Tesi: "Mathematics and numeracy"

1

Kemp, Marian. "Developing critical numeracy at the tertiary level". Thesis, Kemp, Marian (2005) Developing critical numeracy at the tertiary level. Professional Doctorate thesis, Murdoch University, 2005. https://researchrepository.murdoch.edu.au/id/eprint/122/.

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Students at university encounter quantitative information in tables and graphs or through prose in textbooks, journals, electronic sources and in lectures. The degree to which students are able to engage with this kind of information and draw their own conclusions, influences the extent to which they need to rely on the interpretation of others. In particular, students who are studying in non-mathematical disciplines often fail to engage seriously with such material for a number of reasons. These may include a lack of confidence in their ability to do mathematics, a lack of mathematical skills required to understand the data, or a lack of an awareness of the importance of being able to read and interpret the data for themselves. In this thesis, the successful choice and use of skills to interpret quantitative information is referred to as numeracy. The level of numeracy exhibited by a student can vary depending on the social or cultural context, his/her confidence to engage with the quantitative information, the sophistication of the mathematics required, and his/her ability to evaluate the findings. The first part of the thesis is devoted to the conceptualisation of numeracy and its relationship to mathematics. The empirical study that follows this is focused on an aspect of numeracy of importance to university students: the reading and interpreting of tables of data in a range of non-mathematical contexts. The students who participated in this study were enrolled in degree programs in the social sciences. The study was designed to measure the effectiveness of a one-hour intervention workshop aimed at improving the levels of the students? numeracy. The short length of the intervention was dictated by practical and organisational constraints. This workshop involved reading and interpreting a table of data using strategies based on the SOLO taxonomy (Biggs and Collis, 1982). The SOLO taxonomy was developed mainly as a means of classifying the quality of responses across both arts and science disciplines. The categorisation uses five levels: prestructural, unistructural, multistructural, relational and extended abstract. It can be used as a diagnostic tool at all levels of education as it can be seen as a spiral learning structure repeating itself with increasing levels of abstraction. It can also be used as a teaching tool in feedback to students. A measuring instrument, also based on the SOLO taxonomy, was designed to gauge the levels of the students' responses to these tasks. Each response was allocated a level that was subsequently coded as a number from zero to seven. Because the responses were in distinct ordered categories, it was possible to analyse the scores using the Rasch Model (Rasch 1960/80) for polytomous responses, placing both the difficulty of the tasks and the ability of the students on an equal interval scale. The Rasch Model was also used to evaluate the measuring instrument itself. Some adjustments were made to the instrument in the light of this analysis. It was found that it is possible to construct an instrument to distinguish between levels of students' written responses for each of the chosen table interpretation tasks. The workshop was evaluated through a comparison of the levels achieved by individual students before and after the workshop. T-tests for dependent samples indicated a significant improvement (p < 0.01) in student performance.

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Kemp, Marian. "Developing critical numeracy at the tertiary level /". Access via Murdoch University Digital Theses Project, 2005. http://wwwlib.murdoch.edu.au/adt/browse/view/adt-MU20060831.171947.

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3

Hurle, Gillian Dawn. "Numeracy support for year two students". Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2013. https://ro.ecu.edu.au/theses/609.

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Research of teaching theories and intervention programs internationally and in Australia suggests that the implementation of numeracy support programs can improve student achievement levels (Fuchs, 2005; Ketterlin-Geller, Chard & Fien, 2008; Van Kraayenoord & Elkins, 2004). An intervention program was conducted for a small group of Year Two students with the aim of improving their numeracy skills over a 20 week period. Results of two mathematics assessments, together with information provided by teachers based on classroom observations and informal assessments were combined to select a group of twelve students who were considered to be at risk of developing mathematical difficulties. The program comprised of two 85 minute lessons and one 40 minute lesson per week in a room adjacent to the Year Two classroom. A social constructivist method of teaching was put into practice within the structure of a small group setting. A case study approach recorded the learning journey of each student with an individual profile of each participant maintained for the duration of the program. At the conclusion of the program data obtained from formative assessments, teacher observations, and feedback from the student participants were used to evaluate the program’s effectiveness. Students who were members of the intervention program improved their level of basic numeracy skills in the areas of addition, subtraction, multiplication, division, and number sequencing, and also demonstrated a positive disposition towards mathematics.

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4

Gleeson, Laura Jane. "Grouping students to target specific deficiencies in numeracy: investigating an evidenced based Numeracy Program". Thesis, Griffith University, 2018. http://hdl.handle.net/10072/377618.

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Numeracy has a significant impact on a student’s further study prospects, employment possibilities and retention in the workplace. Ultimately, numeracy skills are a necessary requirement for informed, critical thinking citizens. This study investigated the journey of a Year 8 cohort, through to Year 9, measuring and exploring the impact of a three-term numeracy program intervention. Student numeracy was recorded at the end of Year 8, and again midway through Year 9. This numeracy program saw 205 students sorted into twelve numeracy classes for one lesson per week. Some class groupings targeted specific skill deficiencies, and some were streamed to group higher or lower performing students together. This research investigated the pre- and post-program diagnostic test performances charted by these students using quantitative statistical analysis (comparative means paired t-tests across groups). To further explore these outcomes, two teachers were interviewed before and after this numeracy program. These interviews addressed the themes of teacher expectation and plans, implementation of the numeracy program, and reflection. There is a large amount of literature investigating the effects of streaming on student outcomes in numeracy, and it is known to have mixed results. Key themes from this literature are student identity, student performance outcomes, and the impact of streaming on pedagogical choices. However, there is a gap in the literature addressing streaming by specific skill weakness, rather than mean ability. This is an area explored by this research, which finds that grouping students according to specific skill weakness, for the duration of a numeracy intervention, does remediate those key deficiencies, but possibly at the expense of other skill areas. This research finds that streaming lower performing students by mean ability has a strong and positive impact on student performance. Conversely, the findings for high-performing students suggest that grouping them together, and the teaching and learning experiences that resulted from that, had no measurable positive impact on outcomes. This research suggests a need for future iterations of this numeracy program to continue to target specific skills, but on a cyclical basis; ensuring that all students are exposed to all requisite ideas and skills, benefitting from targeted intervention.
Thesis (Masters)
Master of Education and Professional Studies Research (MEdProfStRes)
School Educ & Professional St
Arts, Education and Law
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McDonald, Susan Ellen. "Improving numeracy: Co-constructing a whole-school numeracy plan in a secondary school". Thesis, Queensland University of Technology, 2007. https://eprints.qut.edu.au/16618/3/Susan%20McDonald%20Thesis.pdf.

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Numeracy is a cross-curricular priority, an intersystemic priority and, of late, a federal government priority. Yet as a priority "numeracy" is inadequately defined and the term is used to describe a wide-range of notions. Many educators are unsure of what constitutes numeracy, unaware of how it differs from mathematics, and uncertain as to how its demands may be met in their planning and teaching. Secondary schools have few models upon which to develop a whole-school numeracy plan. This study describes the journey of a secondary school staff as they developed a shared understanding of numeracy, identified the numeracy demands throughout the curriculum and planned for a whole-school approach to address these demands.

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McDonald, Susan Ellen. "Improving numeracy: co-constructing a whole-school numeracy plan in a secondary school". Queensland University of Technology, 2007. http://eprints.qut.edu.au/16618/.

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Numeracy is a cross-curricular priority, an intersystemic priority and, of late, a federal government priority. Yet as a priority "numeracy" is inadequately defined and the term is used to describe a wide-range of notions. Many educators are unsure of what constitutes numeracy, unaware of how it differs from mathematics, and uncertain as to how its demands may be met in their planning and teaching. Secondary schools have few models upon which to develop a whole-school numeracy plan. This study describes the journey of a secondary school staff as they developed a shared understanding of numeracy, identified the numeracy demands throughout the curriculum and planned for a whole-school approach to address these demands.

