Abstract In a charter school in the Southwest United States, elementary students were struggling to attain proficiency in math and have been failing to meet the standards in math on the Arizona Instrument to Measure Standards test. As a result, these students may not have been prepared for more advanced math courses as they continued their schooling, and this failure to attain proficiency in math may continue to impact the school's ability to make adequate yearly progress. The purpose of this explanatory case study was to explore the perspectives of elementary math teachers toward teaching math, their preparation to teach math, and the possible influences they may have on their students' math skills development. The theoretical framework was self-efficacy theory. Data were gathered through questionnaires completed by 5 participants teaching kindergarten through 5th grade and through the investigation of archival data of their students' achievement test scores. Emerging themes were coded to record and organize relevant information. The participants indicated that they did not feel prepared to teach elementary math when entering the classroom after their teacher preparation programs and that they want to gain more content knowledge and learn more strategies to teach math. Social change may occur as the elementary math teachers are given a voice concerning the teaching of math, and this voice could be used in producing staff development and improving instruction.

No description available.

Federal dollars are utilized to develop instructional programs for students not demonstrating mathematical proficiency on state standardized mathematics assessments, but there is a lack of empirical data on the effectiveness of two different approaches that were used in the local context. The purpose of this quantitative, nonexperimental, casual-comparative study was to determine if state achievement test scores of students in fourth grade who received instruction from a Mathematics Specialist (MS) during the 2007-2009 academic years demonstrated a statistically significant difference from the mathematics state achievement test scores of fourth grade students who received instruction from Grades 1-8 credentialed teachers supported by a Math Coach (MC) during the 2012-2014 academic years. The theoretical base includes two components: National Council of Teachers of Mathematics Standards and Federal No Child Left Behind educational policy, which focus on standards-based education, curriculum, assessment, and instruction to meet students' mathematical needs. Data was collected from a census sample of 13,671 students' state scores from school years 2007-2008, 2008-2009 (MS) and 2012-2013, 2013-2014 (MC). The research question was whether there is a difference in MS and MC scores. An independent samples t test was used to compare the means of all the scores. The results show that the MS program produced statistically higher math scores than the MC. This supports the limited literature in favor of MS. Positive social change includes supporting increasing the use of the MS program in the local context to increase mathematics test scores and the potential for redistribution of federal funds to develop MS programs nationwide.

