwyseropleiding behoort te wees. Die data in hierdie gemengde metode navorsing is verkry uit 'n Getalbegrip, 'n Skriftelike Berekeninge en 'n Hoofrekene Vraelys. Hierdie vraelyste is gebaseer op die instrumente wat ontwikkel is deur Professor Der-Ching Yang vir graad 6 en 8 leerlinge in Taiwan. Onderwyservertroue is gemeet deur die McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Ses ewekansig geselekteerde voordiens-onderwysers is ondervra om te bepaal watter sinvolle strategieë hulle gebruik om vrae oor getalbegrip te beantwoord. Die korrelasie-analise toon 'n sterk verband tussen getalbegrip en hoofrekene; tussen getalbegrip en vertroue in die vermoë om wiskunde te doen en te leer, en tussen vermoë om hoofrekene en skriftelike bewerkinge te doen. Die algehele resultate van hierdie studie dui daarop dat die finale jaar primêre voordiens-onderwysers oor beperkte getalbegrip en baie min van die aanwysers van getalbegrip wat deur Kalchman, Moss en Case (2001) beskryf is, beskik. Die bevindinge toon ‘n gebrek aan begrip van die domein van getalle en bewerkings, veral in die domein van rasionale getalle en die bewerkings vermenigvuldiging en deling. Die voordiens-onderwysers beskik oor min of geen soepel strategieë om probleme op te los en hoofrekene te doen nie. Hulle beskik nie oor die vlotheit in basiese feite en bewerkings om skriftelike berekeninge doeltreffend en korrek uit te voer nie. Die vertroue wat voordiens-onderwysers uitgespreek het in hulle vermoë om wiskunde te doen en onderrig staan in sterk teenstelling met hierdie bevindige. Dit word aanbeveel dat hoofrekene en skatting 'n fokus van primêre skool wiskunde-onderwys behoort te wees. Instansies gemoeid met onderwyseropleiding behoort die getalbegrip van voordiensonderwysers te onwikkel en navorsing te doen oor effektiewe en lang-termyn programme vir professionele ontwikkeling. Onderwysers se vertroue en bereidwilligheid om te leer kan as 'n belangrike hulpbron gebruik word.

Many countries have made considerable changes to their education systems in response to the forces of globalisation. Tanzania is no exception. The most recent educational change attempt in Tanzania relates to the introduction of the 2005 Tanzanian Inquiry and Student- Centred Curriculum. Sound change-leadership is a necessary condition for the realisation of change, particularly in influencing its adoption. Within the descriptive qualitative research paradigm, this study employed a Type IV (embedded and multiple) case-study design to examine and describe science teachers’ lived experiences in dealing with this latest Tanzanian curriculum and the role played by school-based leaders in influencing such experiences. The study was carried out in three case-study schools. Data regarding change leadership were collected from both teachers and school leaders by means of personal interviews, observations, and document reviews. Data regarding science teachers’ levels of adoption of this curriculum and related concerns, all of which helped to gauge the effectiveness of change-adoption leadership provided by School-Based Leaders, were collected using semi-structured interviews and a Stage of Concern Questionnaire and were triangulated through document reviews and inclass observations. The findings show that school-based leaders in all case-study schools guided adoption of change primarily using authoritarian strategies. Nevertheless, there was some evidence to suggest that school-based leaders in the high performing and the medium performing casestudy schools tended to employ additional strategies that inclined towards collective and empowering leadership approaches. This difference appeared to covary with the science teachers’ levels of use of this curriculum and their concerns about it in the three case-study schools. Adoption challenges and those affecting leadership of change are also detailed. These findings extend the ongoing academic discussion about the leadership of adoption of educational changes in schools. The understanding of pedagogical change gained through this study has implications for both policy and practice, and these are discussed in the last chapter. Leaders of these and other schools in equivalent contexts may use findings of this study to reflect upon their change-leadership practices in schools and improve the way they enhance pedagogical transformations and the professional development of their teachers.