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Angelis, Desi. "Adult numeracy, mathematical education and social meanings". Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/17496.

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Bibliography: pages 74-83.
In sum, the theoretical framework proposed here for adult numeracy, and developed from a discourse of mathematics education, has as its task the elaboration of the social implications of principles in adult education and the pedagogic outcomes of three sets of numeracy materials.

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Carter, Merilyn Gladys. "Year 7 students’ approaches to understanding and solving NAPLAN numeracy problems". Thesis, Queensland University of Technology, 2011. https://eprints.qut.edu.au/46648/1/Merilyn_Carter_Thesis.pdf.

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This study investigated how the interpretation of mathematical problems by Year 7 students impacted on their ability to demonstrate what they can do in NAPLAN numeracy testing. In the study, mathematics is viewed as a culturally and socially determined system of signs and signifiers that establish the meaning, origins and importance of mathematics. The study hypothesises that students are unable to succeed in NAPLAN numeracy tests because they cannot interpret the questions, even though they may be able to perform the necessary calculations. To investigate this, the study applied contemporary theories of literacy to the context of mathematical problem solving. A case study design with multiple methods was used. The study used a correlation design to explore the connections between NAPLAN literacy and numeracy outcomes of 198 Year 7 students in a Queensland school. Additionally, qualitative methods provided a rich description of the effect of the various forms of NAPLAN numeracy questions on the success of ten Year 7 students in the same school. The study argues that there is a quantitative link between reading and numeracy. It illustrates that interpretation (literacy) errors are the most common error type in the selected NAPLAN questions, made by students of all abilities. In contrast, conceptual (mathematical) errors are less frequent amongst more capable students. This has important implications in preparing students for NAPLAN numeracy tests. The study concluded by recommending that increased focus on the literacies of mathematics would be effective in improving NAPLAN results.

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Cobb, Sarah Catherine Jane. "“You use your imagination:”An investigation into how students use ‘imaging’ during numeracy activities". Thesis, University of Canterbury. School of Sciences and Physical Education, 2012. http://hdl.handle.net/10092/7168.

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Developing knowledge about how students acquire mathematical understanding is a focus of mathematics curricula and research, including the ability of students to move from manipulating concrete materials to abstract number properties when solving problems. This study, informed by the Numeracy Development Projects (Ministry of Education 2007a, 2008b) and the work of Pirie and Kieren (1989, 1992, 1994a, 1994b), examines the role of ‘imaging’ in supporting the development of students’ mathematical thinking and understanding. Imaging is an important phase of the teaching model advocated by the Numeracy Development Project. The context of this study is a primary school mathematics programme, which involved the teaching of two mathematics units that focused on the addition and subtraction of decimal fractions and whole numbers. There is considerable research about what is effective in mathematics education for diverse learners, and how students learn. There is, however, very limited research about the role of imaging in mathematical learning. This qualitative study adopted a case study approach and focused on a group of Year 6 students. Data collection methods included observation, interviews, field notes and document analysis. A thematic approach was used to analyse data and to develop and inform an emerging theoretical framework. During this study I developed a model, entitled A Model for the Development of Students’ Mathematical Understanding, which illustrates six mathematical resources students use as they solve problems. These resources are: materials, mental picture images, drawn picture images, transformed mental images, transformed drawn images and number properties. Students’ engagement with these six resources illustrates how they develop understanding of mathematical concepts. The students identified a preference for using drawn rather than mental images when solving problems. This study also emphasizes the complexity of the imaging process, and the fluid and multifaceted nature of learning in mathematics. This study serves to highlight the complexities of the teaching and learning process in mathematics for both teachers and students.

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Norris, Kelly. "Raising Teacher Sensitivity to Key Numeracy Competencies in the Early Years". Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2014. https://ro.ecu.edu.au/theses/1473.

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Mathematical competence is a key capability for success in adult life, and yet many students do not achieve functional levels of numeracy during their school lives. Furthermore, many teachers report that they lack the confidence in teaching mathematics that they have for teaching literacy. Research indicates that it is possible to predict which students are likely to have difficulties in mathematics as early as the Pre-Primary year, and interventions can be provided which are effective in minimising such difficulties. The assumption framing this project is that raising teachers’ understanding of and thus sensitivity to markers of the skills most predictive of mathematical success in the early years will result in teachers planning more targeted and responsive learning programs and positively influence classroom practice. A professional learning intervention focussed on raising professional knowledge about the sequence of number development and the predictors of mathematical difficulties was provided to teachers of five to eight-year-old students. Tools were provided which focussed on linear tracks (board games) as an external model of number magnitude. The study utilised a pre-test post-test design and surveys, teacher interviews, reflective discussions and student estimation tests to examine effects on four outcomes: teacher self-efficacy beliefs, confidence for teaching number and aspects of Pedagogical Content Knowledge; and, student estimation skills. The data revealed that the intervention was successful in improving teacher self-efficacy beliefs and confidence, particularly with regard to planning and providing intervention for students with mathematical difficulties. Teachers’ Pedagogical Content Knowledge was improved, particularly with regard to understanding the sequence of number skills development and building mental representations of number, but the extent to which this was reflected in changes to classroom practice differed markedly between teachers. The teachers who made the greatest changes taught in the Pre-Primary year and were those who reported the most substantial changes in Pedagogical Content Knowledge. The study indicates that board game use could be beneficial in raising the accuracy of student number line estimation when combined with such changes in teacher PCK and associated practice. Although the research supporting the use of board games to develop mental number line representations is compelling, teachers who did not experience a shift in thinking tended to use these as additional tools to complement existing programs, with little noticeable effect. The implications of these findings are discussed with regard to planning professional learning interventions for teachers which are narrow in focus, supported by a small number of specific classroom tools which can be used within existing whole-class or rotational structures, and targeted towards inducing particular changes in thinking.

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11

Liu-Trofimovsky, Jia. "School Psychologists' Early Numeracy Training and Practices". Thesis, State University of New York at Albany, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3621899.

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An emergent area of research pertains to early numeracy, or number sense. Early numeracy plays a significant role in the development of mathematics skills, and researchers have recognized its importance for overall academic achievement. This study surveyed practicing school psychologists to investigate current early numeracy training and practices. A nationwide sample of 279 school psychologists completed a Web-based survey modeled after the available early numeracy research. The majority of individuals reported receiving at least one professional development training for academic concerns per year. A larger number of participants had training for reading and early literacy compared to early numeracy. Related to early numeracy practices, more respondents reported being involved in screening and assessment in contrast to intervention and progress-monitoring. Typically, students were screened in kindergarten through fifth grade using measures such as AIMSweb: Computation and AIMSweb: Problem-Solving. The most often utilized early numeracy instrument was AIMSweb: Number Identification. Most frequently, group academic assessments used were comprised of state tests, and individual measures were often broadband or screener-type measures. Commonly used curricular interventions have demonstrated limited to moderate levels of evidence. Only Classwide Peer Tutoring had a strong level of intervention effectiveness. Intensive interventions that were noted as being regularly implemented (e.g., Board Games, Explicit Instruction, Peer Tutoring, Touch Math) were mainly instructional in nature. The results for consistently used progress-monitoring tools were similar to those for screening (computation, problem-solving, and number identification). Perceived facilitators of participants' early numeracy involvement entailed administrator support and the topic being a current need in schools. School psychologists noted lack of resources and time as two main hindrances for their involvement in early numeracy activities. The implications of this study include increased early numeracy training, involvement in intervention and progress-monitoring, screening practices, alignment with the Common Core Standards, and time allocation and resources. Limitations of the current research were: low response-rate, lengthy survey, and non-response for specific early numeracy components. Finally, potential future research includes investigating progress-monitoring instruments for students in earlier grades, interventions for students with mathematics disabilities (e.g., retention, generalization of skills), home-school partnerships for early numeracy skills, and validation of technological applications.

