Significant work has been done modeling cancerous tumor growth and response to therapy under certain simplifying assumptions, specifically, the assumption of spatial homogeneity. We have chosen a spatially heterogenous model for cancer cell growth using a hybrid Lattice-Gas Cellular Automata method. Cell mitosis, apoptosis, and necrosis are explicitly modeled along with the diffusion of nutrients and a necrotic signal. The model implementation is verified qualitatively and is modified to execute on a parallel computer.

This thesis explores the range of strategies used for educational provision for gifted children in mathematics in a group of schools in England. A review of literature relating to international theory and existing research in gifted education and empirical work into the teaching of gifted mathematicians were carried out. The literature review examined the dominant theories of intelligence and giftedness in general, including the historical background of definitions of giftedness and methods for its measurement, before specifically focusing on the concept of mathematical giftedness. The study was located in primary schools within Greater London, where schools are required to implement the ‘Gifted and Talented’ policy of the UK government. The research was conducted in two stages during the school years 2007-2008 and 2008-2009. The first stage involved a questionnaire survey sent to primary schools within five Local Educational Authorities. For the second stage of the research, which constituted the main study, a case study approach was used. The main methods of data collection employed within the case study were observations of mathematics lessons, semi-structured interviews with children nominated as able or gifted mathematicians and their teachers, as well as analysing documentary evidence (i.e., school policy, teacher’s planning, children’s assessment records and children’s written work). It was found that schools were responding to the policy in pragmatic terms, although no specific training was provided for practising teachers or school co-ordinators as part of the national training programme in making provision for mathematically gifted children. In practice, in classrooms, it was found that teachers’ level of confidence and expertise, the level of focused attention given to gifted children, the level of support and extension through higher-order questioning, as well as the size of the class and the nature of the work set were factors which affected the progress, perceptions and attitudes of children who were nominated to be able mathematicians. There is a paucity of research which has investigated aspects of provision for gifted and talented children, particularly in mathematics, in the UK. By specifically addressing this topic, this study makes a distinct contribution to current literature in both understanding aspects of mathematical giftedness and the range of provision used. This study makes a particular contribution to finding out how practising teachers in England are responding to a government initiative, which should be of interest to both policy-makers and practitioners. This thesis also presents examples for organising and teaching mathematics to gifted children at higher cognitive levels, within regular classrooms; this may be of interest to audiences internationally, including countries where there are no policies of provision for mathematically gifted children.

I conducted a study among the middle school students to examinetheir attitudes to school mathematics both inside and outside of the classroom. Also, I have examined teachers’ perceptions of how everyday math examples can be integrated into the classroom experience. The purpose of the study is to investigate the effect of using everyday mathematics in teaching and how this will contribute to a further development of students' ability to think mathematically in different contexts. Parallels between prior research efforts and my study “The art of thinking mathematically - School mathematics in everyday life”are drawn by using qualitative analysis techniques such as the organized empirical data based on student survey questionnaire and teacher interviews. The theoretical perspectives utilized in the study are about the pragmatic perspective and its centralized concepts emphasizing continuity, experience, and interaction. The socio-cultural perspective sheds light on interaction between people and perceptions of themselves and others. Within a broader context I will address the proximal developmental zone (ZPD) by Vygotsky, scaffolding and mediating as those concepts apply to the aforementioned issues. In conclusion I will provide what advantages and disadvantages do teachers and students experience in linking everyday mathematics to the school mathematics.  I will give also approaches for teachers and suggestions for further research and investigation.

Denna fältöversikt kartlägger olika aspekter av matematisk begåvning med särskild fokus på reguljär matematikundervisning. Av forskningsfältet framhålls och exemplifieras varierade synsätt på hur matematikundervisning kan utformas för att erbjuda matematiskt begåvade elever en positiv kunskapsutveckling. De mångfacetterade och varierande infallsvinklarna som finns att tillgå kan göra det svårt för lärare att välja ut lämpliga strategier, metoder och anpassningar för de matematiskt begåvade eleverna de själv har i sina klasser. Resultaten av fältet indikerar att lärares ämneskunskaper och pedagogiska kompetens har störst inverkan på vilket stöd och bemötande elever erbjuds. Det som källorna även framhåller är att begåvade elever behöver identifieras. Identifikationsprocesser beskrivs som en kartläggning av elevernas förmågor, kunskaper och inlärningsstilar men bör även innehålla kontinuerlig utvärdering, analysering och återkoppling av elevers kunskapsutveckling. I källor föreslås det att matematiskt begåvade elever gynnas av individuellt utformad undervisning som inkluderar utmananande och snabbt accelererande uppgifter som med fördel även utgår från elevernas egna intresseområden. / This survey presents a summary of strategies and methods for mathematically gifted individuals’ whit special focus on regular education. Researches exemplify a various spectra of learning environments and methods for gifted students. Although, it can be challenging for teachers to figure out what constitutes an optimal learning environment for mathematically gifted students. According to findings it’s of most interest for gifted children’s positive knowledge development that teachers are professional in both pedagogical and theoretical manners. Manny sources also indicate that mathematically gifted students first of all need to be identified as talented. The identification processes will serve as a form of map in which gifted students skills, knowledge and learning styles are gathered and it also consists of a continual evaluating of student learning processes and knowledge development. Data exemplify that gifted students’ knowledge needs to be challenged and rapidly accelerate in order to interest and motivate them in their learning process. Findings also show that gifted students require personalized solutions that advantageously are originated from students own interests to ensure a positive knowledge development.