Despite a century of educational reforms, no matter how achievement is measured, learning and opportunity gaps can still be predicted by race and socioeconomic status. Teachers and schools are blamed for functioning to reproduce social inequality. This study investigated teacher agency and transformative potentials. It considered how teachers modified their pedagogical practices when teaching low-income and high-poverty students. In order to capture teacher beliefs and logic, a qualitative approach was used involving in-depth interviews of a small number of participants. The research used the context of the dislocation of students from high-poverty Orleans Parish schools in the year following Hurricane Katrina and their absorption into often higher income schools to understand middle-class teachers’ perspectives on their new students’ learning needs and how they adjusted their practice. Participants were middle-school mathematics teachers ranging in experience and orientation. Evacuees had weaker mathematics backgrounds (often two years below grade level). In all cases, evacuees were in classes with non-evacuees. Teachers made different pedagogical choices: continuing to use diverse methods aimed at higher-order understanding, or moving to direct instructional strategies; remediating or accelerating students with below-grade-level mathematics skills; and whether or not to help students acculturate (code-switch) from one set of classroom norms and etiquettes to another. Key factors influencing choices included: socioeconomic makeup of their classes; teachers’ level of mathematics expertise; emphasis on test scores; teachers’ views of students’ culture; and teachers’ peer environments. The study provides insights into teacher and classroom mechanisms that contributed to Katrina evacuee multi-year achievement gains.

The aim of this study was to investigate the changes on what the prospective elementary mathematics teachers noticed as they watched video cases and discussed online. More specially, I wanted to answer the question &ldquo
To what extent the elementary prospective mathematics teachers&rsquo
noticing with respect to reform-minded teaching changes during their video case-based teacher education, in terms of teacher and student roles?&rdquo
With this question in mind, I asked senior prospective mathematics teachers at METU to watch six video cases depicting real elementary mathematics classrooms, and then discuss these cases in an online forum. The research was conducted during the 2008-2009 fall semester. Participants were asked to write reflection papers after watching a video each week. The online discussions took place in Metu Online-Net ClassR online forum, and each discussion was about a long week. The research study was qualitative in nature. Specifically, it was a case study research. Prospective teachers&rsquo
reflection papers on the videos, the online discussions, and interviews with the selected 15 focus participants at the beginning, in the middle and at the end of the study were the data sources. The data were analyzed through the qualitative data analysis techniques. The findings suggested that prospective teachers&rsquo
noticing skills with respect to the teacher and student roles in reform-minded teaching and learning were developed throughout the online video-case based discussions.

This mixed methods case study documents an effort to implement authentic science and engineering instruction in one teacher’s ninth grade science classrooms in a science-focused public school. The research framework and methodology is a derivative of work developed and reported by Newmann and others (Newmann & Associates, 1996). Based on a working definition of authenticity, data were collected for eight months on the authenticity in the experienced teacher’s pedagogy and in student performance. Authenticity was defined as the degree to which a classroom lesson, an assessment task, or an example of student performance demonstrates construction of knowledge through use of the meaning-making processes of science and engineering, and has some value to students beyond demonstrating success in school (Wehlage et al., 1996). Instruments adapted for this study produced a rich description of the authenticity of the teacher’s instruction and student performance.

The pedagogical practices of the classroom teacher were measured as moderately authentic on average. However, the authenticity model revealed the teacher’s strategy of interspersing relatively low authenticity instructional units focused on building science knowledge with much higher authenticity tasks requiring students to apply these concepts and skills. The authenticity of the construction of knowledge and science meaning-making processes components of authentic pedagogy were found to be greater, than the authenticity of affordances for students to find value in classroom activities beyond demonstrating success in school. Instruction frequently included one aspect of value beyond school, connections to the world outside the classroom, but students were infrequently afforded the opportunity to present their classwork to audiences beyond the teacher.

When the science instruction in the case was measured to afford a greater level of authentic intellectual work, a higher level of authentic student performance on science classwork was also measured. In addition, direct observation measures of student behavioral engagement showed that behavioral engagement was generally high, but not associated with the authenticity of the pedagogy. Direct observation measures of student self-regulation found evidence that when instruction focused on core science and engineering concepts and made stronger connections to the student’s world beyond the classroom, student self-regulated learning was greater, and included evidence of student ownership.

