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Cheng, Elizabeth. "Cognitive styles and mathematical problem solving." Thesis, University of Bristol, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297974.
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Yee, Sean P. "Students' Metaphors for Mathematical Problem Solving." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1340197978.
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Klein, Ana Maria. "Children's problem-solving language : a study of grade 5 students solving mathematical problems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0030/NQ64590.pdf.
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Walden, Rachel Louise. "An exploration into how year six children engage with mathematical problem solving." Thesis, Brunel University, 2015. http://bura.brunel.ac.uk/handle/2438/14285.
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This thesis provides some new insight into children’s strategies and behaviours relating to problem solving. Problem solving is one of the main aims in the renewed mathematics National Curriculum 2014 and has appeared in the Using and Applying strands of previous National Curriculums. A review of the literature provided some analysis of the types of published problem solving activities and attempted to construct a definition of problem solving activities. The literature review also demonstrated this study’s relevance. It is embedded in the fact that at the time of this study there was very little current research on problem solving and in particular practitioner research. This research was conducted through practitioner research in a focus institution. The motivation for this research was, centred round the curiosity as to whether the children (Year Six, aged 10 -11 years old) in the focus institution could apply their mathematics to problem solving activities. There was some concern that these children were learning mathematics in such a way as to pass examinations and were not appreciating the subject. A case study approach was adopted using in-depth observations in one focus institution. The observations of a sample of Year Six children engaged in mathematical problem solving activities generated rich data in the form of audio, video recordings, field notes and work samples. The data was analysed using the method of thematic analysis utilising Nvivo 10 to code the data. These codes were further condensed to final overarching themes. Further discussion of the data shows both mathematical and non-mathematical overarching themes. These themes are discussed in more depth within this study. It is hoped that this study provides some new insights into children’s strategies and behaviours relating to problem solving in mathematics.
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Wong, Man-on. "The effect of heuristics on mathematical problem solving." [Hong Kong : University of Hong Kong], 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13834265.
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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.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).
M.Ed.
Masters
Teaching, Learning, and Leadership
Education and Human Performance
K-8 Math and Science
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Wong, Man-on, and 黃萬安. "The effect of heuristics on mathematical problem solving." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31957523.
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Pieterse, Susan-Mari. "Teachers mediation of metacognition during mathematical problem solving." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/96054.
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Thesis (MEd)--Stellenbosch University, 2014.ENGLISH ABSTRACT: Recent national and international assessments single problem solving out as an important but problematic factor in the current mathematical capacities of South African learners. It is evident that the problem escalates as learners progress to the Intermediate Phase. Research indicates a significant link between metacognition and successful mathematical problem solving. From a Vygotskian sociocultural perspective which formed the theoretical framework of this study, metacognition can be regarded as a higher-order function developing through interaction within social and cultural contexts known as mediation. This qualitative collective case study, informed by an interpretivist paradigm, was designed to explore and compare how Foundation and Intermediate Phase mathematics teachers mediate metacognition during mathematical problem solving. It aimed to offer a deeper understanding of the process of mediation, the complex interplay between cognition and metacognition, and how teachers differentiate the mediation process to accommodate diversity among their learners. To address this, two cases were identified involving a sample of six mathematics teachers each of an urban primary school in the Western Cape Province. The first case was Foundation Phase teachers and the second Intermediate Phase teachers. Semi-structured individual interviews, non-participant classroom observations, and semi-structured focus group interviews were used as methods to gather and triangulate data. Themes that emerged from constantly comparing the data informed the findings. The findings suggest that there are cognitive, non-cognitive and contextual factors which could influence the quality and outcomes of the mediation of metacognition during mathematical problem solving in diverse classrooms. It emphasized the significance of the active role the teacher as a more knowledgeable other plays in the mediation process. Furthermore, it underlined the importance of giving learners challenging mathematical problems requiring metacognition within their zones of proximal development. It was also found that the teacher as mediator should not only have the necessary professional knowledge and strategies, but should also consider the affective factors, perceptions and reactions of learners, during the mediation process. Keywords: metacognition, mediation, mathematical problem solving, sociocultural theory, differentiated instruction, Foundation Phase teachers, Intermediate Phase teachers.