The purpose of this study is to examine whether Olympiad participation can develop problem-solving skills in mathematically-gifted learners from disadvantaged schools. My methodological approach was QUAN→Qual, using a quasi-experimental design with a non-equivalent comparison group. I chose two schools from the same disadvantaged area, and identified the top 50 Grade 7 learners in each school by mathematics marks. The study consisted of a pre-test, three mathematics sessions and a post-test. The Study Orientation in Mathematics Questionnaire (SOM) (Maree, Prinsloo, & Claassen, 2011) was used as the pre- and post-test, and a focus group explored the learners’ experience of the SOM. In the mathematics sessions, the intervention group worked through past papers of the SA Mathematics Challenge (South African Mathematics Foundation, 2018), and the alternative intervention group completed worksheets from a Department of Basic Education workbook. My study revealed a positive relationship between success in traditional Mathematics and Study Attitude, Study Habits and overall Study Orientation, and an interaction between disadvantage and success in Mathematics. Participants were less disadvantaged than their surroundings would indicate, and had higher Mathematics anxiety than expected for their achievement level. The intervention did not increase problem-solving behaviour and both the quantitative and qualitative findings showed that the participants found the Olympiad type questions unfamiliar and difficult. This unfamiliarity is indicative of the limited enrichment opportunities for mathematically-gifted learners in disadvantaged areas of South Africa. Greater experience of Mathematics Olympiads is suggested to help mathematically-gifted disadvantaged learners live up to their problem-solving potential. / Dissertation (MEd)--University of Pretoria, 2020. / Educational Psychology / MEd (LSGC) / Unrestricted

Denna studie syftar till att undersöka lärares syn på arbetet med särskilt begåvade elever i matematik, samt de möjligheter och hinder som upplevs i det arbetet. Studiens valda metod i undersökningen är kvalitativa semistrukturerade intervjuer som vänder sig till lärare. Totalt 18 lärare intervjuades. Data analyserades utifrån ett händelselogiskt perspektiv som ser till både inre och yttre påverkansfaktorer. Av resultatet framkommer det att lärares definition av matematisk särskild begåvning varierar. Samtliga lärare betraktar de inre faktorerna hos eleven som mest betydande i fråga om eleven uppfattas som särskilt begåvad i matematikämnet. Likt elevens motivation, förmåga att kommunicera, dra slutsatser och flexibilitet i ämnet. Majoriteten av de deltagande lärarna i studien förknippar matematiskt särskilt begåvade elever med ett logiskt tänkande. Lärarna ser då till elevens förmåga att se samband, mönster, generalisera och kreativa behärskning i ämnet. Lärarens definition av matematisk särskild begåvning bestämmer vilka elever som identifieras som särskilt begåvade i matematikämnet. Majoriteten lärare, 12 stycken, anser att de har goda förutsättningar att identifiera eleverna i fråga. Ändå är det 13 av lärarna i studien som anser att de inte kan ge de särskilt begåvade eleverna den stimulans som de behöver i matematikundervisningen. Vilket tyder på att en stor del lärare inte vet hur de ska möta de särskilt begåvade elevernas behov i matematikundervisningen. Faktorer som möjliggör arbetet med eleverna i fråga är få och majoriteten lärare anser att de skapar sina egna möjligheter, i den egna undervisningen. Således är lärares inre faktorer, i fråga om erfarenhet och kompetens, av stor betydelse. Däremot upplever lärarna att det finns betydligt fler hinder i arbetet med de särskilt begåvade eleverna i matematik. Dessa hinder utgörs i större utsträckning av yttre faktorer som brist på tid, resurser i form av personal och kompetensutveckling. / This study aims to examine teachers' views on the work with promising students in mathematics, as well as the opportunities and obstacles experienced in that work. The study’s chosen method for data collection is qualitative semistructured interviews aimed at teachers. Data was ana- lyzed from an event logic perspective that comprises both internal and external influencing factors. By looking at the result, it reveals that the teachers’ definition of mathematical promising ability varies. All teachers consider the internal factors of the pupil as most significant in terms of whether the pupil is perceived as promising in the subject of mathematics. Such as the pupils’ motivation, ability to communicate, draw conclusions and flexibility on the subject. The majority of the participating teachers in the study associates mathematically promising pupils with a logical thinking. The teachers then look at the pupil's ability to see connections, patterns, generalize and creative mastery of the subject. The teachers' definition of mathematical promising ability determines which students are identified as promising in the subject. The majority of teachers, twelve, consider themselves to have good chances to succeed with identi- fying the pupils in question. Yet, thirteen of the teachers in the study believe that they do not provide the mathematically promising students with the stimulus they need. Suggesting that a large number of teachers do not know how to meet the needs of mathematically promising pupils. Factors that enable the work with the pupils in question are few and the majority of teachers believe that they create their own opportunities, in their own classroom teaching. Thus, the teachers' internal factors, in terms of experience and competence, are of great importance. However, the teachers experience that there are far more obstacles in the work with the mathematically promising pupils. These barriers consist to a greater extent of external factors such as lack of time, resources in the form of staff and professional development.