In light of the alignment between the model of authenticity used in this study and the Next Generation Science Standards (NGSS), the results suggest that further research on the value beyond school component of the model could improve understanding of student engagement and performance in response to the implementation of the NGSS. In particular, it suggests a unique role environmental education can play in affording student success in K-12 science and a tool to measure that role.

Clicking is a theory that explains how students in this study developed quantitative literacy for learning mathematics in an enabling course at university. Using a grounded theory methodology, thirteen students from an enabling course at one institution were interviewed about what helped or hindered them in learning mathematics in a tertiary environment. Students who come to enabling courses often have had barriers and disruptions in prior learning experiences. While most come to enabling courses with the aim of improving their skills, progressing on to bachelor degrees and then professions, they often struggle in the formal learning environment. This is particularly so with mathematics with many students reporting that they do not like, or are not good at the subject. Despite the best intentions for this ‘second chance’ learning, numerous students continue to struggle, withdraw, or fail. This attrition is detrimental to students’ confidence, and also undesirable for the university. Even for those who remain, or are able to pass some assessment, they are still not confident in their ability to learn mathematics. Through this study, the concept of ‘clicking’ was found to be central to students’ understanding of the content, in particular, developing literacy practices that resonated with a literacy resource model for learning. Seven interrelated categories reported by the students were theorised through this model, with the key category of clicking emerging as a process for explaining how quantitative literacy was constructed by learners themselves. Clicking for quantitative literacy was constructed through a student learning cycle of relating, holding interest, exploring ways, taking time, practising, and working through confusion; with tailoring of ways of learning mathematics provided by teachers and others such as peers, family, friends. When used alongside adult learning principles, these findings offer a practical guide for teachers in enabling courses to use with their students to develop their knowledge of how to learn mathematics. For students, being quantitatively literate in ‘learning how to learn mathematics’ through clicking, has implications for success in mathematics learning in their chosen professional studies at university.

"Bridging students aiming to attend university need to bridge the gaps in their mathematical knowledge. For this, they need a confirmation of their current knowledge status, and individual study schedules to advance their knowledge within the bridging program. Yet there is very little literature available to guide the design of suitable testing programs or diagnostic procedures, particularly for students studying independently at a distance. To address this problem, a working prototype has been designed and developed to provide a student self-administered, computer-based diagnostic testing model for placement of students enrolled in a distance educational university bridging mathematics program..." -- abstract.

This study investigates the possibilities and limitations of "constructivist" methods of teaching in a mathematics "methods" course in pre-service teacher education. The research undertaken responds to the Discipline Review of Teacher Education in Mathematics and Science (1989, p.17) which states that teachers of mathematics must themselves "have learned mathematics by constructing their own knowledge through discovery, exploration and problem solving in relevant and supportive environments".

In the initial cycles of the research I concentrated on the implementation of "constructivist" practice informed by Habermas' (Can and Kemmis, 1986) critical social theory. I found liberal humanistic assumptions of the individual and knowledge within action research and constructivism problematic in that they did not afford any way of making sense of many of the actions and practices of myself and students. I turned to Foucauldian genealogy for a post-structuralist theorisation of power-knowledge operating within the discourse of constructivist mathematics constituting subjectivities and effecting instances of marginalisation.

In the third and final cycle of the research I moved hesitantly towards an understanding of myself and students as discursively constituted, variously positioned and positioning others within the discourse. Epistemologically I began to recognise and appreciate both knowledge as cognitive construct, and a knowing or knowledge as production of meaning. That is, as students constructed the authoritative mathematical and pedagogical knowledges, meanings were also produced which were at times discriminatory.

Concluding chapters focus on the production of meaning within myself and students as pedagogical desire. With reference to my practice, I reflect on the importance of distinguishing between discourse as a linguistic function and discourse in the Foucauldian sense as the operation of power-knowledge within practice if teacher education is to move beyond its present conservative influence on students. That is, perhaps teacher education in mathematics needs to move beyond talking differently about mathematics, for example constructivist mathematics or mathematics from minority cultures, to an emphasis on being differently in mathematics through affording students the space to examine meanings produced through the operation of power-knowledge as unquestioned liberal-humanistic assumptions of the individual in constructivist pedagogy and collaborative action research.

