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Koong, May-kay Maggie. "Development of addition strategies in young children." Hong Kong : University of Hong Kong, 1990. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18033672.
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Mustoe, Leslie. "Strategies for teaching engineering mathematics." Thesis, Loughborough University, 1988. https://dspace.lboro.ac.uk/2134/15428.
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This thesis is an account of experiments into the teaching of mathematics to engineering undergraduates which have been conducted over twenty years against a background of changing intake ability, varying output requirements and increasing restrictions on the formal contact time available. The aim has been to improve the efficiency of the teaching-learning process. The main areas of experimentation have been the integration in the syllabus of numerical and analytical methods, the incorporation of case studies into the curriculum and the use of micro-based software to enhance the teaching process. Special attention is paid to courses in Mathematical Engineering and their position in the spectrum of engineering disciplines. A core curriculum in mathematics for undergraduate engineers is proposed and details are provided of its implementation. The roles of case studies and micro-based software are highlighted. The provision of a mathematics learning resource centre is considered a necessary feature of the implementation of the proposed course. Finally, suggestions for further research are made.
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Moutsios-Rentzos, Andreas. "University mathematics students : thinking styles and strategies." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/2285/.
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This study concentrates on the relationship between the students’ thinking styles (Stenberg, 1999) and the strategies (Kirby, 1988) the students employ when dealing with exam-type questions in mathematics. Thinking styles are the “preferred way[s] of using the ability one has” (Sternberg, 1999, p. 8) and are conceptualised to be relatively stable over time and context. A strategy is the “combination of tactics, or a choice of tactics, that forms a coherent plan to solve a problem” (Kirby, 1988, p. 230-231). The students’ attainment, the nature of task and the students’ views are also considered in this study. A three-phase study including both quantitative and qualitative techniques was designed with the aim of delineating this relationship. The study was conducted with 2nd year students (N=99) following a BSc in Mathematics in the Department of Mathematics of the University of Athens, although, for methodological reasons, additional data were collected from a broader group of undergraduates (NUG=224). The students’ thinking styles were identified through a version of the Sternberg-Wagner Thinking Styles Inventory (Sternberg, 1999), translated into Greek. Two main Style Cores were identified: Core I (creative, original, critical and non-prioritised thinking) and Core II (procedural, already tested and prioritised thinking). Based on these cores, the students were assigned to two clusters: Cluster 1C2C (High Core I/Low Core II) and Cluster 3C4C (High Core II/Low Core I). In order to identify the students’ strategies, the A-B-Δ strategy classification was introduced, expanding on Weber’s (2005) semantic, syntactic and procedural strategies. The AB-Δ strategies were grouped in three Strategy Types depending on their links with truth,memory and flexibility, respectively identified as: α-type, β-type and δ-type. Students assigned to Cluster 1C2C appeared to prefer more α-type and less β-type Initial Strategies than those assigned to Cluster 3C4C. The nature of the task appeared to affect this link. On the other hand, in the context of Back-Up Strategies, stylistic preferences and ‘high’ attainment appeared to regulate a link between the nature of the task and a Back-Up Strategy, rather than forming a style-strategy link (as in the case of Initial Strategy). Drawing from Skemp’s (1979) views about reality (inner and social) and survival (respectively, internal consistency and social survival), it is argued that the students choose different strategies, because they essentially perceive the given task in qualitatively different ways. The students’ different stylistic preferences indicate differences in their inner reality, thus affecting their choice of an ascertaining argument, which in turn determines their selection of Initial Strategy. The failure of the students’ Initial Strategy leads them to re-evaluate the task itself, thus resulting in a change of the reality in which the students have to survive and this, in turn, determines the students’ Back-Up Strategies.
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Swan, Paul, and Linda Marshall. "Mathematics games: Time wasters or time well spent?" Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80997.
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Globally education authorities are placing increasing emphasis on the development of literacy and numeracy in primary schools. This paper reports on research designed to assist teachers to improve the
numeracy of their students by making the use of mathematics games a more focused aspect of the teaching and learning experience in mathematics. Classroom experience and anecdotal evidence suggest
that games are often used without really focussing on the mathematics involved in playing the game,and are justified simply on the basis of children having ‘fun’. In this paper we report on the use of one game, Numero and how teachers made use of the game and the impact on the children’s learning when using the game.
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Eriksson, Isabelle. "Lärares arbete med problemlösning i grundskolan : problemlösning som mål eller medel?" Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-62554.
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Syftet med denna studie var att försöka ta reda på hur lärare ser på problemlösning i matematikundervisningen och hur de väljer att göra den mer central i matematikundervisningen. Ambitionen var att finna lärarnas syn på problemlösning och strategier för hur de integrerar det i undervisningen. Jag valde att använda mig av fenomenografiska intervjuer som metod då den har som syfte att lyfta uppfattningar kring fenomenet. Tre lärare intervjuades, varav en undervisar i förskoleklass, en i årskurs 1 och en i årskurs 4. Utifrån studien framkommer det av resultatet att lärarna har som syfte att utveckla fler förmågor än bara problemlösningsförmågan. De intervjuade lärarna lyfter vikten av att problemlösning bör vara en central del i matematikundervisningen då den utvecklar flera förmågor/kompetenser. Lärarna hävdar även att de olika förmågorna utvecklas med varandra och behärskar inte eleven de andra förmågorna så är det svårt att vidga kompetenserna i problemlösning då den är den del i den stora förmågan. Det framkommer även att lärarna har egna strategier för hur man kan integrera problemlösning i undervisningen men ingen uttrycker att de har en gemensam strategi på respektive skola.<br>The purpose of this study was about to find out how teachers look at problem solving in teaching mathematics. The ambition was to find the teachers view of problem solving and strategies, and how they integrate it in their teaching. I choosed the phenomenographic interviews as a method. The purpose of phenomenographic interviews is raising perceptions about the phenomenon, that’s why I choosed this method. Three teachers were interviewed, in wich one are teaching in preschool, the second one in first grade and the third one in fourth grade. The results from the study reveal that the teachers have the purpose to develop several abilities/comptences. The teachers also claim that the different abilities develop with eachother, and if the student doesn’t master the other skills, it will be difficult to expand in problem solving as it is a part of the great competence. It also appears that the teachers have their own strategies for integrating problem solving in the teaching, but no one express that they have a common strategi in the respective school.
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Heron, Michele. "How does Self-Regulation impact student’s use of Mathematical Strategies in a Remedial Mathematics Course?" Kent State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1290048945.