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Thereesha, Fathimath. "Students' Perceptions of the Secondary Numeracy Project". The University of Waikato, 2007. http://hdl.handle.net/10289/2305.

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This thesis explores the perceptions and experiences of twenty four Year 9 students from two schools in New Zealand who had participated in the Secondary Numeracy Project. The two schools were in their first year of SNP at the time of data collection. The main focus was on four areas of mathematics learning: group work, equipment, communication and teachers. Data was collected mainly by using semi-structured and clinical interviews. Findings revealed that equipment was particularly important and were used more frequently by students in Low ability group. Students liked using equipment, working in groups and sharing multiple solutions. However, communication was not used much as a means of making sense of mathematics in these classrooms. Furthermore the students' responses depended on the ability groups. These findings complemented the work of other researchers who have explored students' perspectives at the primary level. These findings suggest that the SNP would be more successful if students were explicitly taught good communication and cooperative learning skills.

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Alamu, Adrian. "Teacher beliefs, knowledge, and reported practices regarding numeracy outcomes in the Solomon Islands : a thesis submitted to the Victoria University of Wellington in partial fulfilment of the requirements for the degree of Master of Education /". ResearchArchive@vuw.ac.nz, 2010. http://hdl.handle.net/10063/1314.

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Walker-Glenn, Michelle L. "Leadership for School Numeracy: How School Leaders' Knowledge and Attitudes Impact Student Mathematics Achievement". Oxford, Ohio : Miami University, 2010. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=miami1271640843.

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Genis, Amelia. "Numbers count: the importance of numeracy for journalists". Thesis, Stellenbosch : Stellenbosch University, 2001. http://hdl.handle.net/10019.1/52371.

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Thesis (MPhil) -- Stellenbosch University, 2001.
Bibliography
ENGLISH ABSTRACT: Few news subjects or events can be comprehensively covered in the media without numbers being used. Indeed, most reports are essentially 'number stories', or could be improved through the judicious use of numbers. Despite this there are frequent complaints about poor levels of numeracy among journalists. Although numbers are fundamental to virtually everything they write, the most superficial review of South African newspapers indicates that most encounters between journalists and numbers of any sort are uncomfortable, to say the least. Reporters shy away from using numbers, and frequently resort to vague comments such as "many", "more", "worse" or "better". When reports do include numbers, they often don't make sense, largely because journalists are unable to do simple calculations and have little understanding of concepts such as the size of the world's population, a hectare, or a square kilometer. They frequently use numbers to lend weight to their facts without having the numerical skills to question whether the figures are correct. Numeracy is not the ability to solve complicated mathematical problems or remember and use a mass of complicated axioms and formulas; it's a practical life skill. For journalists it is the ability to understand the numbers they encounter in everyday life - percentages, exchange rates, very large and small amounts - and the ability to ask intelligent questions about these numbers before presenting them meaningfully in their reports. This thesis is not a compendium of all the mathematical formulas a journalist could ever need. It is a catalogue of the errors that are frequently made, particularly in newspapers, and suggestions to improve number usage. It will hopefully also serve to make journalists aware of the potential of numbers to improve reporting and increase accuracy. This thesis emphasises the importance of basic numeracy for all journalists, primarily by discussing the basic numerical skills without which they cannot do their job properly, but also by noting the concerns of experienced journalists, mathematicians, statisticians and educators about innumeracy in the media. Although the contents of this thesis also apply to magazine, radio and television journalists, it is primarily aimed at their counterparts at South Africa's daily and weekly newspapers. I hope the information contained herein is of use to journalists and journalism students; that it will open their eyes to the possibility of improving number usage and thereby reporting, serve as encouragement to brush up their numerical skills, and help to shed light on the numbers which surround them and which they use so readily.
AFRIKAANSE OPSOMMING: Min nuusonderwerpe of -gebeure kan in beriggewing tot hul reg kom sonder dat enige getalle gebruik word. Trouens, die meeste berigte is in wese 'syferstories', of kan verbeter word deur meer sinvolle gebruik van syfers. Tog is daar vele klagtes oor joemaliste se gebrekkige syfervaardigheid. Ten spyte van die ingeworteldheid van getalle in haas alles wat hulle skryf, toon selfs die mees oppervlakkige ondersoek na syfergebruik in Suid-Afrikaanse koerante joemaliste se ongemaklike omgang met die meeste syfers. Hulle is skugter om syfers te gebruik, en verlaat hulle dikwels op vae kommentaar soos "baie", "meer", "erger" of "beter". Indien hulle syfers gebruik, maak die syfers dikwels nie sin nie: meermale omdat joemaliste nie basiese berekeninge rondom persentasies en statistiek kan doen nie, en min begrip het vir algemene groothede soos die wereldbevolking, 'n hektaar of 'n vierkante kilometer. Hulle sal dikwels enige syfer gebruik omdat hulle meen dit verleen gewig aan hul feite en omdat hulle nie die syfervaardigheid het om dit te bevraagteken nie. Syfervaardigheid is nie die vermoe om suiwer wiskunde te doen of 'n magdom stellings en formules te onthou en gebruik nie; dis 'n praktiese lewensvaardigheid, die vermoe om die syferprobleme wat die daaglikse roetine oplewer - persentasies, wisselkoerse, baie groot en klein getalle- te verstaan en te hanteer. Hierdie tesis is nie 'n versameling van alle berekeninge wat joemaliste ooit sal nodig kry nie; maar veel eerder 'n beskrywing van die potensiaal van syfers om verslaggewing te verbeter en joemaliste te help om ag te slaan op die getalle rondom hulle en die wat hulle in hul berigte gebruik. Die doel van die tesis is om die belangrikheid van 'n basiese syfervaardigheid vir alle joemaliste te beklemtoon, veral die basiese syfervaardighede waarsonder joemaliste nie die verslaggewingtaak behoorlik kan aanpak nie, te bespreek, en ook om ervare joemaliste, wiskundiges, statistici en opvoeders se kommer oor joemaliste se gebrek aan syfervaardigheid op te teken. Hoewel alles wat in die tesis vervat is, ewe veel van toepassing is op tydskrif-, radio- en televisiejoemaliste, val die klem hoofsaaklik op hul ewekniee by Suid-Afrikaanse dag- en weekblaaie. Ek hoop die inligting hierin vervat sal van nut wees vir praktiserende joemaliste en joemalistiekstudente om hulle bewus te maak van die moontlikhede wat bestaan om syfergebruik, en uiteindelik verslaggewing, te verbeter en as aanmoediging dien om hul syfervaardigheid op te skerp.

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Forder, Kate. "A study to evaluate the impact of a Numicon-based intervention on the numeracy attainment and attitude towards numeracy of children in lower Key Stage 2 identified as experiencing difficulties in mathematics". Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/36971/.

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“The evidence base on numeracy interventions is patchy” (DfE, 2012, p. 6), and in the majority of studies the statistical analysis of data is not without its limitations (Dowker, 2009). The purpose of this study is therefore to add to this evidence base. A mixed methods explanatory sequential design was used to explore the efficacy of a Numicon-based intervention on the numeracy attainment and attitudes towards numeracy of children in Year 3 experiencing mathematical difficulties. Phase 1 implemented a pre-test post-test quasi-experimental design to explore the impact of a Numicon-based intervention across four primary schools. Twenty-five children aged 7 to 8, working at Levels 1C to 2B in numeracy, were allocated to the experimental condition (n = 15) and waiting list control (WLC) condition (n = 10). Interventions were delivered during the autumn term to children in the experimental condition by trained staff within school. The duration and content of sessions varied depending upon the needs of the children. The WLC condition received the intervention during the spring term. The Sandwell Early Numeracy Test- Revised (SENT-R) was administered to investigate the impact of the intervention on numeracy attainment. At post-testing, no statistical significance was found between the experimental and WLC conditions. The null hypothesis was therefore accepted. The ‘Maths and Me Survey’ was used to measure children’s attitudes towards numeracy. Again, at post-testing, no statistical significance was found between conditions, and so the null hypothesis was accepted. During phase 2 of the study, interviews were conducted to obtain the facilitators perceptions of the intervention. Using thematic analysis, two overarching themes were identified: ‘outcomes of the intervention’ which focussed on affective factors and children’s knowledge and understanding; and ‘factors and underpinning mechanisms’, which considered the importance of a whole school ethos, the role of parents, features of Numicon, practicalities of implementing an intervention and theoretical underpinnings. The findings of the current study are considered in light of previous research, as are the implications for Educational Psychologists and other professionals. Methodological issues that arose during the study are also discussed. Areas of future research are considered, focussing on the need for more research into the efficacy of Numicon-based interventions and on the development of attitudes towards numeracy.