Software components expose Application Programming Interfaces (APIs) as a means to access their functionality, and facilitate reuse. Developers use APIs supplied by programming languages to access the core data structures and algorithms that are part of the language framework. They use the APIs of third-party libraries for specialized tasks. Thus, APIs play a central role in mediating a developer's interaction with software, and the interaction between different software components. However, APIs are often large, complex and hard to navigate. They may have hundreds of classes and methods, with incomplete or obsolete documentation. They may encapsulate concurrency behaviour that the developer is unaware of. Finding the right functionality in a large API, using APIs correctly, and maintaining software that uses a constantly evolving API are challenges that every developer runs into. In this thesis, we design automated techniques to address two problems pertaining to APIs (1) Concurrency analysis of APIs, and (2) API mining. Speci cally, we consider the concurrency analysis of asynchronous APIs, and mining of math APIs to infer the functional behaviour of API methods. The problem of concurrency bugs such as race conditions and deadlocks has been well studied for multi-threaded programs. However, developers have been eschewing a pure multi-threaded programming model in favour of asynchronous programming models supported by asynchronous APIs. Asynchronous programs and multi-threaded programs have different semantics, due to which existing techniques to analyze the latter cannot detect bugs present in programs that use asynchronous APIs. This thesis addresses the problem of concurrency analysis of programs that use asynchronous APIs in an end-to-end fashion. We give operational semantics for important classes of asynchronous and event-driven systems. The semantics are designed by carefully studying real software and serve to clarify subtleties in scheduling. We use the semantics to inform the design of novel algorithms to find races and deadlocks. We implement the algorithms in tools, and show their effectiveness by finding serious bugs in popular open-source software. To begin with, we consider APIs for asynchronous event-driven systems supporting pro-grammatic event loops. Here, event handlers can spin event loops programmatically in addition to the runtime's default event loop. This concurrency idiom is supported by important classes of APIs including GUI, web browser, and OS APIs. Programs that use these APIs are prone to interference between a handler that is spinning an event loop and another handler that runs inside the loop. We present the first happens-before based race detection technique for such programs. Next, we consider the asynchronous programming model of modern languages like C]. In spite of providing primitives for the disciplined use of asynchrony, C] programs can deadlock because of incorrect use of blocking APIs along with non-blocking (asynchronous) APIs. We present the rst deadlock detection technique for asynchronous C] programs. We formulate necessary conditions for deadlock using a novel program representation that represents procedures and continuations, control ow between them and the threads on which they may be scheduled. We design a static analysis to construct the pro-gram representation and use it to identify deadlocks. Our ideas have resulted in research tools with practical impact. Sparse Racer, our tool to detect races, found 13 previously unknown use-after-free bugs in KDE Linux applications. Dead Wait, our deadlock detector, found 43 previously unknown deadlocks in asynchronous C] libraries. Developers have fixed 43 of these races and deadlocks, indicating that our techniques are useful in practice to detect bugs that developers consider worth fixing. Using large APIs effectively entails finding the right functionality and calling the methods that implement it correctly, possibly composing many API elements. Automatically infer-ring the information required to do this is a challenge that has attracted the attention of the research community. In response, the community has introduced many techniques to mine APIs and produce information ranging from usage examples and patterns, to protocols governing the API method calling sequences. We show how to mine unit tests to match API methods to their functional behaviour, for the specific but important class of math APIs. Math APIs are at the heart of many application domains ranging from machine learning to scientific computations, and are supplied by many competing libraries. In contrast to obtaining usage examples or identifying correct call sequences, the challenge in this domain is to infer API methods required to perform a particular mathematical computation, and to compose them correctly. We let developers specify mathematical computations naturally, as a math expression in the notation of interpreted languages (such as Matlab). Our unit test mining technique maps subexpressions to math API methods such that the method's functional behaviour matches the subexpression's executable semantics, as defined by the interpreter. We apply our technique, called MathFinder, to math API discovery and migration, and validate it in a user study. Developers who used MathFinder nished their programming tasks twice as fast as their counterparts who used the usual techniques like web and code search, and IDE code completion. We also demonstrate the use of MathFinder to assist in the migration of Weka, a popular machine learning library, to a different linear algebra library.