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Galante, Dianna Rich Beverly Susan. "Web-based mathematics an examination of assessment strategies implemented in the online mathematics classroom /." Normal, Ill. Illinois State University, 2002. http://wwwlib.umi.com/cr/ilstu/fullcit?p3088022.
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Thesis (Ph. D.)--Illinois State University, 2002.<br>Title from title page screen, viewed January 5, 2006. Dissertation Committee: Beverly Rich (chair), Sherry Meier, Norma Presmeg. Includes bibliographical references (leaves 164-176) and abstract. Also available in print.
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Young, Po-yuk. "Profile of good computational estimators related mathematical variables and common strategies used." [Hong Kong] : University of Hong Kong, 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B14420478.
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Klingler, Kelly Lynn. "Mathematic Strategies for Teaching Problem Solving: The Influence of Teaching Mathematical Problem Solving Strategies on Students' Attitudes in Middle School." Master's thesis, University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5381.
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The purpose of this action research study was to observe the influence of teaching mathematical problem solving strategies on students' attitudes in middle school. The goal was to teach five problem solving strategies: Drawing Pictures, Making a Chart or Table, Looking for a Pattern, Working Backwards, and Guess and Check, and have students reflect upon the process. I believed that my students would use these problem solving strategies as supportive tools for solving mathematical word problems. A relationship from the Mathematics Attitudes survey scores on students' attitudes towards problem solving in mathematics was found. Students took the Mathematics Attitudes survey before and after the study was conducted. In-class observations of the students applying problem solving strategies and students' response journals were made. Students had small group interviews after the research study was conducted. Therefore, I concluded that with the relationship between the Mathematics Attitudes survey scores and journal responses that teaching the problem solving strategies to middle school students was an influential tool for improving students' mathematics attitude.<br>ID: 031001486; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Adviser: Enrique Ortiz.; Title from PDF title page (viewed July 24, 2013).; Thesis (M.Ed.)--University of Central Florida, 2012.; Includes bibliographical references (p. 88-92).<br>M.Ed.<br>Masters<br>Teaching, Learning, and Leadership<br>Education and Human Performance<br>K-8 Math and Science
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Lescault, Julia M. Rich Beverly Susan. "Problem-solving strategies of eighth-grade accelerated mathematics students." Normal, Ill. Illinois State University, 2002. http://wwwlib.umi.com/cr/ilstu/fullcit?p3064533.
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Thesis (Ph. D.)--Illinois State University, 2002.<br>Title from title page screen, viewed February 7, 2006. Dissertation Committee: Beverly S. Rich (chair), Sherry L. Meier, Graham A. Jones, George A. Padavil, Larry D. Stonecipher. Includes bibliographical references (leaves 166-172) and abstract. Also available in print.
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Keffer, Jeremy. "Constructing strategies for games with simultaneous movement." Thesis, University of Delaware, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3730247.
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<p> From the early days of AI, computers have been programmed to play games against human players. Most of the AI work has sought to build world-champion programs to play turn-based games such as Chess and Checkers, however computer games increasingly provide for entertaining real-time play. In this dissertation, we present an extension of recursive game theory, which can be used to analyze games involving simultaneous movement. We include an algorithm which can be used to practically solve recursive games, and present a proof of its correctness. We also define a game theory of lowered expectations to deal with situations where game theory currently fails to give players a definitive strategy, and demonstrate its applicability using several example games.</p>
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Mitchell, Karen E. "The effect of postorganizers on mathematics achievement following lectures." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=682.
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Thesis (Ed. D.)--West Virginia University, 1999.<br>Title from document title page. Document formatted into pages; contains ix, 209 p. : ill. (some col.) Vita. Includes abstract. Includes bibliographical references (p. 172-195).
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Grandowicz, James A. Jr. "Instructional Strategies of First Year Graduate Student Instructors in Mathematics." Bowling Green State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1471427729.
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Paulsson, Clara. "Elevers problemlösningsstrategier : En studie av gymnasieelevers val av strategier vid problemlösning." Thesis, Karlstad University, Faculty of Technology and Science, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-1767.
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<p>The purpose of this study is to examine senior high school students’ strategies and reasoning when solving mathematical problems and make a review of the concept problem solving. The purpose is also to examine if the students’ choice of strategies are influenced when their mathematical knowledge is improved.</p><p>The study was conducted in two science classes at a senior high school. All the students were asked to individually solve two mathematical problems. After that, a few randomly chosen students were interviewed and asked to elucidate their process of thought when solving the problems. The study revealed that the students had preferred to use graphic strategy, algebraic strategy and reverse counting strategy. A small number of other strategies are also represented.</p><p>Moreover, the result showed that students with a higher mathematical level of knowledge tended to choose algebraic strategy.</p><br><p>Denna studie syftar till att undersöka gymnasieelevers strategier och tankemönster vid problemlösning i matematik samt att göra en genomgång av begreppet problemlösning. Studien syftar även till att undersöka huruvida elevernas val av strategier påverkas av att de matematiska kunskaperna utvecklas.</p><p>Undersökningen genomfördes i två Naturvetenskapsklasser på en gymnasieskola. Eleverna fick lösa två problemlösningsuppgifter enskilt varefter jag genomförde en intervju med ett antal slumpvis utvalda elever där de fick chans att förtydliga sitt resonemang och sina tankegångar då de löste problemen.</p><p>I resultatdelen presenteras elevernas val av strategier och det resonemang de fört då de löst problemen. Det har visat sig att eleverna framförallt använde grafisk strategi, algebraisk strategi samt strategin att räkna bakifrån. Ett litet antal andra strategier presenteras också.</p><p>Resultatet har även visat att elever med högre matematisk kunskap har tenderat att välja algebraisk strategi då de löste problemen.</p>
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Moench, Megan Elaine. "Modeling literacy strategies for English language learners in mathematics class." Laramie, Wyo. : University of Wyoming, 2009. http://proquest.umi.com/pqdweb?did=1939263631&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.
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Principato, Angela M. "Readin', Writin', an' 'Rithmetic| Literacy Strategies in High School Mathematics." Thesis, Wayne State University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10257666.