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Kelly, Angela. "Mathematics teachers' pedagogy in preparation for OLNA numeracy high-stakes testing: A Western Australian case study". Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2022. https://ro.ecu.edu.au/theses/2513.

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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.

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Divett, Vicky, e n/a. "A profile of the adult numeracy student in the Australian Capital Territory". University of Canberra. Education, 1997. http://erl.canberra.edu.au./public/adt-AUC20060704.164546.

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19

Turvill, Rebecca Anne. "How are young children developing number sense, post national numeracy strategy". Thesis, Brunel University, 2016. http://bura.brunel.ac.uk/handle/2438/13798.

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This thesis examines number sense in primary mathematics. I begin by presenting literature to demonstrate how a cognitive definition of number sense, dominates understandings of mathematical development. I argue that this has influenced fixed-ability practices in mathematics (e.g. Boaler, 1997; Marks, 2014) presenting number-sense as a natural ability. I outline the political landscape and explore data which demonstrates that mathematics education systematically disadvantages some people (Zevenbergen, 2001). After reviewing mathematics learning from a range of theoretical perspectives, I demonstrate a gap in the literature: a sociological exploration of number sense in primary school and illustrate the need to examine school structures and their implications for equitable outcomes for all children. To address this gap I have employed Bourdieusian tools of habitus, field and capital, to explore number sense development. Through ethnographic methods in Year 4 classrooms, I examine how number sense positions children in the field of primary mathematics. This research was undertaken during the first year of statutory implementation of the National Curriculum (DfE, 2013) allowing insight into the lived experiences of children at this time. My findings show that facts, fluency and flexibility are key ways children demonstrate their number sense. Through rapid recall of facts children are seen by their teachers, peers and themselves as ‘able’ at mathematics, leading to explicit reproduction of social class, as these facts are usually learned at home. Similarly, a demand for fluency has led to a focus on procedural accuracy with calculation. Based on this, children are sorted into ability groups magnifying infinitesimally small differences between them (Bourdieu, 1986). Finally, children demonstrate flexibility through different calculation strategies; however, lessons usually rehearse single methods, hiding this key mathematical practice. Each aspect of number sense differentiates children, advantaging those with middle-class habitus and therefore reproducing educational inequalities.

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Esplin, Jacob A. "Comparing the Predictive Power of Executive Function Assessment Strategies on Preschool Mathematics Performance". DigitalCommons@USU, 2018. https://digitalcommons.usu.edu/etd/7283.

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A child’s executive function (aspects: working memory, response inhibition, and set-shifting between sets of rules) capabilities have been found to strongly relate to their mathematics skills. However, while the relationship has been strongly supported by researchers, a consensus has not been reached regarding the specifics of the relationship between executive function and math skills, including which executive function aspect is most predictive of mathematical performance and the differences in said relationship that might be found when examining both numeracy, such as counting skills and basic operations, and geometry skills. The lack of consensus may be in part because researchers have assessed both executive function and mathematics in a variety of ways. To address the consensus issue, this study used a panel of face-to-face measures of executive function, a paper-and-pencil measure of executive function, and a broader measure of mathematical performance than has typically been used, one including numeracy and geometry. Using a longitudinal approach, with two assessment periods about six months apart (M = 5.61 mos., SD = 1.12), this study examined this relationship among 118 children (61 girls), ages 39 to 68 months (M = 52.58, SD = 6.35), living in both rural (n = 64) and urban (n = 54) areas in a state in the western United States. A longitudinal approach allowed for comparisons between results from the two assessment periods. Results suggest that while numeracy and geometry skill among preschool-age children are connected, there are some independent elements. Additionally, because of rapid cognitive growth, age is an important factor when selecting both assessments and analytic strategies, as statistically significant variations in the predictive power of measures and strategies occurred between assessment periods. Connections between younger children’s executive function and numeracy skills appeared to be best assessed through a non-number-based measure, older children’s numeracy ability can be predicted by a greater variety of executive function measures. Face-to-face executive function measures included in this study were more predictive of numeracy skill than geometry skill, and geometry skill appears to be connected to inhibitory control. Differences between rural and urban children were found on numeracy skill and working memory ability, but not on geometry skill. Statistically significant differences by gender were found on an inhibitory control measure, with boys scoring higher than girls in our sample.

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Stott, Deborah Ann. "Learners' numeracy progression and the role of mediation in the context of two after school mathematics clubs". Thesis, Rhodes University, 2015. http://hdl.handle.net/10962/d1017181.

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National and international assessment results, research studies and reports point to South Africa as having educational challenges, specifically with mathematics, science and language. Addressing some of these issues is a key aim for the SANC project at Rhodes University, the context in which this study takes place. Working from a broad Vygotskian perspective of learning and development, this study had a dual focus and investigated how Grade 3 learners’ mathematical proficiency progressed (or not) whilst participating in after school maths clubs over the course of a year, and explored how the mediation offered in the clubs enabled or constrained the emergence of zones of proximal development (ZPD) and thus learning for the club learners. Methodologically, this study works within a largely qualitative, interpretive research paradigm and is designed using a longitudinal case study research strategy. Two after school maths clubs formed the empirical field. The study drew on a range of data collection methods to investigate the dual nature of the research questions for Grade 3 learners. Examples include adapted one-to-one mathematical proficiency interviews and paired task based interviews. The study highlighted the relationship between the multiple roles I played both within the research study and within the SANC project context and emphasises the influence and future implications for these various roles within the SANC project and beyond in terms of my own role as club mentor, for the future design of the SANC project maths club programme and for broader teacher and club facilitator development within and beyond the project. This study has offered insight into how mathematical proficiency may develop in Grade 3 South African learners and as such is an important contribution to the newly developing field of both numeracy and primary educational research in Southern Africa. Additionally, the research findings point to the clubs, as an example of an out-of-school time (OST) programme, providing potentially enabling spaces for both recovery and extension of mathematical proficiency in learners as these spaces are free from several contextual constraints that teachers face in their classrooms. Furthermore, it was found that learners showed development of their conceptual understanding, procedural fluency and adaptive reasoning as proposed by Kilpatrick, Swafford and Findell (2001). The use of various elements of the Maths Recovery (MR) programme (Wright, 2003) in the research process has highlighted various important contributions for broader research. For example, the need to investigate less time consuming approaches to both diagnostic assessment and learner mathematical profiling. Findings from this study support Meira and Lerman’s (2001, 2009) recently developed notion that catching attention is key to the creation or emergence of a ZPD. The study found that a combination of ‘attention catching’ and ‘tuning in’ enabled the creation (emergence) and sustainment of ZPDs in club learners. The study proposed the notion of tuning in where participants in a mathematical interaction continually adjust to each other in order to communicate mathematically. Furthermore, the study found that when attention is not caught or the participants are not tuned in, the learning activity may still be useful in assisting learners to consolidate their existing learning and / or build confidence and as such is particularly relevant to the South African context where fluency in calculating is weak (Hoadley, 2012; Schollar, 2008). This emergent notion of ‘flow’ additionally can play a supporting role in the emergence of a ZPD. The study also found that the manner in which the mediation was offered is important. The results show that the mathematical contributions learners make during interactions captured the mentors’ attention and resulted in mediation that was intentional but spontaneous, flexible, responsive and in-the-moment. This study makes theoretical and methodological contributions to various aspects of mathematics education research particularly with regard to how ZPDs emerge and are sustained and how mediation is offered to facilitate the emergence of ZPDs. Additionally, some aspects of the Learning Framework in Number (LFIN) as part of the Maths Recovery programme have been extended to work in a South African after school club context and to provide useful information for both learner progression over time and for planning of club activities. As such this study thus also contributes to the newly developing field of primary mathematics research in South Africa and to the body of research on primary after school learning programmes both locally and internationally.