Submitted by WILLIAM VIEIRA GONCALVES null (williamvieira@unemat.br) on 2016-09-21T00:29:22Z No. of bitstreams: 1 TESE_GONCALVES_William_Vieira.pdf: 4325935 bytes, checksum: b52e7f80ac7d448c1c0d65aecda11b20 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-09-22T20:43:16Z (GMT) No. of bitstreams: 1 goncalves_wv_dr_bauru.pdf: 4325935 bytes, checksum: b52e7f80ac7d448c1c0d65aecda11b20 (MD5) / Made available in DSpace on 2016-09-22T20:43:16Z (GMT). No. of bitstreams: 1 goncalves_wv_dr_bauru.pdf: 4325935 bytes, checksum: b52e7f80ac7d448c1c0d65aecda11b20 (MD5) Previous issue date: 2016-07-01 / Este trabalho tem como principal objetivo demonstrar que o GeoGebra apresenta uma maneira diferente de produzir significados matemáticos, com isso, sugerindo sua relevância para o ensino de matemática e de se discutir sua linguagem, possibilidades e limitações. A base inicial da pesquisa foi um estudo imersivo em diferentes comunidades virtuais, literatura acadêmica correlata, cursos específicos do software, produção e análise de diferentes construções dinâmicas. Por fim, optou-se por delimitar a análise aprofundada em entrevistas semiestruturadas com sete professores de matemática, usuários experientes do software. Confrontando-se estes entrevistados com algumas limitações do software, buscou-se estudar como eles transitam entre diferentes modos de produção de significados matemáticos. Pautando-se em reconhecer os diferentes jogos de linguagem, advindos das explicações dos sujeitos da pesquisa, foram sintetizadas três adjetivações que caracterizam os diferentes modos de produção de significados matemáticos: a Matemática do Matemático (MM), a Matemática da Escola (ME) e a Matemática do GeoGebra (MG). Esta pesquisa pautou-se na técnica de investigação qualitativa livre, em função da sua tentativa de compreender mais detalhadamente os significados e características situacionais. A análise dos dados foi realizada à luz de alguns elementos da Análise Textual Discursiva segundo Moraes e Galiazzi (2007). As categorias criadas, a posteriori, foram as seguintes: Matemática do Matemático (MM); Matemática da Escola (ME); Matemática do GeoGebra (MG); Trânsito entre as matemáticas; Percepção da MG; Necessidade de compreensão da MG; aparente Compreensão da MG e aparente Incompreensão da MG. A partir da análise dos dados foi possível confirmar o uso de diferentes jogos de linguagem e, portanto, confirmar o transitar entre a MM, a ME e a MG. Ainda, percebeu-se e analisou-se diferentes formas de transitar, concluindo-se que existe um modo de transitar, comum a todos os entrevistados. Parte-se das possibilidades semióticas da MG, aproveitando-se da maleabilidade da ME, para formalizar-se significados matemáticos, legítimos a MM. Finalmente, a partir da análise aprofundada de uma entrevista, propõe-se o reconhecimento de diferentes aspectos da MG e da história do GeoGebra, como uma forma de aprender sobre como lidar com suas possibilidades e limites. / This work aims to demonstrate that GeoGebra presents has a different way of producing mathematical meanings, suggesting its relevance to mathematics teaching and to discuss its language, possibilities and limitations. Research initial framework was an immersive study in different virtual communities, academic literature, specific courses, production and analysis of different dynamic constructions. In the end, the choice was to delimitate a depth analysis on semi-structures interviews with seven math teachers, experienced software users. Confronting this respondents with some limitations of the software, we sought to study how they transit between different modes of production of mathematical meanings. Based on recognizing the different language games, arising of research subjects were synthesized three adjectives that characterize the different mathematical modes of production: Math from Mathematician (MM), Math from School (ME, in Portuguese) and Math from Geogebra (MG, in Portuguese too). This research used the free qualitative investigation for its attempt to understand with more details the meanings and situational characteristics. Data analysis was carried out with some elements of Discursive Textual Analysis from Moraes and Galiazzi (2007). The categories created, a posteriori, were: Mathematics from Mathematician (MM); Math from School (ME); and Math from Geogebra (MG); Transit between the mathematics; Perception from MG; need of comprehension from MG; apparent comprehension from MG and incomprehension from MG. Data analysis enable to confirm the use of different languages games and, thus, confirm the transition between MM, ME and MG. I still realized and analyzed different ways of transition, concluding that there is a common way to transit between all respondents. We set of semiotic possibilities from MG, taking advantage of the malleability from ME, to formalized mathematical meanings, legitimate from MM. Finally, from the depth analysis of an interview, it is proposed to recognize different aspects from MG and of the GeoGebra history, as a way to learn about how to deal with its possibilities and limits.