AFRIKAANSE OPSOMMING: Onlangse nasionale en internasionale assesserings lig probleemoplossing uit as 'n belangrike, maar problematiese faktor in die huidige wiskundige prestasie van Suid-Afrikaanse leerders. Dit is duidelik dat die probleem toeneem dermate leerders na die Intermediêre Fase vorder. Navorsing toon 'n beduidende verband tussen metakognisie en suksesvolle wiskundige probleemoplossing. Vanuit 'n Vygotskiaanse sosiokulturele perspektief, wat die teoretiese raamwerk van hierdie studie gevorm het, word metakognisie as 'n hoër-orde funksie gesien wat ontwikkel deur interaksie binne die sosiale en kulturele konteks bekend as mediasie. Hierdie kwalitatiewe kollektiewe gevallestudie, ingelig deur 'n interpretivistiese paradigma, was ontwerp om te verken en te vergelyk hoe Grondslag- en Intermediêre-Fase onderwysers metakognisie tydens wiskundige probleemoplossing medieer. Dit het ten doel gehad om 'n beter begrip te bied van die proses van mediasie, die komplekse wisselwerking tussen kognisie en metakognisie en hoe onderwysers mediasie differensieer om die diversiteit van hul leerders te akkommodeer. Om dit aan te spreek was twee gevalle geïdentifiseer wat elk uit ses wiskunde-onderwysers van 'n stedelike primêre skool in die Wes-Kaap bestaan het. Een geval was Grondslagfase-deelnemers en die ander Intermediêre-Fase- deelnemers. Semi-gestruktureerde individuele onderhoude, nie-deelnemer klaskamer-waarnemings en semi-gestruktureerde fokusgroep-onderhoude was gebruik as metodes om data in te samel en te trianguleer. Temas wat ontluik het na die konstante vergelyking van data het die bevindinge ingelig. Die bevindinge het getoon dat daar kognitiewe, nie-kognitiewe en kontekstuele faktore is wat die kwaliteit en uitkomste van die mediasie van metakognisie tydens wiskundige probleemoplossing in diverse klaskamers kan beïnvloed. Die bevindinge beklemtoon die noodsaaklikheid van die aktiewe rol wat die onderwyser as die meer kundige ander speel in die mediasieproses. Verder word die belangrikheid benadruk van die daarstelling van uitdagende wiskundige probleme, wat metakognisie vereis, binne leerders se sones van proksimale ontwikkeling. Dit is ook gevind dat die onderwyser as mediator nie net oor die nodige professionele kennis en strategieë moet beskik nie, maar ook die affektiewe faktore, persepsies en reaksies van leerders in ag moet neem tydens die mediasieproses. Sleutelwoorde: metakognisie, mediasie, wiskundige probleemoplossing, sosiokulturele teorie, gedifferensieerde onderrig, Grondslagfase-onderwysers, Intermediêre Fase-onderwysers.
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Petersen, Belinda. "Writing and mathematical problem-solving in grade 3." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2366.
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Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016.The mathematics curriculum currently used in South African classrooms emphasises problem-solving to develop critical thinking. However, based on the local performance of South African Foundation Phase learners as well as performance in comparative international studies in mathematics, there is concern regarding their competence when solving mathematical problems and their use of meaningful strategies. This qualitative research study explores how writing can support Grade 3 learners’ mathematical problem-solving abilities. Writing in mathematics is examined as a tool to support learners when they solve mathematical problems to develop their critical thinking and deepen their conceptual understanding. The study followed a case study design. Social constructivist theory formed the theoretical framework and scaffolding was provided by various types of writing tasks. These writing tasks, specifically those promoted by Burns (1995a) and Wilcox and Monroe (2011), were modelled to learners and implemented by them while solving mathematical problems. Writing tasks included writing to solve mathematical problems, writing to record (keeping a journal or log), writing to explain, writing about thinking and learning processes and shared writing. Data were gathered through learners’ written work, field notes, audio-recordings of ability group discussions and interviews. Data were analysed to determine the usefulness of Burns’ writing methodology to support learners’ problem-solving strategies in the South African context. The analysis process involved developing initial insights, coding, interpretations and drawing implications to establish whether there was a relation between the use of writing in mathematics and development of learners’ problem-solving strategies. This study revealed an improvement in the strategies and explanations learners used when solving mathematical problems. At the end of the eight week data collection period, a sample of eight learners showed marked improvement in verbal and written explanations of their mathematical problem-solving strategies than before the writing tasks were implemented.
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Santos, Trigo Luz Manuel. "College students' methods for solving mathematical problems as a result of instruction based on problem solving." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/31100.
