Thesis (Ed.M.)--Boston University

<p> Women are underrepresented in the STEM workforce. Trends are starting to change as more and more women are starting to choose majors that are related to STEM. However, the numbers decline sharply in engineering, physical sciences and computer sciences. This project was created as a resource to be used in schools to encourage the increase of women studying, and eventually working, in STEM fields. Research has shown that many women who choose STEM majors and careers were heavily influenced by informal STEM enrichment opportunities outside of the school day and female role models in STEM. This project is an NGSS aligned lesson that incorporates a historical vignette highlighting the work of a female scientist. The vignette can be used in a lesson or as a pull out in a different class or program.</p><p>

The Cockcroft Report claimed that "mathematics provides a means of communication which is powerful, concise and unambiguous". Such precision in language may be a conventional aim of mathematics, particularly when communicated in writing. Nonetheless, as this thesis demonstrates, vagueness is commonplace when people talk about mathematics. In this thesis, I examine the circumstances in which vagueness arises in mathematics talk, and consider the practical purposes which speakers achieve by means of vague utterances in this context. The empirical database, which is considered in Chapters 4 to 7, consists almost entirely of transcripts of mathematical conversations between adult interviewers (including myself) and one or two children. The data were collected from clinical interviews focused on a small number of tasks, and from fragments of teaching. For the most part, the pupils involved in the study were aged between 9 and 12, although the age-range in Chapter 7 extends from 4 to 25. I draw on a number of approaches to discourse associated with 'pragmatics' -a field of linguistics - to analyse the motives and communicative effectiveness of speakers who deploy vagueness in mathematics talk. I claim that, for these speakers, vagueness fulfills a number of purposes, especially 'shielding', i. e. self-protection against accusation of being wrong. Another purpose is to give approximate information; sometimes to achieve shielding, but also to provide the level of detail that is deemed to be appropriate in a given situation. A different purpose, associated with a particular form of vagueness (of reference), is to compensate for lexical gaps in pursuit of effective communication of concepts and ideas. I show, in particular, how speakers use the pronouns 'it' and 'you' in mathematics talk to communicate concepts and generalisations. Some consideration is given to the intentions of 'expert speakers of mathematics when they deploy vague language. Their purposes include some of those identified for novices. Teachers also use vagueness as a means of indirectness in addressing pupils; this strategy is associated with the redress of 'face threatening acts'. My thesis is that vagueness can be viewed and presented, not as a disabling feature of language, but as a subtle and versatile device which speakers can and do deploy to make mathematical assertions with as much precision, accuracy or as much confidence as they judge is warranted by both the content and the circumstances of their utterances. I report on the validation and generalisation of my findings by an Informal Research Group of school teachers, who transcribed and analysed their own classroom interactions using the methods I had developed.

'Higher school mathematics' connotes typical upper secondary school and early college mathematics. The mathematics at this level is characterised by moves to (1) rigour in justification,(2) abstraction in content and (3) fluency in symbolic manipulation. This thesis investigates these three transitions - towards rigour, abstraction, and tluencyusing philosophical method: for each of the three transitions a proposition is presented and arguments are given in favour of that proposition. These arguments employ concepts and results from contemporary English language-medium philosophy and also rely crucially on classroom issues or accounts of mathematical experience both to elucidate meaning and for the domain of application. These three propositions, with their arguments, are the three sub-theses at the centre of the thesis as a whole. The first of these sub-theses (1) argues that logical deduction, quasi-empiricism and visualisation are mathematical warrants, while authoritatively based justification is essentially non-mathematical. The second sub-thesis (2) argues that the reality of mathematical entities of the sort encountered in the higher school mathematics curriculum is actual not metaphoric. The third sub-thesis (3) claims that certain 'mathematical action' can be construed as non-propositional mathematical knowledge. The application of these general propositions to mathematics in education yields the following: 'coming to know mathematics' involves:(1) using mathematical warrants for justification and self conviction; (2) ontological commitment to mathematical objects; and (3)developing a capability to execute some mathematical procedures automatically.

In the Introduction I explore the reasons for my enquiry, and outline the inadequacies of some of the existing attempts to determine the aims and purposes of mathematics in education. In Part 1 I discuss the scope and validity of the justification of mathematics on the basis of its supposed usefulness. From there I defend the view that, in principle at least, there are different kinds of reasons for learning mathematics. In Parts 2 and 3 I attempt to explain whether or not mathematics is fit for two particular non-utility purposes claimed by various writers, and if so, how. Thus, in Part 2, I examine the rather strong claim that mathematics is afine art, and hence or otherwise that it is a source of aesthetic satisfaction. In Part 3, I explore the claim that mathematics provides mental training. Here I shall show that 'mental training', is a broad notion ranging from the rather moral character training to the more restricted notion of training in logic. Between these extremes lies a more modest notion which I argue is the most plausible. The thesis is thus both a history of ideas and a clarification of the concepts used in describing fairly established purposes and rejecting those that seem to me to be unattainable or at least scarcely attainable by studying mathematics. The reason for the study is twofold. I see it as a particular case of the general enquiry into the aims of education. So that my conclusions should inform those who want to justify the place of mathematics on the curriculum. Also, however, I want to suggest that the purposes of mathematics education are internally related to understanding the subject, so that the pupil will gain understanding from a clearer notion of what he or she is doing mathematics for.