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<p> Stagnant growth on national standardized tests in mathematics and reading and a focus on disciplinary literacy in the Common Core State Standards in ELA, history/social studies, science, and technical subjects has prompted a resurgence in utilizing literacy strategies in the content areas in high school. While literacy standards in mathematics are not explicitly identified in the Common Core State Standards, there may be a place for the use of literacy strategies in high school mathematics. This study explored the relationships between students’ mathematics and reading achievement scores at a small, suburban high school and the implementation of a school wide literacy program to inform curriculum development and instructional strategies. </p><p> The reading and mathematics achievement of students in ninth through eleventh grade was retroactively analyzed to identify changes in student achievement over a two-year period. In the first year, the ninth grade cohort showed statistically significant improvement on both measures of mathematics achievement. Within this ninth grade cohort, students who qualified for free lunches also saw statistically significant improvement in mathematics. None of the other groups showed improvement on both measures of mathematics achievement or reading achievement. In the second year, both the ninth and tenth grade cohorts showed statistically significant increases on both mathematics and reading achievement. Within each of these grade level cohorts, females and white students also saw statistically significant increases in both mathematics and reading. The eleventh grade cohort did not have any significant increases on either measure. On the state top-to-bottom ranking, this high school has moved from the 4<sup> th</sup> percentile to the 25<sup>th</sup> percentile during the implementation of the school wide literacy program. </p><p> While national standardized tests have shown little to no improvement over the last several administrations, this small, suburban high school has seen continued growth over the last several years. Though the results of this study cannot be used to determine a causal relationship between the implementation of literacy strategies and the academic achievement of students in either mathematics or reading, it does provide a case for further investigation into such a relationship.</p><p>
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Sanders, Sharon Parris. "Embedded strategies in mathematics vocabulary instruction a quasi-experimental study /." Connect to this title online, 2007. http://etd.lib.clemson.edu/documents/1202500268/.
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Nimmo, Elizabeth Frances. "Comparing Wait-Time Strategies in a Year 7 Mathematics Class." Thesis, University of Canterbury. Educational Studies and Human Development, 2009. http://hdl.handle.net/10092/3078.
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The use of formative assessment in the classroom is becoming a more widely used practice and acceptable way to support students’ learning. There are several different strands to the formative concept of assessment for learning as opposed to assessment of learning. This research project looks at one strand of formative assessment, namely, the use of wait-time in the classroom. Three wait-time strategies were investigated and examples of their use are provided in an upper primary situation with three students of lower ability and challenging behaviours. Findings from this brief study show no conclusive evidence to support either the widely recognised use of increased wait-time to support a learner’s needs or the opposing view that brief wait-time, when used with students with behavioural issues, might increase academic responses and improve on-task behaviours. The use of one of the strategies, that of ‘talking partners’, demonstrated a slight increase in academic responses with members of the focus group. This research project, together with limitations and further research suggestions, is discussed.
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Jones, Dorian A. "Administrative strategies in developing a real-life skills mathematics unit." CSUSB ScholarWorks, 1992. https://scholarworks.lib.csusb.edu/etd-project/1047.
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Lam, Mau-kwan. "Secondary three students' strategies in solving algebraic equations." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20058019.
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Reller, Susan R. "Reliability diagnostic strategies for series systems under imperfect testing." Thesis, Virginia Tech, 1987. http://hdl.handle.net/10919/45926.
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An expected cost model was developed for failure detection in series systems under imperfect testing. Type I and type II error probabilities are included and single-pass sample paths are required. The model accounts for the expected costs of testing components, false positive termination, and no-defect-found outcomes.
Based on the model, a heuristic was developed to construct the cost minimizing testing sequence. The heuristic algorithm utilizes elementary arithmetic computations and has been successfully applied to a variety of problems. Furthermore, the algorithm appears to be globally convergent. Choice of a starting solution affects the rate of convergence, and guidelines for selecting the starting solution were discussed. Implementation of the heuristic was illustrated by numerical example.<br>Master of Science
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Koong, May-kay Maggie, and 孔美琪. "Development of addition strategies in young children." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B31955927.
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Nieuwoudt, Susanna Maria. "Strategiese onderrig en leer van skoolwiskunde in 'n videoklasstelsel / Susanna Maria Nieuwoudt." Thesis, Potchefstroom University for Christian Higher Education, 2003. http://hdl.handle.net/10394/6.
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Clark, Heather J. "Investigating students' proportional reasoning strategies." abstract and full text PDF (free order & download UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1453188.
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Ingalls, Victoria A. "A Mixed Methods Comparison Study of Placement Strategies for College Mathematics Courses." Ashland University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ashland1227036887.
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Lee, Wen-shin. "Early Termination Strategies in Sparse Interpolation Algorithms." NCSU, 2001. http://www.lib.ncsu.edu/theses/available/etd-20011106-101821.
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<p>A black box polynomial is an object that takes as input a valuefor each variable and evaluates the polynomial at the given input.The process of determining the coefficients and terms of a blackbox polynomial is the problem of black box polynomialinterpolation. Two major approaches have been addressing suchpurpose: the dense algorithms whose computational complexities aresensitive to the degree of the target polynomial, and the sparsealgorithms that take advantage of the situation when the number ofnon-zero terms in a designate basis is small. In this dissertationwe cover power, Chebyshev, and Pochhammer term bases. However, asparse algorithm is less efficient when the target polynomial isdense, and both approaches require as input an upper bound oneither the degree or the number of non-zero terms. By introducingrandomization into existing algorithms, we demonstrate and developa probabilistic approach which we call "early termination." Inparticular we prove that with high probability of correctness theearly termination strategy makes different polynomialinterpolation algorithms "smart" by adapting to the degree or tothe number of non-zero terms during the process when either is notsupplied as an input. Based on the early termination strategy, wedescribe new efficient univariate algorithms that race a denseagainst a sparse interpolation algorithm in order to exploit thesuperiority of one of them. We apply these racing algorithms asthe univariate interpolation procedure needed in Zippel'smultivariate sparse interpolation method. We enhance the earlytermination approach with thresholds, and present insights toother such heuristic improvements. Some potential of the earlytermination strategy is observed for computing a sparse shift,where a polynomial becomes sparse through shifting the variablesby a constant.<P>
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Norling, Malin, and Sofia Hjulfors. "Bidding strategies in the Swedish housing market." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-134399.