Den här studien syftar till att undersöka hur elevers matematikprestationer påverkas av eventuell prov- och / eller matematikångest, om det finns åtgärder som reducerar eventuellprov- och / eller matematikångest och om lärarens sätt att examinera har betydelse. För att besvara syftet söker studien svar på hur matematiklärare förstår prov- och / eller matematikångest, på vilket sätt de beskriver att de försöker hjälpa elever att reducera sådan ångest och om matematiklärare ser examinationsformen som faktor för utlösande av prov- och/ eller matematikångest. Resultaten visar att provångest är situationsbunden och utlöses i stressande situationer när personer tror att de befinner sig i en bedömningssituation. Det kan leda till sämre förmåga att koncentrera sig på uppgifterna. Det finns utöver detta risk att den utlösta provångesten triggarigång matematikångest, vilket i sin tur kan leda till ytterligare sämre förmåga att koncentrera sig på uppgifterna, försämrad prestation och dåliga provresultat. Matematikångest kan också utlösas på grund av social påverkan, dåligt självförtroende samt biologiska faktorer, den beror således inte enbart på provångest. För att reducera provångest krävs att lärare får kunskap om hanteringen av känslor som uppstår så att de kan hjälpa elevernaatt förstå och handskas med sina känslor. Åtgärder mot matematikångest handlar om att förebygga att elever hamnar efter i grundläggande kunskaper i matematik, alternativt reparera brister så fort de upptäcks och att undvika och bearbeta negativa associationer förknippat med matematik. Lärare som intervjuades i denna studie hade endast begränsad kunskap om provångest ochmatematikångest och om hur dessa kan reduceras eller förebyggas. Deras svar antydde dessutom att de inte hade kännedom om att det är två olika typer av ångest och att dessa behöver olika sätt för att reduceras eller åtgärdas. De använde inte variation av examinationsformer som ett medel för att hjälpa sina elever trots att de i princip var överens om att olika examinationsformer kan uppfattas som olika stressande och att alternativa examinationsformerskulle kunna reducera denna stress som leder till provångest och eventuellt vidare till utlösandet av matematikångest. Konsekvensen av detta är att elever inte får den hjälpen de behöver, eller att de får fel hjälp och att de därmed riskerar att misslyckas trots att det hade varit möjligt att lösa.

In this confirmatory factor analysis, factors previously identified to explain the variability in Middle School Mathematics Teachers’ perception of the Common Core State Standards of Mathematics were considered as factors hypothesized to effect high school math teachers’ perceptions of challenging math tasks (CMTs). The factor of student characterization (i.e., disposition, academic preparation, and student behavior) was additionally considered as a factor hypothesized to explain teachers’ perceptions of CMTs, as well as site-based variables (i.e., curriculum, assessment and evaluation, professional development, and collaboration). In addition, teachers’ understanding of the importance of the mathematical practice standards and teacher familiarity with enacting CMTs were factors considered in the model. The original septenary factor structure was modified and good model fit was achieved. In addition to the confirmatory factor analysis model which provides a structure for considering teachers perceptions of CMTs, descriptive statistics are presented from the survey developed that captured teachers’ perceptions of CMTs relative to their sites.

No description available.

Doctor of Philosophy / Department of Mathematics / Andrew G. Bennett / The main objective of the study is to identify the general characteristics of groups within a typical Studio College Algebra class and then adapt aspects of the course to best suit their needs. In a College Algebra class of 1,200 students, like those at most state funded universities, the greatest obstacle to providing personalized, effective education is the anonymity of the students. Data mining provides a method for describing students by making sense of the large amounts of information they generate. Instructors may then take advantage of this expedient analysis to adjust instruction to meet their students’ needs. Using exam problem grades, attendance points, and homework scores from the first four weeks of a Studio College Algebra class, the researchers were able to identify five distinct clusters of students. Interviews of prototypical students from each group revealed their motivations, level of conceptual understanding, and attitudes about mathematics. The student groups where then given the following descriptive names: Overachievers, Underachievers, Employees, Rote Memorizers, and Sisyphean Strivers. In order to improve placement of incoming students, new student services and student advisors across campus have been given profiles of the student clusters and placement suggestions. Preliminary evidence shows that advisors have been able to effectively identify members of these groups during their consultations and suggest the most appropriate math course for those students. In addition to placement suggestions, several targeted interventions are currently being developed to benefit underperforming groups of students. Each student group reacts differently to various elements of the course and assistance strategies. By identifying students who are likely to struggle within the first month of classes, and the recovery strategy that would be most effective, instructors can intercede in time to improve performance.

Cette thèse présente un calcul des séquents pour la logique linéaire enrichie d'un connecteur non commutatif et autodual "précède" situé entre le "par" et le "tenseur". Il est défini pour des séquents dont les formules sont orientées par un ordre partiel. Un calcul de réseaux de démonstration quotientant ce calcul des séquents est défini en termes de graphes orientés. Ce calcul est doté d'une sémantique dénotationnelle dans les espaces cohérents, préservée par élimination des coupures, un processus convergent et confluent. Des résultats combinatoires nécessaires sur les ordres partiels et sur la structure des graphes de démonstrations sont établies ainsi que quelques propriétés du calcul commutatif avec la règle MIX.