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Orton-Flynn, Susan Jane. "The design of a multimedia calculator and its use in teaching numeracy to those with learning difficulties". Thesis, Coventry University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364161.

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Jackson, Fiona Lynne. "Implementation infidelity or aligned adaptation? : exploring tutors' interpretations and enactments of Catch Up Numeracy®, a primary mathematics intervention". Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707977.

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Tshabalala, Phillip Masibi. "Numeracy performance of Grade 3 learners in rural and urban primary schools". Diss., Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-06302009-171742.

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Fox, Jillian Louise. "Young children and digital-numeracy in the prior-to-school year". Thesis, Queensland University of Technology, 2010.

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In the Digital Age, the development of mathematical proficiency is a key issue for children and their education (Steen, 1997). The process of becoming numerate begins in the early years. Considering the widespread demand for a numerate citizenry in a digital age, it is essential that young children develop the foundations of digital-numeracy. The term "digital-numeracy" is used to describe the numeracy practices and behaviours which are mediated by digital technologies such as microwaves, mobile phones, computers, console games ( e.g., Playstations®), television and DVD players and MP3 players ( e.g., iPods®). The expansive growth of digital technologies has precipitated the demand for specific skills in order to participate fully in 21 st Century digital life. A reality of the digital age is the impact that digital-numeracy has on the lives of young children and the opportunities that digital devices provide for development of mathematics. Likewise, while it has been established that the roles teachers and parents play in children's prior-toschool experiences are significant, there is limited understanding of the role they play in young children's numeracy and technology experiences. According to Vygotskian theory (1978) teachers and parents are More Knowledgeable Others play significant roles in the lives of young children providing the learning experiences and tools that influence children's learning. The key components of Vygotsky's socio-cultural theory of learning, social interactions (MKOs) and use of cultural tools (i.e., digital devices) are important for understanding young children's digital-numeracy experiences. Thus, the central aim of the study was to investigate the influence teachers and parents have on young children's digital-numeracy experiences in the prior-to-school year. The perspectives of MKOs were investigated though an exploratory, single case study design. Data were gathered from parents and teachers of preparatory children. All parents who responded to the research invitation were mothers. Parent data was collected through questionnaires and focus groups. Teacher data was collected through interviews, email correspondence and photographic evidence. The data was reviewed according to five analytical strategies: content analysis, pattern matching, identification of emergent themes, comparative analysis, hypothesis-generation and identification of anomalous cases. There were four significant findings. First, this investigation established foundational evidence that young children use digital devices and experience a range of digital-numeracy opportunities in prior-to-school settings. Second, findings indicated that teachers might not demonstrate the depth of content and pedagogical knowledge that is expected and parents might express a depth of knowledge not expected. Third, it was discovered that teachers were techno-optimists who included digital devices in young children's preparatory experiences. Finally it was found that parents were technopessimists who strongly opposed the inclusion of digital devices in the home. Thus, this research challenges the assumptions of who can be considered More Knowledgeable Others in supporting children to become digitally numerate. This thesis has also identified four pertinent avenues for future research. Teachers' lack of content and pedagogical mathematics knowledge is an important component of effective preparatory classrooms and should be investigated. Additionally, there is a need to explore mothers' unexpected knowledge and their highly emotive negative attitudes to digital devices. There is also a need to investigate fathers' perspectives to digitalnumeracy because they were not represented in the participating parent group. Finally, there is a need to establish how socio-economic factors impact young children's access to digital devices because this research was undertaken within a high socio-economic setting.

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Björkhagen, Lena, e Sounia Barsoum. "Neurodidaktik och matematik : En litteraturstudie om neurodidaktikens betydelse för matematikundervisningen". Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-10471.

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Ämnet neurodidaktik bygger på hjärnforskning och etablerade teorier inom det pedagogiska området. Syftet med vår studie är att dra slutsatser av de rön vi finner inom hjärnforskningen som studerar hur hjärnan fungerar i inlärningssammanhang. Vi har lyft fram ett antal förutsättningar för lärande i vår studie som alla får stöd i aktuell hjärnforskning. Dessa förutsättningar har vi kopplat samman med hur hjärnan utvecklas ur ett matematiskt perspektiv. Litteratursökningen har ägt rum i faktaböcker och databaser och för att få vägledning har vi kontaktat experter inom området. De slutsatser vi drar av våra sammanställda texter visar att kunskaper inom neurologin kan vägleda pedagoger i undervisningen. Vår slutsats är att neurodidaktik bidrar med viktig kunskap om hjärnan som kan lämna värdefulla tillskott för pedagoger i undervisningssammanhang i ämnet matematik och även i övriga ämnen.

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Le, Grange Lynn Louise. "The development of the number concept in Grade R: a case study of a school in the Wellington area". University of the Western Cape, 2014. http://hdl.handle.net/11394/4397.

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Magister Educationis - MEd
Systemic evaluation undertaken by the Department of Basic Education as part of the Literacy and Numeracy Strategy 2006 – 2016 posed a serious challenge in South African schools. The numeracy and mathematics results in 2009 stated that 35% of learners in Grade 3 achieved the required level of competence in Mathematics. This has, however, improved to 48.3% in 2010 but dropped to 47.6% in 2011. The development of early number concept in countries such as the Netherlands, Singapore and Helsinki has shown that early intervention is essential for reaching mathematical success in schooling. The Curriculum and Assessment Policy Statement (CAPS) integrates the three learning programmes: Literacy, Numeracy and Life Skills for Grade R into a daily programme of activities. Within this daily programme it specifies that 35% of each day must be used towards Numeracy. The Grade R method of teaching emphasizes the fact that teaching must take place informally but planned formally. The purpose of this study is to examine how early mathematics is taught in an integrated and informal setting to improve number concept. The theoretical framework underpinning this study is based on the constructivist views of Piaget and Vygotsky and how these theories lay the foundation for the development of number concept in Grade R. Number skills to develop number concept were identified in nine lessons to underpin the content area 1, Numbers, Operations and Relationships as determined by the Grade R Mathematics Curriculum and Assessment Policy Statement (CAPS). The methodology employed to answer the research question were video-recordings, observations and interviews. The findings identified number skills such as emergent number concepts: distinguishing numerosity, imitating resultative counting and symbolizing by using fingers as well as growing number concepts: discovering different meanings of numbers, oral counting, one- to- one correspondence, rote counting, perceptual subitising, resultative counting, representing and symbolizing numbers, ordinality, place value, emergent object-based counting and calculating and golden moments. The discussion of the findings focused on the CAPS content area and how these number skills were used to achieve the demands of the content area 1. The major findings of this study presented a case of the utilization of number skills to achieve the development of number concept in Grade R, how mathematics should be made fun, and how incidental learning, “golden moments” can be used to introduce key mathematical concepts informally. This study has implications for teachers of Grade R and for the training of pre-service Grade R teachers at tertiary level.

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Sidiropoulos, Helen. "The implementation of a mandatory mathematics curriculum in South Africa : the case of mathematical literacy". Thesis, Pretoria : [s.n.], 2008. http://upetd.up.ac.za/thesis/available/etd-06032008-115730.