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This report focuses on an introduction of game theoretical models and how they can be applied in the Swedish housing market. Game theory is a study of mathematical models of human conflicts and cooperation between rational decision makers within a competitive situation. There are several different strategies that a player can use. In this thesis each strategy is assigned to one player. So how will the players behave in a game, and what strategy is the most successful? By using the software MatLab, the authors creates a game where the strategies assigned to each player gets randomly distributed budgets and are randomly selected to place bids during the game. The game is then played 1 000 000 times to see what strategy is the most successful. It is also tested to see what strategy is the most successful if the players have the same budgets. The authors conclude that in practice it is the size of the budget that determines who will win the bidding, hence there are minor differences between the different strategies in how much they pay on average to win.<br>Denna rapport fokuserar på en introduktion av spelteoretiska mo-deller och hur de kan som kopplas till den svenska bostadsmarknaden. Spelteori är en studie om matematiska modeller för mänskliga konflikter och samarbete mellan rationella beslutstagare i en konkurrensut- satt marknad. Det finns flera olika strategier en spelare kan använda sig av. I denna rapport blir varje spelare tilldelad en strategi. Så frågan ställs hur spelarna kommer att bete sig och vilken av strategierna som är den mest framgångsrika. Genom att använda programvaran Matlab, skapar författarna ett program där varje strategi är tilldelad varje spelare och som helt slumpmässigt får en budget och även blir slumpmässigt valda att spela, d.v.s lägga bud under spelets gång. Spelet spelas därefter 1 000 000 gånger för att se vilken av strategierna som är mest framgångsrik. Det är även testat att se vilken strategi som får bäst resultat om de alla har samma budget. Författarna drar slutsatsen att i praktiken är det storleken på budgeten som bestämmer vem som vinner budgivningen, dock att det även finns mindre skillnader mellan strategierna som bestämmer hur mycket de i genomsnitt får betala när de vinner.
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Wagenaar, Elmien. "A mathematical approach to financial allocation strategies." Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52648.
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Li, Mingfei. "Strategies in repeated games." Diss., Connect to online resource - MSU authorized users, 2008.
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Nordström, Therese. "Strategier vid läsning och lösning av textuppgifter i matematik : en studie om strategier elever som läser svenska som andraspråk använder för att lösa textuppgifter i matematik." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-62346.
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Språket har en stor betydelse för förståelsen av delar av matematiken. Det finns flera faktorer i matematiken som kan vara utmanande för elever som läser svenska som andraspråk. En av dem är att gå från ett vardagsspråk till ett matematikspråk då ord som rymmer, volym och udda är ord som har olika betydelse beroende på kontext. De elever som inte behärskar matematikspråket fullt ut får det svårare att lösa textuppgifter i matematiken. Syftet har därför varit att, genom observationer och intervjuer, ta reda på vilka strategier elever som läser svenska som andraspråk använder när de löser textuppgifter i matematik. Syftet var även att ta reda på vad som kan ligga bakom de val eleverna gör utifrån de dolda regler som kan finnas i klassrummet och det didaktiska kontraktet. Åtta strategier framkom där fyra strategier kunde kopplas till de dolda reglerna eller det didaktiska kontraktet. Två strategier kunde förklaras med övriga orsaker. Slutsats som kan dras är att eleverna använder sig av flera strategier och att det kan vara av värde att medvetandegöra hur regler och det didaktiska kontraktet kan påverka elevernas strategival.<br>Language has a big impact on how we understand some parts in the subject of mathematics. Thera are several factors in mathematics that can be challenging for second language students. One of these factors is to go from everyday language to a mathematic language because there are words that have different meaning depending on the context they are in. It is more challenging for students, who do not fully understand the mathematic language, to solve word problems in mathematics. The purpose of this study was therefore, through observations and interviews, to find out what strategies second language students use to solve word problems in mathematics. It was also to find out what lies behind their choices. This connected to the hidden rules that can exist in a classroom and the didactical contract. Eight strategies where found and four of them could be connected to the hidden rules or the didactical contract. Two strategies where explained with other reasons. Conclusions are that students use several strategies to solve word problems and that there in value in realizing how the hidden rules and the didactical contact can have an impact on student choices.
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Dimitriadis, Christos. "Developing mathematical giftedness within primary schools : a study of strategies for educating children who are gifted in mathematics." Thesis, Brunel University, 2010. http://bura.brunel.ac.uk/handle/2438/4608.
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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.
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Takami, Linda J. "A content analysis of reading strategies in teacher editions of mathematics textbooks." Pullman, Wash. : Washington State University, 2009. http://www.dissertations.wsu.edu/Dissertations/Fall2009/l_takami_112409.pdf.
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Thesis (Ed. D.)--Washington State University, December 2009.<br>Title from PDF title page (viewed on Dec. 28, 2009). "Department of Teaching and Learning." Includes bibliographical references (p. 96-110).
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Björklund, Elias. "Trading strategies based on a pattern detection algorithm." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-184412.
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This thesis aims to develop a method to algorithmically detect patterns used in technical analysis. Non-parametric Kernel regression is used to smoothen the otherwise extremely noisy data of how stock prices develop over time. To find these patterns, Previously described quantitatively defined criteria are used with some modifications. In total six patterns are searched for, where three of them are intended to predict an incline of the asset price and three to predict a decline. As a basis for the study, data of 500 U.S stocks are analyzed. These 500 stocks were all present in the S&P500 index at the beginning of 2010 and the daily closing price of each of these assets is obtained from the beginning of 2010 until the end of 2020. This period is divided into two periods, one training set and one test set. The longer training set period is used to optimize trading strategies, and the shorter test period is used to test these strategies. The algorithm to detect these patterns was successfully implemented and this resulted in detection of a sufficient amount of each pattern to be able to evaluate their efficiency during the training period. All of the patterns intended to predict a decline in the asset price failed. This is most likely due to the fact that the stock market has had a nearly continuous increase during the entire study period. These patterns are therefore not used for the analysis of the test period. In contrast, the three remaining patterns, which are all intended to predict an incline of the assets price, could generate excess returns of the risk-free rate, before adjusting for risk. After risk adjustment, two of these patterns outperformed a Buy-and-hold strategy during the training period. The best combinations of parameters for each of these three patterns are then applied on the test data. The most interesting conclusion from the analysis of the test period is that none of the pattern-based strategies that could outperform the Buy-and-hold strategy during the training period can do that during the test period. The conclusion is therefore that the strategies that are able to beat the Buy-and-hold during the training period have a high probability of being over-optimized on that particular data set and do not perform well enough to be relied on.