Made available in DSpace on 2014-06-11T19:24:36Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-10-05Bitstream added on 2014-06-13T20:12:40Z : No. of bitstreams: 1 gimenes_j_me_rcla.pdf: 916734 bytes, checksum: 82fc8e36dbd49a1e5764d0d10585e6f6 (MD5) / See / Esta dissertação apresenta uma pesquisa norteada pela seguinte pergunta: Quais as contribuições de um grupo de estudo para o professor que busca conhecer os porquês de conteúdos matemáticos? Seus dados são provenientes de um grupo constituído por professoras para estudar os porquês do sistema de numeração decimal e das operações fundamentais, assuntos que foram escolhidos por elas, pois, segundo seus depoimentos, são conceitos difíceis de ensinar e que mereciam um maior aprofundamento. Os dados foram coletados por meio de filmagem, caderno de campo, entrevistas semi-estruturadas e fichas de acompanhamento. A análise teve como suporte teórico os estudos sobre formação de professores e grupos de estudos. Os resultados nos mostram que as contribuições têm a ver com troca de experiências, segurança, valorização e reflexão sobre a prática que já vem sendo desenvolvida, e principalmente, contribuições em relação às justificativas dos conteúdos matemáticos mencionados. Considera-se que essas contribuições podem refletir positivamente na atuação do professor em sala de aula o que é um dos principais objetivos da pesquisa. Além de trazer subsídios para estudos em diferentes esferas que tratam de formação de professores e, ainda, contribuir para organizações e estruturações de grupos de estudos. / This dissertation reports on a research guided by the following question: What is the benefit of participating in a study group for a teacher who is trying to understand the why(s) and wherefore(s) of mathematical content? The research draws on data obtained from a study group constituted by teachers who wanted to study the why(s) and wherefore(s) of the decimal system and the four fundamental operations (+, -, *, /), contents which were chosen by them because according to their speech they are difficult conceipts to teach and deserve to be studied. The data where collected through video recordings, interviews, field notes by the researcher and notes by the teachers. The data analysis was based on the literature on teacher education and on study groups. The results show the benefits of participation are related to the possibility of sharing experiences and reflecting on the ongoing practice as well as to the justification of the mathematical content that were studied. All this together helped to increase the teachers self confidence. It is considered that this could positively reflect on teacher way of acting in the classroom. Besides offering tools for studies on different fields of teachers graduation can still contribute to structures and organizations of study groups.

abstract: Past research has shown that students have difficulty developing a robust conception of function. However, little prior research has been performed dealing with student knowledge of function composition, a potentially powerful mathematical concept. This dissertation reports the results of an investigation into student understanding and use of function composition, set against the backdrop of a precalculus class that emphasized quantification and covariational reasoning. The data were collected using task-based, semi-structured clinical interviews with individual students outside the classroom. Findings from this study revealed that factors such as the student's quantitative reasoning, covariational reasoning, problem solving behaviors, and view of function influence how a student understands and uses function composition. The results of the study characterize some of the subtle ways in which these factors impact students' ability to understand and use function composition to solve problems. Findings also revealed that other factors such as a students' persistence, disposition towards "meaning making" for the purpose of conceptualizing quantitative relationships, familiarity with the context of a problem, procedural fluency, and student knowledge of rules of "order of operations" impact a students' progress in advancing her/his solution approach. / Dissertation/Thesis / Ph.D. Mathematics 2014

<p> The purpose of this study was to examine the effects of Latino parental involvement on children&rsquo;s mathematical skills development and to increase family participation in and out of school with Take-Home Math Literacy Bags. The participants in the study were 13 preschoolers 3 to 5 years of age from a private urban bilingual child care program in northern New Jersey. The researcher conducted a 4-week bilingual (Spanish/English) family math program for Latino English Language Learner families. Data were collected through the use of pre/post student assessment interviews, family pre/post surveys, family experience surveys, researcher journal and anecdotes, and teacher interview and notes. Data analysis revealed improvement in the participants&rsquo; counting, shape recognition skills, and increased visits to the math center. Findings also indicated that Latino families enjoyed using the Take-Home Math Literacy Bags and that they helped them support their children&rsquo;s math skills at home. </p><p>

<p> This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students&rsquo; understanding of elementary mathematics. Realistic Mathematics Education (RME) served as a roadmap for the development of models and problem contexts during the design process, and maintained the focus on mathematics as human activity. Key ideas and insights from scholars who have employed embodied, enactive, ecological, multimodal, and inclusive materialist theories of mathematical activity/cognition on spatiality, human vision, and perception also informed the work. Departing from the sedentary approach to U.S. elementary school mathematics learning and instruction, the designed activities intentionally required students to use their bodies and tools in space to coordinate solutions to mathematical problems. As a design experiment, the research took place in two phases over the course of a year. Phase 1 occurred over 17 days in a suburban 2^nd grade public school classroom, and phase 2 consisted of six 55-minute clinical interviews with six student pairs from two 3^rd grade classrooms in an urban public school. Findings from this research included students using the designed models to support mathematical arguments and to increase levels of precision in their mathematical activity. Themes also emerged around the ways that students responded to affordances and constraints of the models, by shifting orientations, authority, and re-purposing and creating new tools. Multi-scalar mathematical models, activities, and activity spaces afforded novel and intentionally embodied ways for students to participate in model-centric mathematical activity.</p><p>

Philosophiae Doctor - PhD / This study in an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. the current study investigates how new content could be introduced into a school mathematical curriculum. The new topic under discussion for this study is the topis of Cryptology. Two research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities weere developed from the second design research cycle which was worked through with gade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instrutional materials was the development of a hypothetical learning trajetory about the learning and teaching of each activity. the results of the study indicated that the way learners understood the content and the different ways in which they presented solutions augers well for the introduction of a specific new content strand, cryptology, into a new school mathematical curriculum. It is also important for developers of instructional material to have a strong mathematical content knowledge for the design of instructional materials / South Africa