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Carter, Merilyn G. "A multiple case study of NAPLAN numeracy testing of Year 9 students in three Queensland secondary schools". Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/79906/1/Merilyn_Carter_Thesis.pdf.

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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.

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Pausigere, Peter. "Primary maths teacher learning and identity within a numeracy in-service community of practice". Thesis, Rhodes University, 2015. http://hdl.handle.net/10962/d1017183.

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This study focuses on the processes of primary maths teacher learning and how their identities and practices evolve in relation to participation in a primary maths focused in-service teacher education programme, called the Numeracy Inquiry Community of Leader Educators (NICLE).Additionally it investigates activities, relations and forms of participation within the Community of Practice (CoP) which enable or constrain evolving primary maths identities and practices and how these relate to the broader context. The study draws from the situative-participationists (Lave, 1996; Wenger, 1998; Sfard & Prusak, 2005; Wenger et al, 2002) theoretical framework supplemented by Bernstein’s (2000) pedagogic identity model. Using a qualitative educational interpretive approach I sampled 8 primary teachers drawn from NICLE and gathered data through participant observations, interactive interviews, document analysis and reflective journals. Analysing the key data themes that emerged from teacher learning stories, which I have called stelos, the study explains the nature of the primary maths teachers’ learning, transformation and participation experiences in NICLE using the synonyms reinvigoration and remediation and activation and relating these semantics to the teachers’ mathematical identities and histories. The study also explains the processes through which primary maths teacher identities evolve in relation to participation in an in-service CoP as ‘insiding’ and ‘outcropping’. Interpreting qualitative data from the empirical field indicates that teachers participating in NICLE mostly took-up into their maths classrooms key numeracy-domain concepts, resources and issues presented by primary maths experts which are informed by research and theory that link to practices. Teachers collaboratively and actively engaged in a range of activities that relate to classroom practices. Teacher learning was also enabled when teachers engaged in maths overlapping communities of practice, shared classroom experiences in friendly ways with fellow NICLE teachers and engaged with NICLE presenters who mutually respected and regarded them as professionals. Such affordances were said to enable teachers to engage learners in maths classes and improve their understanding of specific primary maths concepts. On the other hand teachers felt challenged by the travelling distance, limited time and also raised the tension of how to scale-up maths professional development initiatives to include schools from their community. The study makes a theoretical contribution by illustrating how Bernstein’s pedagogic identity model and its elaboration by Tyler (1999) provides analytical tools to interrogate macro educational changes and connect these to the micro processes and teacher identities.

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Barnard, Elna. "An investigation into Grade R teachers' experiences of implementing numeracy in Grade R". Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1004529.

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This research study investigates how selected Grade R teachers implement numeracy in their classrooms, based on their experiences, personal beliefs and perceptions. This study adopts the view that a teacher's practice is not only informed on what she believes about her learners, but also on how she organises her classroom environment and her own teaching practice. However, the teacher cannot be divorced from the political and historical background of Early Childhood Development (ECD), as these factors have an impact on her numeracy implementation. Integrated in this research study is thus not only a comprehensive historical analysis of the historical and political background of ECD, but also an in-depth look at the complex curriculum road the Grade R teacher had to travel over the past twelve years. The aim of this case study is to understand and describe what is happening in Grade R classrooms when numeracy is implemented, as well as identifying possible barriers which Grade R teachers may experience in implementing numeracy. The author utilized an adapted Interactive Qualitative Analysis Framework to explore Grade R teachers' views and experiences. Open-ended focus group interviews were used to develop a framework for individual interviews. This interview framework guided the data collection of nine audio-video tapes of classroom activities and nine semi-structured individual interviews. Analysis of the individual interviews revealed each teacher's understanding as well as her perceptions and needs regarding the implementation of numeracy in her classroom. The transcriptions of the individual interviews were compared to the audio-video tapes of what happened in each classroom. This was done in order to determine whether the teachers' practices were consistent with what they said in the interviews. Paradoxes and inconsistencies were documented. The historical and political analysis of ECD illustrates the complex development of ECD in South Africa over the last few decades. It therefore also highlights and brings to the fore the complex journey that Grade R teachers had to navigate in adapting their practice to ever changing curriculum requirements. The empirical results show that there are inconsistencies between what selected teachers know and believe, and what they are implementing. However, "silent themes" which did not come to the fore in the focus group or individual interviews, were identified in the audiovideo tapes of classroom activities. Also, many "silent themes" indicate that there are numerous concerns, such as lack of proficiency in bridging the gap between theory and practice, regarding the implementation of numeracy in Grade R. It was found that many of the selected Grade R teachers struggle to implement numeracy in their classrooms, as they lack the skills and support to teach numeracy in a Grade R context.

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Salgado, Maria do Carmo. "Investigação sobre competências numéricas reveladas por estudantes egressos da Educação Básica". Pontifícia Universidade Católica de São Paulo, 2014. https://tede2.pucsp.br/handle/handle/10999.

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Made available in DSpace on 2016-04-27T16:57:31Z (GMT). No. of bitstreams: 1 Maria do Carmo Salgado.pdf: 4233888 bytes, checksum: d579b2a53a6648a175102026ea7f8287 (MD5) Previous issue date: 2014-06-09
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

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Iglesias, Chavely Lissette. "Investigating the Status of Early Numeracy Skills in Bilingual Dual Language Learner Latino Children Attending Head Start and the Association with Parent Demographic Characteristics". Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4084.

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Research on mathematics achievement has become increasingly important with today's technological advances and demand for specialized knowledge. Though there is much literature regarding mathematics achievement in monolingual speakers, little is known regarding the mathematical abilities of Dual Language Learner (DLL) Latino children. This study examined the early numeracy skills in English and Spanish of 132 DLL Latino children attending Head Start programs in five counties across Florida. Relationships and differences among their performance in both languages were examined, along with the contribution of specific parent demographic variables to math achievement. Findings indicated that DLL Latino Head Start children's performance on early numeracy tasks in both English and Spanish ranged from average to low average when compared to national normative samples of monolingual peers. Child participants' performance on early numeracy tasks in English and Spanish was related to some extent. In addition, multiple regression analyses revealed that combined demographic variables predicted math performance in English and Spanish, but only mothers' level of education uniquely predicted the child participants' math performance in Spanish. This study is an important contribution to the literature, as it provides data regarding the early numeracy skills of DLL Latino Head Start children, as well as implications for the field of school psychology. Future directions for research are also discussed.

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Petronzi, Dominic. "The development of the Numeracy Apprehension Scale for children aged 4-7 years : qualitative exploration of associated factors and quantitative testing". Thesis, University of Derby, 2016. http://hdl.handle.net/10545/619167.