<br>I den här studien är målet att utveckla en algoritm för att kunna upptäcka mönster som används inom teknisk analys. Icke-parametrisk Kernel regression används för att utjämna aktiepriser som annars är väldigt volatila. För att hitta dessa mönster har sex stycken, tidigare kvantitativt definierade, kriterier med några modifikationer använts. Totalt används sex mönster, där tre av dessa är avsedda för att förutspå en uppgång i aktiepriset, medan de tre andra är avsedda för att förutspå en nedgång i aktiepriset. Som bas för studien används 500 amerikanska aktier. Dessa 500 aktier utgjorde indexet S&P 500 vid början av 2010 och det dagliga avslutspriset för dessa tillgångar samlades in från början av 2010 till slutet av 2020. Denna tidsperiod delas i två perioder, en längre period som utgör data för träning samt en kortare period som används för testning. Träningsdatan används för att optimera handelsstrategierna, medan den kortare tidsperioden nyttjas för att testa dessa strategier. Algoritmen för att hitta de avsedda mönstren implementeras på ett framgångsrikt sätt och resulterar i att ett tillräckligt antal av varje mönster hittas och deras effektivitet utvärderas. Samtliga mönster som är förknippat med framtida nedgång av aktiepriset fungerar inte. Detta beror mest troligt på att priset av de studerade aktierna har haft närmast kontinuerligt positiv utveckling under den valda tidsperioden. På grund av detta används dessa tre mönster inte på den data som utgör testperioden. De tre andra mönstren visar goda resultat vid analys av den data som används för att träna och optimera mönster. Alla tre mönster påvisar resultat av att kunna generera högre avkastning än den riskfria räntan, åtminstone innan de justeras för den medförda risken. Efter riskjustering av avkastningen kan två av dessa mönster överträffa avkastningen av en strategi där man i början av träningsperioden köper aktier för en lika stor summa av vart och ett av de 500 bolagen och sedan behåller dessa aktier till träningsperiodens sista dag, en så kallad ”Buyand- hold” strategi. De bästa parametrerna av de tre mönstren som påvisar en högre avkastning än den riskfria räntan av används sedan på datan avsed för testning av strategierna. Från det testet är den mest intressanta slutsatsen att ingen av de två tidigare strategierna som påvisar högre riskjusterad avkastning än ”Buy-and-hold” strategin nu kan göra detta. Utifrån detta dras slutsatsen att parametrarna för dessa strategier mest troligt är överoptimerade för träningsdatan och att de därmed inte fungerar tillräckligt bra för att kontinuerligt kunna påvisa en riskjusterad överavkastning. iii
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Olofsson, Richard. "Portfolio Optimization : Constructing portfolios by combining investment strategies." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-164096.
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I detta arbete tillämpas en metod för att erhålla en optimal kombination av portföljer som följer olika investeringsstrategier. Detta görs genom att använda en datamängd av historiska stängningspriset för olika typer av värdepapper. Resultatet blir ett urval av totalt 58 olika portföljer vars optimala kombinationer med avseende på riskbenägenhet utvärderas med tre olika riskmått. Det huvudsakliga resultatet presenterat i denna uppsats är den optimala kombinationen för era olika strategier beroende på riskbenägenhet. Portföljavkastning och risken är även utvärderad för sex olika investeringshorisonter, från ett år till totalt tretton år. Det visas att conditional value at risk jämförd med varians och mean absolute deviation resulterar i högre diversi ering. Det visas även att e ekter av tidsdiversi ering har stor negativ påverkan av risken i relation till avkastning.<br>In this work a method for nding the optimal portfolio diversi cation among a set of nite investment strategies is applied. This is done by implementing a simulation method for a data set of historical daily closing prices for di erent types of securities. This results in a total of 58 di erent portfolios for which the optimal combinations in regard to risk propensity is evaluated using three di erent risk measures. The main result of this thesis is the optimal combination of these strategies for several di erent risk propensities. The portfolio returns and risk is also evaluated for six di erent investment horizons, ranging from one year to a maximum thirteen years. It is shown that conditional value at risk compared to variance and mean absolute deviation o ers greater diversi cation. It is also shown that e ects of time diversi cation greatly reduces risk in relation to returns.
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Avril, Luc-Lao. "ESG Integration in AP1 Systematic Equity Strategies." Thesis, KTH, Matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-234854.
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Responsible investing consists of buying more sustainable stocks, or green stocks, and selling the controversial ones. As a pension fund, and with the current climate regulations, it is a concern for Första AP-fonden to know if responsible investing is a plus value for financial aspects. Since our commissioner also has interests in factor strategies, rule-based systematic investment strategies, and possesses some, we will study and explain what are factor strategies. Financial benefits from responsible investing could be explained by savings made on carbon taxes, if a company has a strong environmental policy. On the other hand, factor strategies have proven to work well historically, like the Fama-French value strategy which performed more than decently during the 80s, growing up to around 10 times the initial budget. By using an optimization approach, that maximizes ESG and factor scores with equal importance, we observed that half of the factors had lower performance when combined with ESG. Moreover, the factor portfolios lost their initial characteristics after ESG integration. We concluded that quality was the most promising candidate for a potential new systematic strategy.<br>Hållbart värdeskapande kan definieras som ett sätt att skaffa en mer hållbar portfölj, genom att investera i hållbara företag, som bidrar till att använda naturresurser, humankapital och finansiellt kapital mer ansvarsfullt än andra. Som allmän pensionsfond med de pågående diskussionerna om klimatförändringar gör det intressant att undersöka om integration av ESG-(miljöansvar, socialt ansvarstagande, bolagsstyrning) aspekter i investeringsbesluten kan bidra till att leverera en långsiktigt hög avkastning i linje med Första AP-fondens uppdrag. Dessutom är regelbaserade systematiska strategier (så kallade faktor strategier) av stort intresse för Första AP fonden. Hållbart värdeskapande skulle kunna förbättra dessa strategier genom att tillföra mer robust information än den som vanligtvis finns i de mest bolagens balansräkningar. Därför är det naturligt att undersöka effekterna av integrering av ESG i mest vanliga systematiska aktie strategierna. Genom att lösa ett optimeringsproblem får vi portföljer som maximerar både ESG och traditionella riskfaktorer. Analysen har visat att efter ESG integreringen, förlorade faktorportföljerna delvis sina egenskaper. Det går att konstatera att Quality factor portfölj är den bästa kandidaten för ESG integrering.
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Abdullah, Mohd Faizal Nizam Lee. "Communicating mathematically : self regulating strategies and mathematics learning in secondary school." Thesis, University of East Anglia, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.543374.
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Good, Sarah C. "Exploring Early Mathematics Curriculum and Instructional Strategies: A Three Article Dissertation." Ohio University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1616670781137523.
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Mali, Angeliki. "Lecturers' tools and strategies in university mathematics teaching : an ethnographic study." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/25385.