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This study investigates the effects of implementing mathematical problem solving instruction in a regular calculus course taught at the college level. Principles associated with this research are: i) mathematics is developed as a response to finding solutions to mathematical problems, ii) attention to the processes involved in solving mathematical problems helps students understand and develop mathematics, and iii) mathematics is learned in an active environment which involves the use of guesses, conjectures, examples, counterexamples, and cognitive and metacognitive strategies. Classroom activities included use of nonroutine problems, small group discussions, and cognitive and metacognitive strategies during instruction.
Prior to the main study, in an extensive pilot study the means for gathering data were developed, including a student questionnaire, several assignments, two written tests, student task-based interviews, an interview with the instructor, and class observations.
The analysis in the study utilized ideas from Schoenfeld (1985) in which categories, such as mathematical resources, cognitive and metacognitive strategies, and belief systems, are considered useful in analyzing the students' processes for solving problems. A model proposed by Perkins and Simmons (1988) involving four frames of knowledge (content, problem solving, epistemic, and inquiry) is used to analyze students' difficulties in learning mathematics.
Results show that the students recognized the importance of reflecting on the processes involved while solving mathematical problems. There are indications suggesting that the students showed a disposition to participate in discussions that involve nonroutine mathematical problems. The students' work in the assignments reflected increasing awareness of the use of problem solving strategies as the course developed. Analysis of the students' task-based interviews suggests that the students' first attempts to solve a problem involved identifying familiar terms in the problem and making some calculations often without having a clear understanding of the problem. The lack of success led the students to reexamine the statement of the problem more carefully and seek more organized approaches. The students often spent much time exploring only one strategy and experienced difficulties in using alternatives. However, hints from the interviewer (including
metacognitive questions) helped the students to consider other possibilities. Although the students recognized that it was important to check the solution of a problem, they mainly focused on whether there was an error in their calculations rather than reflecting on the sense of the solution. These results lead to the conclusion that it takes time for students to conceptualize problem solving strategies and use them on their own when asked to solve mathematical problems.
The instructor planned to implement various learning activities in which the content could be introduced via problem solving. These activities required the students to participate and to spend significant time working on problems. Some students were initially reluctant to spend extra time reflecting on the problems and were more interested in receiving rules that they could use in examinations. Furthermore, student expectations, evaluation policies, and curriculum rigidity limited the implementation. Therefore, it is necessary to overcome some of the students' conceptualizations of what learning mathematics entails and to propose alternatives for the evaluation of their work that are more consistent with problem solving instruction.
It is recommended that problem solving instruction include the participation or coordinated involvement of all course instructors, as the selection of problems for class discussions and for assignments is a task requiring time and discussion with colleagues. Periodic discussions of course directions are necessary to make and evaluate decisions that best fit the development of the course.Education, Faculty of
Curriculum and Pedagogy (EDCP), Department of
Graduate
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Tso, Wai-chuen. "Enhancing students' mathematical problem solving abilities through metacognitive questions." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35384347.
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Tanner, H. F. R. "Using and applying mathematics : developing mathematical thinking through practical problem solving and modelling." Thesis, Swansea University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639162.
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Using and Applying Mathematics in the National Curriculum focuses on the development of reasoning skills through problem solving, and links the processes involved in learning new mathematics with the application of existing knowledge to new situations. This thesis begins by examining how mathematical knowledge is constructed and how children make sense of it. The nature of practical problem solving and modelling is considered and the literature on teaching and learning problem solving and modelling is reviewed with particular emphasis on metacognition and social practices. The research reports a quasi-experiment in which 314 pupils aged between 11 and 13 followed a mathematical thinking skills course and were compared with matched control pupils using pre-tests, post-tests, delayed texts and structured interviews. Assessment instruments were devised to assess pupils' mathematical cognitive development, their metacognitive skills and their metacognitive self knowledge. Statistical data were supported by participant observations. On average, experimental pupils performed slightly better than control pupils in metacognitive skill and mathematical development in the post and delayed-tests. The content of the mathematical development test had not been taught directly by the course and far transfer is claimed. The teachers were divided into four groups according to teaching approach, based on analysis of the qualitative data. The most successful teachers used a flexible form of scaffolding and encouraged reflection. Their classes demonstrated a substantial advantage over their controls in metacognitive skill, metacognitive self knowledge and mathematical development. Recommendations are made about teaching approaches.
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Krawec, Jennifer Lee. "Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability." Scholarly Repository, 2010. http://scholarlyrepository.miami.edu/oa_dissertations/455.