This design experiment research introduces a mathematical inquiry titled Pattern Math. The Pattern Math activities create an atmosphere where students can think mathematically, communicate mathematically and make connections between different mathematical concepts. Based on simple patterns with complex explanations, the Pattern Math activities provide students with the opportunity to develop their conceptual understanding of mathematics. Through reflections on the activities, students are able to reexamine their views of learning mathematics. This design experiment research has a narrative approach and incorporates the teaching and research technique of interactive writing. The research highlights the power of inquiry. By providing students with the opportunity to work within their zone of proximal development, the Pattern Math activities provide students with the opportunity to make mathematical discoveries and come to understand algebra and arithmetic with conceptual understanding.

This design experiment research introduces a mathematical inquiry titled Pattern Math. The Pattern Math activities create an atmosphere where students can think mathematically, communicate mathematically and make connections between different mathematical concepts. Based on simple patterns with complex explanations, the Pattern Math activities provide students with the opportunity to develop their conceptual understanding of mathematics. Through reflections on the activities, students are able to reexamine their views of learning mathematics. This design experiment research has a narrative approach and incorporates the teaching and research technique of interactive writing. The research highlights the power of inquiry. By providing students with the opportunity to work within their zone of proximal development, the Pattern Math activities provide students with the opportunity to make mathematical discoveries and come to understand algebra and arithmetic with conceptual understanding.

A dimensionally compatible system of equations for stand basal area, volume, and basal area and volume growth was derived using dimensional analysis. These equations are analytically and numerically consistent with dimensionally compatible individual tree volume and taper equations and share parameters with them. Parameters for the system can be estimated by fitting individual tree taper and volume equations or by fitting stand level basal area and volume equations. In either case the parameters are nearly identical. Therefore, parameters for the system can be estimated at the tree or stand level without changing the results. Data from a thinning study in loblolly pine (Pinus taeda L.) plantations established on cutover site-prepared lands were used to estimate the parameters. However, the developed system of equations is general and can be applied to other tree species in other locales. / Ph. D.

<p>Oda kao umjetnička forma, lijepo i uzvi&scaron;eno, razum i ma&scaron;ta, dinamički i<br />matematički uzvi&scaron;eno, uzvi&scaron;enost forme i uzvi&scaron;enost ideje, subjektivizacija uzvi&scaron;enosti, neki<br />su od ključnih pojmova kojima se bavi ovo istraživanje. Međutim, u &scaron;irem kontekstu, ono<br />obuhvata i pojmove individualnog i op&scaron;teg, vječnog i prolaznog, konačnog i beskonačnog,<br />ljudskog i mitskog, ljudskog i božanskog, čovjeka i prirode. Sva ta pitanja, naime, prožimaju<br />se u uzvi&scaron;enim okvirima ode, koja je svojim postojanjem obilježavala najsvjetlije tačke<br />pojedinih epoha i upisivala ih u veličanstvenu hroniku ljudske istorije. Ovaj rad predstavlja<br />osvrt na tu zlatnu hroniku u kojoj će, nadamo se, i na&scaron;a epoha upisati nekoliko stihova.</p> / <p>Ode as an artistic form, beautiful and sublime, reason and imagination,<br />dynamically and mathematically sublime, the sublimity of a form and the sublimity of an<br />idea, subjectivity of the sublime, are some of the key terms of this study. However, in<br />somewhat wider context, it also includes the individual and the universal, eternal and<br />temporal, finite and infinite, human and mythical, human and divine, man and nauture. All<br />these questions are intertwined in the sublime frame of an ode, which, by its own existence,<br />has marked the brightest spots of each epoch and written them in the magnificent chronicle of<br />human history. This work represents the retrospect of that golden chronicle in which our own<br />epoch will hopefully write a few lines.</p>