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The thesis presents the analytical process and the findings of a study on: lecturers teaching practice with first year undergraduate mathematics modules; and lecturers knowledge for teaching with regard to students mathematical meaning making (understanding). Over three academic semesters, I observed and audio-recorded twenty-six lecturers teaching to a small group tutorial of two to eight first year students, and I discussed with the lecturers about their underlying considerations for teaching. The analysis of this thesis focuses on a characterisation of each of three (of the twenty-six) lecturers teaching, which I observed for more than one semester. I chose the teaching of three experienced lecturers, due to diversity in terms of ways of engaging the students with the mathematics, and due to my consideration of their commitment to teaching for students mathematical meaning making. The distinctive nature of the study is concerned with the conceptualisation of university mathematics teaching practice and knowledge within a Vygotskian perspective. In particular, I used for the characterisation of teaching practice and of teaching knowledge the notions tool-mediation and dialectic from Vygotskian theory. I also used a coding process grounded to the data and informed by existing research literature in mathematics education. I conceptualised teaching practice into tools for teaching and actions with tools for teaching (namely strategies). I then conceptualised teaching knowledge as the lecturers reflection on teaching practice. The thesis contributes to the research literature in mathematics education with an analytical framework of teaching knowledge which is revealed in practice, the Teaching Knowledge-in-Practice (TKiP). TKiP analyses specific kinds of lecturer s knowing for teaching: didactical knowing and pedagogical knowing. The framework includes emerging tools for teaching (e.g. graphical representation, rhetorical question, students faces) and emerging strategies for teaching (e.g. creating students positive feelings, explaining), which were common or different among the three lecturers teaching practice. Overall, TKiP is produced to offer a dynamic framework for researcher analysis of university mathematics teaching knowledge. Analysis of teaching knowledge is important for gaining insights into why teaching practice happens in certain ways. The findings of the thesis also suggest teaching strategies for the improvement of students mathematical meaning making in tutorials.
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Comeaux, Brian. "A Comparison of Instructional Strategies: Does How You Teach Mathematics Matter?" ScholarWorks@UNO, 2018. https://scholarworks.uno.edu/honors_theses/123.
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For most of the twentieth and all the twenty-first century, there has been a great debate over educational reform for teaching mathematics. From these debates have come a critical look at how to properly instruct students so they can actively learn in the classroom, yet still retain the information for use in their later life. These questions are rooted in the larger debate between philosophical and psychological dimensions of human growth and development. Some educators, therefore, believe structuring their instruction around some philosophies such as idealism, realism, pragmatism, or existentialism was the key to success for their students. Others took the psychological approach and featured behaviorist or cognitive ideas in their teaching. Most feel that the approaches to psychology reflect these philosophical and psychological theories. These positions have resulted in the emergence of specific suggested teaching strategies that each proponent believes provide the solutions to the dilemma of how to best educate today’s students. This study examines what effect two different instructional strategies have on student acquisition of mathematical concepts and procedures.
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Francis, Lisa Marie. "Instructional Strategies That Homeschooling Parents Use to Teach Their Children Mathematics." ScholarWorks, 2018. https://scholarworks.waldenu.edu/dissertations/5464.
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Homeschooling has become a viable educational choice for families; however, limited research has been conducted on the instructional strategies homeschooling parents use to instruct their children and whether these reflect a learner-centered teaching approach. The purpose of this qualitative case study was to explore the learner-centered instructional strategies homeschooling parents use to teach their children mathematics. The conceptual framework for this single-case study was based on Weimer's learner-centered teaching model. Participants included 4 parents who homeschooled students in Grades 6-12 in a Western state and who received instructional support from a private school. Data were collected from interviews with homeschooling parents, online reflective journals maintained by homeschooling parents, and documents related to the homeschooling mathematics program. Data analysis included coding and examining emerging themes and patterns and discrepant data. The results indicated that the homeschooling parents aligned only a small amount of their instructional strategies with Weimer's learner-centered teaching model by trying to make mathematics fun, interesting, and relevant to their children's lives. They also differentiated instruction and chose curriculum that included some critical-thinking problems. The homeschooling parents taught using more traditional methods in which they were the primary instructors and made most of the decisions about the instructional content. The results of this study can contribute to positive social change by aiding curriculum designers and educators in their exploration of learner-centered and other instructional strategies they can use to design curriculum and instruct their students.
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Williams, Elizabeth. "Strategies for Hiring Managers in Science, Technology, Engineering, and Mathematics Fields." ScholarWorks, 2018. https://scholarworks.waldenu.edu/dissertations/5147.
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One-third of science, technology, engineering, and mathematics (STEM) jobs are unfilled, resulting in less revenue for companies. The purpose of this qualitative single case study, grounded in the human capital theory, was to explore strategies that 2 hiring managers used to recruit STEM professionals in an organization in central Virginia. Data were collected from semistructured interviews, member checking, and company documents on STEM recruitment. The 4 themes that emerged from the data, analyzed using Yin's 5-step process, were as follows: partnerships with state government and local colleges, leadership and employee development programs used as recruitment incentives, competitive compensation package and work-life balance to entice new hires, and meticulous investigation, evaluation, and trial periods. The findings of this study could provide hiring managers with strategies to improve recruitment of skilled STEM professionals. The implications for positive social change could include a reduction in employee turnover, a decrease in employee recruiting costs, an increase in employee retention, more motivated and engaged employees, and an increase in employee production, all of which could increase profits and positively influence the company and the health of the community.
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du, Toit Gawie. "Conceptualization - a necessity for effective learning of mathematics at school." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82474.
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Fuentes, Martinez Ana. "Teachers’ tactics when programming and mathematics converge." Licentiate thesis, Högskolan Väst, Avd för medier och design, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hv:diva-16379.