Quantitative literacy, or numeracy, has been discussed as an essential component of mathematics instruction. In recent years community colleges around the nation introduced a quantitative literacy alternative to the developmental algebra curriculum for students placed into remedial mathematics. The QL curriculum consists of problem situations that are meant to improve numeracy through a combination of collaborative work and a student-centered pedagogy. There is little research that investigates the enactment of that curriculum. Research in K-12 indicates that teachers’ beliefs influence the enactment of curriculum, but studies that connect instructional practices and faculty beliefs are scarce. This study employs a multiple qualitative case study approach to investigate the alignment between four community college instructors’ beliefs about teaching, learning, the nature of mathematics, and curriculum on their enacted practices in two different developmental mathematics courses at a large urban community college (UCC). One is a standard developmental algebra curriculum and the other curriculum is based on quantitative literacy. Data were collected through semi-structured interviews, classroom observations and field notes. The results indicate an alignment between the professed beliefs and enacted practices for all but one instructor in this study. The findings imply that curriculum plays a significant role when its intended design correlates with instructors’ belief systems. The study also discusses the differences in instructional practices across the quantitative literacy and elementary algebra curricula taught by the instructors in this study.

This mixed methods study is a program evaluation of Newfoundland and Labrador’s Excellence in Mathematics Strategy commencing in 2007 with a curriculum review leading to the implementation of the Western and Northern Canadian Protocol Common Curriculum Framework in K-12 mathematics along with the implementation of numeracy support teachers in classrooms across the province. The goals of the Strategy were to improve student achievement with the curriculum change; to support teachers, students, and parents; and to encourage an increased interest and enthusiasm for mathematics. This study included a quantitative analysis of the provincial mathematics assessment results in Grades 3, 6, and 9 from 2007 to 2012 by comparing assessment items that were common to both the old and new curricula, and comparing results of items anchored in 2011 and 2012. Assessment results demonstrated inconsistent results on common curriculum items. Results of items anchored decreased in all grades in 2011 but items anchored in 2012 increased in all grades. Another quantitative analysis was conducted on the effect of numeracy support teachers (known elsewhere as mathematics specialists, coaches, or mentors) on students’ mathematics achievement in schools having Grade 3 and 6 classrooms receiving numeracy support from 2007 to 2011. Schools with numeracy support in Grades 3 and 6 for four years were mostly lower-achieving schools and had achievement results move closer over time to schools receiving one or no years of support which were mostly higher achieving schools. Schools receiving support in both Grades 3 and 6 had the highest proportion of students moving from below standard to at/above standard on rubric-scored open-constructed response questions. A qualitative analysis was conducted of focus groups with numeracy support teachers and supported the quantitative analysis of the provincial assessment results. Numeracy support teachers shared their observations of teachers’ unconventional assessment methods and students’ increase in communicating, reasoning, problem solving, and strategizing about mathematics. Lower-achievers were more engaged in these classrooms and manipulative use in problem solving improved. Numeracy support teachers witnessed physical and attitudinal changes through planning, modelling, co-teaching, and reflecting with teachers thereby helping change the culture of students’ classrooms. The goal of numeracy support teachers to build capacity in their teachers through collaboration was evident in some classrooms as beliefs and habits were changing, but some were resistant.
Graduate
0280
0727
karen.m.moore@gmail.com

This research is focused on the intersection of secondary teachers’ data-use to inform instructional decisions and their teaching of STEM in STEM-focused high schools. Teaching STEM requires presenting more than just the content knowledge of the STEM domains. The methods of inquiry (e.g., scientific inquiry, engineering design) are skills that should be taught as part of STEM activities (e.g., science labs). However, under the data- and standards-based accountability focus of education, it is unclear how data from STEM activities is used in instructional decision-making. While teachers give tremendous weight to the data they collect directly from their observations of their classrooms, it is data from standardized testing that strongly influences practices through accountability mandates. STEM education alters this scenario because, while there is a growing focus on teaching STEM, important aspects of STEM education are not readily standardized. This mixed-methods study will examine the perspectives of 9th through 12th grade science and mathematics teachers, in STEM-focused schools, on data-use and STEM teaching. We developed a framework, adapted from existing frameworks of data-use, to categorize these perspectives and outline contexts influencing them. Through a concurrent triangulation design we will combine quantitative and qualitative data for a comprehensive synthesis of these perspectives.