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The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD), low-achieving (LA) students, and average-achieving (AA) students. The primary interest was to analyze the problem representation processes students use to translate and integrate problem information as they solve math word problems. Problem representation processes were operationalized as (a) paraphrasing the problem and (b) visually representing the problem. Paraphrasing accuracy (i.e., paraphrasing relevant information, paraphrasing irrelevant linguistic information, and paraphrasing irrelevant numerical information), visual representation accuracy (i.e., visual representation of relevant information, visual representation of irrelevant linguistic information, and visual representation of irrelevant numerical information), and problem-solving accuracy were measured in eighth-grade students with LD (n = 25), LA students (n = 30), and AA students (n = 29) using a researcher-modified version of the Mathematical Processing Instrument (MPI). Results indicated that problem-solving accuracy was significantly and positively correlated to relevant information in both the paraphrasing and the visual representation phases and significantly negatively correlated to linguistic and numerical irrelevant information for the two constructs. When separated by ability, students with LD showed a different profile as compared to the LA and AA students with respect to the relationships among the problem-solving variables. Mean differences showed that students with LD differed significantly from LA students in that they paraphrased less relevant information and also visually represented less irrelevant numerical information. Paraphrasing accuracy and visual representation accuracy were each shown to account for a statistically significant amount of variance in problem-solving accuracy when entered in a hierarchical model. Finally, the relationship between visual representation of relevant information and problem-solving accuracy was shown to be dependent on ability after controlling for the problem-solving variables and ability. Implications for classroom instruction for students with and without LD are discussed.
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Szabo, Attila. "Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils." Doctoral thesis, Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-146542.
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This thesis reports on two different investigations. The first is a systematic review of pedagogical and organizational practices associated with gifted pupils’ education in mathematics, and on the empirical basis for those practices. The review shows that certain practices – for example, enrichment programs and differentiated instructions in heterogeneous classrooms or acceleration programs and ability groupings outside those classrooms – may be beneficial for the development of gifted pupils. Also, motivational characteristics of and gender differences between mathematically gifted pupils are discussed. Around 60% of analysed papers report on empirical studies, while remaining articles are based on literature reviews, theoretical discourses and the authors’ personal experiences – acceleration programs and ability groupings are supported by more empirical data than practices aimed for the heterogeneous classroom. Further, the analyses indicate that successful acceleration programs and ability groupings should fulfil some important criteria; pupils’ participation should be voluntary, the teaching should be adapted to the capacity of participants, introduced tasks should be challenging, by offering more depth and less breadth within a certain topic, and teachers engaged in these practices should be prepared for the characteristics of gifted pupils. The second investigation reports on the interaction of mathematical abilities and the role of mathematical memory in the context of non-routine problems. In this respect, six Swedish high-achieving students from upper secondary school were observed individually on two occasions approximately one year apart. For these studies, an analytical framework, based on the mathematical ability defined by Krutetskii (1976), was developed. Concerning the interaction of mathematical abilities, it was found that every problem-solving activity started with an orientation phase, which was followed by a phase of processing mathematical information and every activity ended with a checking phase, when the correctness of obtained results was controlled. Further, mathematical memory was observed in close interaction with the ability to obtain and formalize mathematical information, for relatively small amounts of the total time dedicated to problem solving. Participants selected problem-solving methods at the orientation phase and found it difficult to abandon or modify those methods. In addition, when solving problems one year apart, even when not recalling the previously solved problem, participants approached both problems with methods that were identical at the individual level. The analyses show that participants who applied algebraic methods were more successful than participants who applied particular methods. Thus, by demonstrating that the success of participants’ problem-solving activities is dependent on applied methods, it is suggested that mathematical memory, despite its relatively modest presence, has a pivotal role in participants’ problem-solving activities. Finally, it is indicated that participants who applied particular methods were not able to generalize mathematical relations and operations – a mathematical ability considered an important prerequisite for the development of mathematical memory – at appropriate levels.At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: In press.
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Pampaka, Maria. "Mathematical problem solving : teachers' attitudes, knowledge, beliefs and practices." Thesis, University of Manchester, 2005. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:122451.
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Tso, Wai-chuen, and 蔡偉全. "Enhancing students' mathematical problem solving abilities through metacognitive questions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35384347.
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Conley, Michele E. "UTILIZING TECHNOLOGY TO ENHANCE READING COMPREHENSION WITHIN MATHEMATICAL WORD PROBLEMS." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/121.