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Teachers’ everyday practices are embedded in school contexts in which their teaching autonomy is constrained by rules, moral obligations, physical settings,and official directives. When a curricular revision mandated that programming was to be a part of mathematics in upper secondary education, teachers’ conditions changed. How teachers adapted to the new curriculum and how they navigated the tensions and contradictions that they encountered is in this thesis analyzed in terms of teachers’ tactics and policy strategies. The overall goal of the investigation is to contribute to a critical understanding of how mathematics teachers integrate programming in their professional practice and how this integration aligns and diverges from the intentions behind the reform. The empirical material is drawn from nine individual interviews with mathematics teachers that were already proficient in programming. The teachers’ unit plans and other lesson materials featuring programming activities served as a trigger point to delve into further reflections upon their own professional practices. To complete the scene, the policy documents were also examined. These included the mathematics curriculum, as well as related official documents and a collection of institutionally sanctioned programming exercises and demonstrations. Two tactical approaches were made apparent when mathematics teachers began to integrate computer programming in their subject: Dual teaching and Interspersed programming. The teacher’s use of dual teaching practices or interspersed programming are tactics shaped by and in response to the conditions of the new curriculum and their own preferences and views on student learning. These two tactics disclose different ontological commitments in relation to the strategies dictated by the curriculum and reflect a cardinal distinction between planning mathematics activities with elements of programming and planning programming activities with elements of mathematics. Of relevance for teachers and curriculum designers is the understanding of (a) how the notion of programming and mathematics as separate subjects oversimplifies teachers’ actual integration practices, and (b) how the curricular choices made by policy can shape the teaching tactics adopted by educators.
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Upton, Deborah Susan. "Students' solution strategies to differential equations problems in mathematical and non-mathematical contexts." Thesis, Boston University, 2004. https://hdl.handle.net/2144/32845.
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Thesis (Ed.D.)--Boston University<br>PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.<br>The present study investigated undergraduate students' understanding of slope fields and equilibrium solutions as they solved problems in differential equations. The following questions were addressed: 1) Does performance on complex problems vary by context (mathematical, non-mathematical)? 2) When considering a complex problem in a mathematical and a non-mathematical context, are participants who answer the problem in one context correctly more likely to answer the corresponding problem in the other context correctly? 3) Does performance on simple problems predict performance on complex problems?
A written test, Differential Equations Concept Assessment (DECA), was designed and administered to 91 participants drawn from three introductory differential equations courses. Of those participants, 13 were interviewed. DECA consists of four complex problems, two in mathematical contexts and two in non-mathematical contexts, and six simple problems that assess aspects of slope fields and equilibrium solutions.
The data obtained from DECA and the interviews showed that participants performed significantly better on complex problems in non-mathematical contexts than on complex problems in mathematical contexts. There was a significant relationship found between performance on a problem in a mathematical context and performance on the isomorphic problem in the context of population growth, but a significant relationship was not found between a different pair of isomorphic problems, one in a mathematical context and the other in the context oflearning. However, for all the complex problems, participants illustrated a preference for algebraic rather than geometric methods, even when a geometric approach was a more efficient method of solution. Although performance on simple problems was not found to be a strong predictor of performance on complex problems, the simple problems proved to elicit difficulties participants had with aspects of slope fields and equilibrium solutions. For example, participants were found to overgeneralize the notion of equilibrium solution as being any straight line and as existing at all values where a differential equation equals zero. Participants were also found to identify slope fields as determining only equilibrium solutions.<br>2031-01-01
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Penlington, Thomas Helm. "Exploring learners' mathematical understanding through an analysis of their solution strategies." Thesis, Rhodes University, 2005. http://hdl.handle.net/10962/d1007642.
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The purpose of this study is to investigate various solution strategies employed by Grade 7 learners and their teachers when solving a given set of mathematical tasks. This study is oriented in an interpretive paradigm and is characterised by qualitative methods. The research, set in nine schools in the Eastern Cape, was carried out with nine learners and their mathematics teachers and was designed around two phases. The research tools consisted of a set of 12 tasks that were modelled after the Third International Mathematics and Science Study (TIMSS), and a process of clinical interviews that interrogated the solution strategies that were used in solving the 12 tasks. Aspects of grounded theory were used in the analysis of the data. The study reveals that in most tasks, learners relied heavily on procedural understanding at the expense of conceptual understanding. It also emphasises that the solution strategies adopted by learners, particularly whole number operations, were consistent with those strategies used by their teachers. Both learners and teachers favoured using the traditional, standard algorithm strategies and appeared to have learned these algorithms in isolation from concepts, failing to relate them to understanding. Another important finding was that there was evidence to suggest that some learners and teachers did employ their own constructed solution strategies. They were able to make sense of the problems and to 'mathematize' effectively and reason mathematically. An interesting outcome of the study shows that participants were more proficient in solving word problems than mathematical computations. This is in contrast to existing research on word problems, where it is shown that teachers find them difficult to teach and learners find them difficult to understand. The findings of this study also highlight issues for mathematics teachers to consider when dealing with computations and word problems involving number sense and other problem solving type problems.
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Kurt, Gonul. "Pre-service Elementary Mathematics Teachers." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612740/index.pdf.
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The current study seeks to investigate pre-service elementary mathematics teachers&rsquo<br>(PEMTs&rsquo<br>) self-regulated learning (SRL) strategies within the context of their teaching practices in the field work. It was aimed to explore the SRL processes and strategies of four PEMTs while preparing mathematics lessons at their practice schools. In addition to PEMTs&rsquo<br>SRL strategies, the changes and adaptations through their teaching practices and reasons of those changes were also examined in the study. In total 22 pre-interviews and 22 post-interviews were made through the study. Observations were also performed for each teaching practice. Besides observations, PEMTs&rsquo<br>end of semester reflection papers in the context of Teaching Practice course were examined in the study. In addition to those multiple data sources, initial interviews representing detailed information about the participants were also analyzed.
The overall data were analyzed by using the SRL framework combined and adapted from Zimmerman&rsquo<br>s and Pintrich&rsquo<br>s SRL models. The findings of the pre-interviews revealed that PEMTs began with a &lsquo<br>lesson planning process&rsquo<br>reflecting the forethought phase. This phase included searching resources, arranging and organizing the available sources, asking for help and feedback when needed, mental planning of the lesson, and setting goals for the teaching session. These strategies were considered as cognitive self-regulation strategies. In addition to cognitive SRL strategies, motivational factors such as self-efficacy, perception of task, and intrinsic interest were appeared in the study. Post-interviews reflecting the self-reflection phase revealed that PEMTs had a self-evaluation process covering various issues for their teaching sessions as a final step through the study. Finally, it was seen that contextual issues related to teaching practice played a substantial role in PEMTs&rsquo<br>SRL strategies.
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Khan, Kaleem Uddin. "Exact methods for comparison of estimation strategies in survey sampling." Thesis, Queen Mary, University of London, 2010. http://qmro.qmul.ac.uk/xmlui/handle/123456789/440.