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Previous psychological literature has shown mathematics anxiety in older populations to have an association with many factors, including an adverse effect on task performance. However, the origins of mathematics anxiety have, until recently, received limited attention. It is now accepted that this anxiety is rooted within the early educational years, but research has not explored the associated factors in the first formal years of schooling. Based on previous focus groups with children aged 4-7 years, ‘numeracy apprehension’ is suggested in this body of work, as the foundation phase of negative emotions and experiences, in which mathematics anxiety can develop. Building on this research, the first piece of research utilized 2 interviews and 5 focus groups to obtain insight from parents (n=7), teachers (n=9) and mathematics experts (n=2), to explore how children experience numeracy and their observations of children’s attitudes and responses. Thematic and content analysis uncovered a range of factors that characterised children’s numeracy experiences. These included: stigma and peer comparisons; the difficulty of numeracy and persistent failure; a low sense of ability; feelings of inadequacy; peer evaluation; transference of teacher anxieties; the right or wrong nature of numeracy; parental influences; dependence on peers; avoidance and children being aware of a hierarchy based on numeracy performance. Key themes reflected the focus group findings of children aged 4-7 years. This contributed to an item pool for study 2, to produce a first iteration of the Numeracy Apprehension Scale (NAS) that described day-to-day numeracy lesson situations. This 44-item measure was implemented with 307 children aged 4-7 years, across 4 schools in the U.K. Exploratory factor analysis led to a 26-item iteration of the NAS, with a 2-factor structure of Prospective Numeracy Task Apprehension and On-line Number Apprehension, which related to, for example, observation and evaluation anxiety, worry and teacher anxiety. The results suggested that mathematics anxiety may stem from the initial development of numeracy apprehension and is based on consistent negative experiences throughout an educational career. The 26-item iteration of the NAS was further validated in study 3 with 163 children aged 4-7 years, across 2 schools in the U.K. The construct validity of the scale was tested by comparing scale scores against numeracy performance on a numeracy task to determine whether a relationship between scale and numeracy task scores was evident. Exploratory factor analysis was again conducted and resulted in the current 19-item iteration of the NAS that related to a single factor of On-line Number Apprehension. This related to the experience of an entire numeracy lesson, from first walking in to completing a task and was associated with, for example, explaining an answer to the teacher, making mistakes and getting work wrong. A significant negative correlation was observed between the NAS and numeracy performance scores, suggesting that apprehensive children demonstrate a performance deficit early in education and that the NAS has the potential to be a reliable assessment of children’s numeracy apprehension. This empirical reinforces that the early years of education are the origins of mathematics anxiety, in the form of numeracy apprehension.

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35

Nivens, Ryan Andrew. "An Investigation of Palindromes and Their Place in Mathematics". Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etsu-works/292.

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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.

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36

Öberg, Karin. "Det behövs ett nytt verktyg för att reparera bristande baskunskaper i matematik : En studie om Elevate My Math´s effekter hos svensla gymnasieelever". Thesis, Högskolan i Gävle, Matematik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-29847.

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Mätningar av kunskaperna inom matematik hos svenska elever har under en längre tid visat på en nedåtgående trend. Samtidigt läser vi dagligen om den svenska lärarkårens höga arbetsbelastning. Syftet med det här examensarbetet är att undersöka en hållbar lösning, som både vänder den nedåtgående kunskapstrenden hos eleverna och dessutom underlättar lärarnas arbete. I Examensarbetet undersöks elevernas upplevelser samt kunskapsutveckling då de arbetar med det digitala verktyget Elevate My Math. Undersökningen, som är både kvantitativ och kvalitativ görs i en ekonomiklass där halva klassen får arbeta med Elevate My Math och den andra halvan får jobba med ett material som vanligtvis används inom undervisningen. Resultaten visar att eleverna upplevelse av att arbeta med Elevate My Math är mycket positiv. Samtidigt visar resultatet att vidare forskning behövs för att säkerställa elevernas kunskapsutveckling vid användandet av Elevate My Math.

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37

Cohen, Victoria. "Tracking the early number skills performance of 5- to 7-year-old students : a longitudinal study". Thesis, University of Exeter, 2010. http://hdl.handle.net/10036/3149.

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This longitudinal study tracks how 5- to 7-year-olds perform with early number skills. The aim of this study is to diagnose at-risk mathematics students by distinguishing the skills that, if not mastered by the end of Kindergarten, lead to greater difficulty in mathematics in 1st grade. This study’s methodology is mixed as it follows an exploratory and inductive path in light of its use of a hypothesis, an interpretive path in light of its interest in the individual student, and a positivist path in light of its focus on developing rules from analyzed data. An oral diagnostic test based on a comprehensive collection of early number skills was used to test students as Kindergarteners and again as 1st graders. The test results created benchmarks, revealing how the majority of the students performed with early number skills. The test results also revealed that each early number skill is highly, moderately, or minimally predictive in terms of student placement by the end of 1st grade. When comparing the individual skill scores of each Kindergarten student to his/her total test results of 1st grade, the predictive power of each skill emerged. Performing poorly with skills that are minimally predictive did not seem to have an impact on how the Kindergarten student finished in 1st grade; performing poorly with moderately predictive skills had a greater impact on 1st grade placement; performing poorly with highly predictive skills in Kindergarten increased the likelihood that the student would finish in the lower attaining group in 1st grade. A third result of the test showed that certain skills serve as preconditions for other skills; success with certain skills usually meant success with other skills. These connections between skills point to a learning model called in this study “simultaneous pathways,” indicating that there are connections between certain skills, and that students can be learning on several pathways simultaneously. The impact of the predictive power of early number skills is that diagnosis becomes more effective. Early diagnosis means early remediation which may prevent at-risk students from falling further behind their peers. The benchmarks developed by this research will help teachers assess their students because they will know the general skill level of Kindergarteners and 1st graders. This oral diagnostic test informs curriculum development. If test results show that students are missing the skills that are highly predictive, teachers can address those gaps in order to insure mastery.

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38

Pennington, Glenda. "A longitudinal cohort study examining the relationship between working memory and UK primary school curricular mathematics". Thesis, Liverpool John Moores University, 2013. http://researchonline.ljmu.ac.uk/4372/.

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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.

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39

Anderson, Margaret Mary. "Should I Just Decide Where I Think They Are At? Exploring The Literacy And Numeracy Assessment Landscape Of Deaf And Hearing-Impaired Students In New Zealand". Thesis, University of Canterbury. Educational Studies and Human Development, 2010. http://hdl.handle.net/10092/4912.

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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.

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40

Wiberg, Sara. "Matematisk vardagskompetens : Svenska gymnasielärares syn och undervisningspraxis". Thesis, Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-78645.

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Syftet med denna studie var att undersöka lärares syn och undervisningspraxis när det handlar om matematisk vardagskompetens. Fyra lärare intervjuades var för sig. När lärarnas svar analyserades framkom en likartad syn, att matematisk vardagskompetens handlar om den matematik man behöver för att klara sig i sin egen vardag. Denna syn går i linje med den definition som Organisation for Economic Co-operation and Development, OECD, har tagit fram och som dessutom är den som forskning i allmänhet refererar till. De uppgifter med fokus på matematisk vardagskompetens som lärarna ger till sina elever handlar både om att klara den egna vardagen och att klara sig i en framtida vardag som vuxen och yrkesarbetare. Lärarnas undervisningspraxis skiljer sig åt då det kommer till matematisk vardagskompetens. En av lärarna har ett tydligt samarbete med yrkeslärarna och eleverna får således mycket matematisk vardagskompetens i undervisningen. Lärarna försöker i övrigt få med det i matematikundervisningen för att motivera eleverna för densamma. Hur detta sker är mer eller mindre strukturerat beskrivet. Brist på tid, för stora undervisningsgrupper och avsaknad av samarbete med yrkeslärarna nämns som faktorer som begränsar hur stort fokus lärarna har på matematisk vardagskompetens i undervisningen.
The aim of this study was to investigate teachers’ views and teaching praxes when it comes to mathematical literacy. Four teachers were interviewed individually. When the teachers’ answers were analyzed, an analogous view was displayed, that mathematical literacy is about the mathematics one needs to be able to cope with one’s own everyday life. This view corresponds to the definition Organisation for Economic Co-operation and Development, OECD, has presented and that research in general refers to. The assignments with focus on mathematical literacy, that the teachers give their students, deals both with managing one’s own everyday life and a future everyday as an adult and skilled worker. The teachers’ teaching praxes differ when it comes to mathematical literacy. One of the teachers has a clear cooperation with the vocational teachers and the students receive therefore much mathematical literacy in the teaching. The teachers try, otherwise, to teach mathematical literacy to motivate the students for the teaching. How this is fulfilled is more or less structurally described. Deficiency of time, too large teaching groups and want of cooperation with the vocational teachers are mentioned as factors confining the focus the teachers have on mathematical literacy in the teaching.