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Many students who are proficient with basic math facts struggle for understanding when it comes to word problems. Teachers time and time again teach and re-teach problem solving strategies in hope that their students will one day acquire all the skills necessary to become proficient in this area. Unfortunately understanding problem solving skills is not the only answer to solving word problems. There has been a significant amount of evidence linking reading comprehension to mathematical reasoning. The development of a website to assist teachers and students who are having difficulties with mathematical word problems is extremely beneficial. The website is designed with links, power points, and examples that enhance reading comprehension within mathematical word problems. Through this project, it has been determined that students who are exposed to an additional mathematical program related to breaking apart word problems show evidence of a greater understanding and mastery of solving mathematical word problems.
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Bahar, Abdulkadir. "The Influence of Cognitive Abilities on Mathematical Problem Solving Performance." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293594.
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Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of students. The author investigated this relationship by separating performance in open-ended and closed situations. The second purpose of this study was to explore how these relationships were different or similar in boys and girls. No significant difference was found between girls and boys in cognitive abilities including general intelligence, general creativity, working memory, mathematical knowledge, reading ability, mathematical problem solving performance, verbal ability, quantitative ability, and spatial ability. After controlling for the influence of gender, the cognitive abilities explained 51.3% (ITBS) and 53.3% (CTBS) of the variance in MPSP in closed problems as a whole. Mathematical knowledge and general intelligence were found to be the only variables that contributed significant variance to MPSP in closed problems. Similarly, after controlling for the influence of gender, the cognitive abilities explained 51.3% (ITBS) and 46.3% (CTBS) of the variance in mathematical problem solving performance in open-ended problems. General creativity and verbal ability were found to be the only variables that contributed significant variance to MPSP in open problems. The author concluded that closed and open-ended problems require different cognitive abilities for reaching correct solutions. In addition, when combining all of these findings the author proposed that the relationship between cognitive abilities and problem solving performance may vary depending on the structure (type) and content of a problem. The author suggested that the content of problems that are used in instruments should be analyzed carefully before using them as a measure of problem solving performance.
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Deragisch, Patricia Amelia. "Electronic portfolio for mathematical problem solving in the elementary school." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1299.
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Electronic portfolio for mathematical problem solving in the elementary school is an authentic assessment tool for teachers and students to utilize in evaluating mathematical skills. It is a computer-based interactive software program to allow teachers to easily access student work in the problem solving area for assessment purposes, and to store multimedia work samples over time.
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Assaf, Fatima. "Multilingual Children's Mathematical Reasoning." Thèse, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/30496.
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This research adopts a sociocultural framework (Vygotsky, 1978) to investigate how multilingual children express their mathematical reasoning during collaborative problem solving. The topic is important because North America is becoming increasingly multicultural, and according to mathematics teachers this has complicated the challenges of teaching and learning mathematics. Many educators assume that children should be competent in the language of instruction before they engage with mathematical content (Civil, 2008; Gorgorió & Planas, 2001). A review of recent research in this area challenges the idea that multilingual students need to have mastered the official language of instruction prior to learning mathematics (Barwell, 2005; Civil, 2008; Moschkovich, 2007). These researchers demonstrate that the knowledge of the language of instruction is only one aspect of becoming competent in mathematics. My research was designed to build on the findings of the current research on multilingual children’s reasoning in order to more fully understand how multilingual children express their mathematical understanding and reasoning. For this study, two multilingual families, each with 3 children between the ages of 8 and 12, participated in a mathematical problem-solving activity. Findings show the children’s mathematical reasoning was evidence-based drawing on mathematical knowledge and world knowledge.
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Bernadette, Elizabeth. "Third grade students' challenges and strategies to solving mathematical word problems." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
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Ely, David P. "Preparing Teachers to Integrate Computer Programming Into Mathematical Problem Solving." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1478266333504353.
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Dahl, Thomas. "Problem-solving can reveal mathematical abilities : How to detect students' abilities in mathematical activities." Licentiate thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-21205.