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Many strategies in survey sampling depend on large sample approximation formulae for design-based inference on finite population parameters, which are not valid for small samples. We develop an approach using matrix algebra to tackle many problems for samples of any size. Poststratification under a general unequal probability sampling design has received little attention and is an area that we will consider. We demonstrate that inference should be made conditional on the observed sampling allocation rather than unconditionally and examine different types of probability weights. For certain strategies we give results that provide sufficient conditions for the superiority of one strategy over another. These methods are based on the exact mean square errors and are used to compare estimators under poststratification both conditionally and unconditionally. We also present a result that gives an exact upper bound on the absolute bias ratio of a strategy which can be used at the design stage to assess the magnitude of the bias. A general problem for unbiased variance estimators under unequal probability sampling is the possibility of obtaining a negative estimate. We show how the eigenvalues of the matrices given by a variance estimator for the ratio estimator under probability proportional to aggregate size sampling can be used to construct a class of nonnegative definite unbiased variance estimators. Our empirical studies show that estimators from this class are generally more efficient than the standard estimator, especially when the coefficient of variation of the size variable is large.
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Cravens, Tammie R. "Effective Technology Strategies Teachers Use in the Urban Middle Grades Mathematics Classroom." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/msit_diss/85.
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The 21st century mathematics classroom looks and operates differently than it did half a century ago. Not only are teachers expected to facilitate activities rather than lecture, they are also expected to utilize technology. The National Council of Teachers of Mathematics established the technology principle to guide teachers into this practice in 2000. Today there are middle school mathematics teachers who use technology effectively in the classroom. However, there is a dearth of literature in this area on how they select and use technology. The purpose of this qualitative study is to understand the process by which these teachers select and use technology in their classroom. Activity theory and teacher thinking process model provided a conceptual framework for this study. The guiding research questions are: (1) How do successful urban middle grades mathematics teachers, who use technology effectively, describe their teaching practices? (2) What are the strategies teachers use when integrating technology effectively in the classroom?
Using a case study approach, the researcher collected data over 4 months from 3 urban middle school teachers – one on each grade level 6th, 7th, and 8th. Data sources included lesson plans, semi-structured interviews, and classroom observations. Findings revealed that teachers consider the types of learners when deciding what technology is appropriate to use. Teachers also preview technology prior to using it in the classroom. Emerging themes were grouped in five categories to describe how teachers plan and implement technology effectively. They are preparation, engagement, assessment, communication, and evaluation. The research findings give strategies to support teacher’s decisions about using technology for all types of learners and how to be effective in every phase of learning – whether it is introducing a lesson, remediating skills, or assessing knowledge. These findings also enable stakeholders to make informed decisions about technology in their school so that teachers will be able to elevate the quality of instruction with appropriate technology resources. Extended research should measure the impact that technology has on student learning. The likelihood of teachers using technology and using it more often would increase at a faster rate if there is evidence that the growth of student achievement occurs more rapidly when using technology.
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Whale, Susan Gaye. "Using language as a resource: strategies to teach mathematics in multilingual classes." Thesis, Nelson Mandela Metropolitan University, 2012. http://hdl.handle.net/10948/1669.
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South Africa is a complex multilingual country. In the majority of schools in the Eastern Cape, a province in South Africa, the teachers and learners share the same home language, isiXhosa, but teach and learn mathematics in English. The purpose of this study was to encourage teachers to use the home language as a resource to teach mathematics in multilingual classes. The study follows a mixed method design, using both qualitative and quantitative data. Qualitative data were collected from a survey and poetry, which teachers crafted, in which they highlighted their perceptions about language in their lives. They also reflected on their practices and submitted pieces of contemplative writing. Quantitative data were collected from participating teachers who administered a pre-test to their learners as well as a post- test approximately nine months later after conducting an intervention. The results showed that where strategies, such as the implementation of exploratory talk and code switching which used language as a resource, had been introduced mathematical reasoning improved and classroom climate became more positive. The learners’ lack of confidence in being able to express their reasoning in English was prevalent throughout the reflective writing. By enabling learners to use isiXhosa in discussions the teachers felt that the learners gained in both confidence and mathematical understanding. This study has demonstrated that using the learners’ and teachers’ home language unlocks doors to communication and spotlights mathematical reasoning, but there is still an urgency to encourage learners to become fluent in Mathematical English. It is important to note that a positive classroom climate is essential for learners to build confidence and to encourage them to attempt to formulate sentences in English - to start on the journey from informal to formal usage of language as advocated by Setati and Adler (2001:250). My main conclusion is that an intervention that develops exploratory talk by using language as a resource can improve learners’ mathematical reasoning. I wish to emphasise that I am not advocating teaching mathematics in isiXhosa only, but the research has shown the advantages of using the home language as a resource together with English in Eastern Cape multilingual mathematics classes. Learners need to be able to express themselves in English, written and spoken, in order to achieve mathematically. This study therefore shows that teachers can gauge their learners’ improvement in mathematical reasoning after an intervention that develops exploratory talk in class by using the home language as a resource.
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Vallines, Mira Raquel. "Teachers' beliefs regarding effective teaching strategies for American Indian students in mathematics." Thesis, Montana State University, 2008. http://etd.lib.montana.edu/etd/2008/vallines_mira/Vallines_MiraR0808.pdf.
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Extensive research has been conducted on teaching strategies that are effective for American Indians in mathematics. Despite the variety of cultural, linguistic, socioeconomic, and geographic factors influencing student learning within and among American Indian communities, common characteristics of learning styles and effective teaching practices have been identified. Though the wording in each definition varies, research based on a variety of theoretical frameworks and using a variety of methodologies and instruments suggests that among American Indian students, there is a tendency to learn better when the following three strategies are used: contextualization, modeling and demonstration, and joint productive activity. Despite the general agreement in education research that the beliefs that teachers hold about mathematics teaching and learning greatly impact their instructional decisions in the classroom, few, if any, of those studies have examined teachers' beliefs regarding effective strategies for American Indians in mathematics. The main purpose of this study was to add the voices of four teachers to the research community conversation about effective teaching strategies for American Indians in mathematics. Two elementary and two high school teachers from two schools in Montana were selected for this study for their experience with and commitment to the mathematics education of American Indian students. Two are American Indians and two are White. Using a combination of classroom observations and a modification of videoclip interviews, the beliefs of the four teachers were identified with particular focus on the three teaching strategies mentioned above. The study shows that teachers' definitions of research-based strategies often differ from those intended by the research. Teachers' views about these strategies seemed to be idiosyncratic to individual teachers and appeared to be shaped by multiple lenses. In this study, some of those lenses emerged including, among others, school structures and teachers' cultural backgrounds. In light of the results of the study, future efforts for constructive bi-directional communication between the research community and practitioners are recommended.