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41

Baturo, Annette R. "Getting to know probability: A descriptive study of the cognitive processes employed by Year 12 students engaged on probability tasks". Thesis, Queensland University of Technology, 1992.

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42

Cai, Jinghong. "The Influence of Non-English Home Language on Kindergarteners’ Acquisition of Early Mathematical Skills: A Study Based on an Early Childhood Longitudinal Program". Ohio University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1547124240464993.

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43

Lindahl, Christina Lauren. "Developing Early Numeracy and Early Literacy Skills in Preschool Children Through a Shared Parent/Child Book Reading Intervention: A Multiple-Baseline Single Case Design Study". Scholar Commons, 2016. http://scholarcommons.usf.edu/etd/6304.

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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.

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44

Ellis, Katrina M. "Communication is a two-way street: investigating communication from counselors to low-risk individuals on the conditional risk of HIV". Thesis, Kansas State University, 2012. http://hdl.handle.net/2097/13761.

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Master of Science
Department of Psychology
Gary L. Brase
In 2006, the Center for Disease Control and Prevention recommended the revision of state HIV testing laws. With these recommendations, more low-risk individuals are tested regardless of their risk group. However, there is a greater chance of a false positive test result for low-risk individuals than for high-risk individuals. Additionally, previous research found that doctors and HIV counselors in Germany did not accurately communicate the relationship between risk factors and false positive tests (Gigerenzer, Hoffrage, & Ebert, 1998). This study aimed to (1) compare the findings of the 1998 German sample to HIV hotline counselors in the United States in 2011; and (2) to investigate the ability of students to calculate the conditional probability of HIV for a low-risk individual after receiving a positive test, based on idealized transcripts of conversations with HIV hotline counselors. The first study found that HIV hotline counselors use both verbal expressions of risk and percentages to communicate HIV testing statistics. Additionally, 2011 American counselors were more aware of the chance of false positives and false negatives than compared to the 1998 German sample. However, no 2011 American counselors were able to provide an accurate positive predictive value for a low-risk woman. The second study found low performance among students in the calculation of the positive predictive value. Performance was facilitated by a natural frequency format for high numerate individuals. There were different patterns of results for the General Numeracy Scale and the Subjective Numeracy Scale. This would suggest that these two scales might be measuring different constructs. These findings are consistent with the two theories supporting the Frequency Effect, namely the Frequentist Hypothesis and the Nested Sets Hypothesis. Additionally, this research suggests computation of the conditional risk of HIV is facilitated by a natural frequency format. Teaching techniques have been developed and demonstrate long lasting improvement in health related computations. If a few hours of training is all that it takes to communicate these life and death statistics in a manner that is consistent with reasoning, health practitioners and students should be required to have more education in communicating and computing probabilities.

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45

Brown, Bruce John Lindsay. "The initial grounding of rational numbers : an investigation". Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1006351.

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This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of interviews that were transcribed and then analysed in detail, interspersed with periods of reading and reflection. The pilot cycle involved a single grade three teacher, the second cycle involved 2 grade three teachers and the third cycle involved 2 grade three children. The research identified a number of different perspectives that were all important for the development of a fundamental intuitive understanding that could be considered personally meaningful to the individual concerned and relevant to the development of rational number concepts. Firstly in order to motivate and engage the child on a personal level the grounding situation needed to be seen as personally significant by the child. Secondly, coordinating operations provided a means of developing a fundamental intuitive understanding, through coordination with affording structures of the situation that are relevant to rational numbers. Finally, goal directed actions that are deliberately structured to achieve explicit goals in a situation are important for the development of more explicit concepts and skills fundamental for rational number understanding. Different explicit structures give rise to different interpretations of rational numbers in grounding situations. In addition to these perspectives, it became evident that building and learning representations was important for developing a more particularly mathematical understanding, based on the fundamental understanding derived from the child's grounded experience. The conclusion drawn in this research as a result of this complexity, is that to achieve a comprehensive and meaningful grounding, children's learning of rational numbers will not follow a simple linear trajectory. Rather this process forms a web of learning, threading coordinating operations for intuitive development, interpretations for explicit grounding and representations to develop more formal mathematical conceptions.

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46

Bentley, Kristen. "The Word Problem Factor: Assessing the Ability of Utah High School Career and Technical Education Students to Do the Math Involved in Formulating and Calculating Energy Cost Factors". BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/4341.

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Much research has been done showing the difficulty people have with word problems. This has been shown to be true for many types of word problems and for different demographics. Questions have remained unanswered regarding the reasons for this difficulty. It has been unclear if the word problems were hard because the people had forgotten or had not yet learned how to do the math calculations involved or for some other reason. This study deals with high school students who are currently in a high school level math class. They were given an assessment involving word problems and number-only problems. The results demonstrate that these students can do the math calculations needed for the problems but that the difficulty lies in their ability to formulate the word problems into correct mathematical expressions. Among the students in math classes higher than Secondary 2, it cannot be shown that those who have passed Financial Literacy demonstrate a significantly higher ability to do word problems with p > 0.05.

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47

Zaram, Gyang Nyam. "An experimental study of self-regulated learning with mathematically gifted pupils in Nigerian primary schools". Thesis, Nelson Mandela University, 2017. http://hdl.handle.net/10948/13381.

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The purpose of this study was to determine whether gifted pupils can master an enriched advanced level curriculum in mathematics using self-regulated learning strategies. A mathematics curriculum for class five primary school learners in Nigeria was developed for this study. An empirical study was conducted on primary five pupils who were seen to be significantly gifted in mathematics. The study employed the quantitative method of research, that is, the true experimental research. The pre-test, post-test control group design was used. Sixty gifted pupils who participated in a mathematics enrichment programme (MEP) were assigned into two groups of the control group and experimental group with thirty pupils forming each group. The control group was exposed to direct teaching (DT) while the experimental group used self-regulated learning (SRL) strategies. Four teachers served as facilitators in the MEP. The teaching and learning activities were carried out at a higher cognitive level as opposed to the regular curriculum, ensuring that the contents of the MEP were enriched and accelerated. Pupils in both the experimental group and the control group were administered a pre-test, problem-solving exercises, and post-test. These pupils also completed an attitudinal questionnaire to provide feedback about the MEP. The empirical results show that gifted pupils in primary five are capable of self-regulating their own learning through self-monitoring, self-evaluation, and self-reinforcement. The empirical results also show that there is a significant relationship between self-regulated learning, gifted learners, and an enriched advanced level differentiated curriculum as a realistic alternative to the present regular curriculum for gifted pupils in the mainstream of education. The findings further show that the lack of differentiation of instruction, lack of facilities such as libraries, media centres, and support materials contributes to low achievement of gifted pupils. Furthermore, the findings show that pupils were challenged and motivated with the MEP to the extent that they were engaged to think divergently and applied their metacognitive skills in finding solutions to mathematical problems. Therefore, the findings of this study could have significant implications for the future direction of gifted primary school education as well as teacher education. This study has made a significant contribution to the existing body of knowledge for implementing an enriched advanced level curriculum using SRL strategies for mathematically gifted pupils in the mainstream of primary school education.

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Courtney-Clarke, Magret Anna Eugenie. "Exploring the number sense of final year primary pre-service teachers". Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/19943.

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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.

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Brennan, Cynthia Reeder. "IMPLEMENTATION OF AUTHENTIC INVESTIGATIVEACTIVITIES IN RATIO AND PROPORTION TO ADULT LEARNERS:A CASE STUDY". Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1425659840.

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50

Baturo, Annette R. "Year 6 students' cognitive structures and mechanisms for processing tenths and hundredths". Thesis, Queensland University of Technology, 1998. https://eprints.qut.edu.au/14769/7/14769_Digitised%20Thesis.pdf.

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Abstract (sommario):

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.

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Tesi sul tema "Mathematics and numeracy"

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