abstract: This study investigates Black male students' perceptions of their teachers' curricular expectations in mathematics classrooms. Curriculum in this study refers to what knowledge students are expected to learn, and the manner in which they are expected to learn it. The topic of this dissertation is in response to persisting and prevailing achievement disparities experienced by secondary Black male students in mathematics. These disparities exist at the school, district, state, and national level. Utilizing an action research methodology, multiple cycles of data collection led to the final iteration of the study, collecting strictly qualitative data and drawing from critical race methodology to address the three research questions. The three research questions of this study seek to address how Black male students perceive their mathematics teachers’ curricular expectations, what practices they have found to be effective in meeting their teachers’ higher curricular expectations, and to determine how they view the reform practices as part of the intervention. Research questions were answered using one-on-one and focus group interviews, classroom observations, and student journals. An intervention was developed and delivered as part of the action research, which was an attempt at curriculum reform influenced by culturally relevant pedagogy, warm demander pedagogy, and youth participatory action research. Findings from the qualitative methods, led to four assertions. The first assertion states, despite achievement disparities, Black male students care very much about their academic success. Second, a primary factor hindering Black male students’ academic success, as communicated by participants, is what they are learning and how they are learning it. Speaking to teachers’ expectations, participants believe their teachers want them to succeed and think highly of them. Additionally, participants preferred interactive, enthusiastic, and caring teachers, even if those teachers are academically demanding. Finally, participants found learning mathematics addressing a problem that affects them, while incorporating components that address their invisibility in the curriculum, increased relevance, interest, and academic self-awareness.
Dissertation/Thesis
Doctoral Dissertation Educational Leadership and Policy Studies 2020

Mathematics has always been a problem at schools, colleges and universities and to address this problem the South African government has introduced a new subject called Mathematical Literacy into schools and colleges. Since this subject places the emphasis on real-life contexts, there has been a special focus on its management at schools and colleges so that its implementation is done in an efficient way. This study therefore focuses on the experiences and interactions of managers of this new subject and how their leadership can improve performance in it. In addition to the literature review, an empirical investigation based on a qualitative approach and involving semi-structured interviews with managers of three public TVET colleges in the Western Cape was conducted to collect data. The other method used was the analysis of documents relevant to the study. The research found that managers of Mathematical Literacy have varying experiences in both their roles and the implementation of the subject. They also face varied challenges in relation to lecturers and students although there are also similarities regarding these at the different colleges in the study. The strategies of instructional leadership in intervention methods to improve performance in the subject which are encouraged by managers also differ, and some have better results than others. Various methods to empower lecturers are recommended. Recommendations are also made on what was found in this study, as are recommendations for further study.
Educational Leadership and Management
M. Ed. (Education Management)

This study employed a qualitative approach to investigate the use of cooperative learning to enhance conceptual understanding of trigonometry in a Grade 11 mathematics classroom, conducted at a high school in Moletlane Circuit, Capricorn District in Limpopo Province, South Africa. A single case study was used as a research design to get an in-depth analysis and collect detailed data using semi-interviews and lesson observation of the cooperative learning of trigonometry in Grade 11 from the learners and the teacher. Participants were purposely chosen and consisted of (n=30) Grade 11 mathematics learners and their mathematics teacher. Data from the participants were collected through semi-structured interviews and observation, with the aid of observation guide (Appendix C) for three weeks. The salient findings from the study showed how cooperative learning was used, research questions, the approaches, the teacher did not adequately highlight the importance of trigonometry to students without integrating the topic to real-life situations. Some students said that the teacher did not teach trigonometry in a manner that they understood, which made trigonometry challenging for them. Concerning cooperative learning, the study found that many learners were passively engaged, listened to or watched the teacher. Mainly, the study recommends teacher-training institutions to host practical workshops to help teachers integrate theoretical training and practical cooperative learning experience. While this study was qualitative in nature, future researchers could conduct quantitative data collection. This would allow for the collection of numerical findings through survey questionnaires.
Mathematics Education
M. Ed. (Mathematics Education)