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Dahl, Thomas (2012). Problemlösning kan avslöja matematiska förmågor. Att upptäcka matematiska förmågor i en matematisk aktivitet (Problem-solving can reveal mathematical abilities: How to detect students‟ abilities in mathematical activities). Linnéuniversitetet 2012; ISBN:978-91-86983-28-4. Written in Swedish.The thesis deals with the problem of identifying and classifying components of mathematical ability in students‟ problem-solving activities. The main theoretical framework is Krutetskii‟s theory of mathematical abilities in schoolchildren. After a short historical background focusing on the question of differentiation or integration among students on the basis of their various aptitudes for studies, the theory of mathematical ability and especially the Krutetskiian theory are described. According to Krutetskii mathematical ability should be looked upon as a structure of seven or eight different components called abilities which may appear and be subject to analysis during a mathematical activity.Krutetskii used school pupils and experimental problems to establish the relevance of his structure of abilities. However, in this work the theme is approached from the opposite perspective: If a problem and an experimental person are given, which mathematical abilities will appear and in what ways do they appear in the mathematical activity? The empirical study uses three so called “rich mathematics problems” and 98 students of which 37 study at the lower secondary school, 39 at the upper secondary school and 22 at the teacher education programme. The output data is either the written outcomes of the students‟ individual work on a problem or the recordings from small groups of students solving a problem in cooperation with their peers.In order to identify and classify abilities, the separate components of mathematical ability must be interpreted and adapted to the specific problem on which the students are working. I call this process of conformation of the abilities operationalization and the question in focus is if such an operationalization can be done successfully. The results indicate that it could be done and several examples are given which show how one or several mathematical abilities may come out more or less strongly in the mathematical activity of problem solving. The results also indicate that even low or average achieving students may show significant creative abilities. Another observation from the empirical study is that creative abilities do not seem to be more abundant among upper than lower secondary students. These two observations point out possible pathways to proceed further in the study of mathematical abilities.
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Miller, Catherine Marie 1959. "Teachers as problem solvers/problem solvers as teachers: Teachers' practice and teaching of mathematical problem solving." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/282150.
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This study investigated the relationship among three high school mathematics teachers definitions and beliefs about mathematical problem solving, their problem solving practices and how they teach mathematical problem solving. Each teacher was interviewed three times and observed once during a problem solving lesson. Data comprised of transcriptions of audio tapes, field notes, and completed problem solving checklists were used to prepare the case studies. While the definitions, practices and teaching of the teachers varied, the findings were consistent within each case. The results suggest that how teachers are taught and what they learn as students are related to how they teach mathematical problem solving.
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Carter, Merilyn Gladys. "Year 7 students’ approaches to understanding and solving NAPLAN numeracy problems." Thesis, Queensland University of Technology, 2011. https://eprints.qut.edu.au/46648/1/Merilyn_Carter_Thesis.pdf.
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This study investigated how the interpretation of mathematical problems by Year 7 students impacted on their ability to demonstrate what they can do in NAPLAN numeracy testing. In the study, mathematics is viewed as a culturally and socially determined system of signs and signifiers that establish the meaning, origins and importance of mathematics. The study hypothesises that students are unable to succeed in NAPLAN numeracy tests because they cannot interpret the questions, even though they may be able to perform the necessary calculations. To investigate this, the study applied contemporary theories of literacy to the context of mathematical problem solving. A case study design with multiple methods was used. The study used a correlation design to explore the connections between NAPLAN literacy and numeracy outcomes of 198 Year 7 students in a Queensland school. Additionally, qualitative methods provided a rich description of the effect of the various forms of NAPLAN numeracy questions on the success of ten Year 7 students in the same school. The study argues that there is a quantitative link between reading and numeracy. It illustrates that interpretation (literacy) errors are the most common error type in the selected NAPLAN questions, made by students of all abilities. In contrast, conceptual (mathematical) errors are less frequent amongst more capable students. This has important implications in preparing students for NAPLAN numeracy tests. The study concluded by recommending that increased focus on the literacies of mathematics would be effective in improving NAPLAN results.
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Cox, Raymond Taylor. "Mathematical Modeling of Minecraft – Using Mathematics to Model the Gameplay of Video Games." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1431009469.
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Gaghlasian, Dikran. "Några elevers tankar kring ett klassiskt matematiskt problem. : Om problemlösningsförmåga och argumentationsförmåga – två matematiska kompetenser." Thesis, Växjö University, School of Education, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-922.
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In this thesis we study four groups of students in grade 8, 9 and 10 when they try to solve a classical mathematical problem: Which rectangle with given circumference has the largest area? The aim of the study was too see how the students did to solve a mathematichal problem?
The survey shows that students have rather poor strategies to solve mathematical problems. The most common mistake is that students don’t put much energy to understand the problem before trying to solve it. They have no strategies. This was clearly obvious when you look at Balacheff’s theory in an article from 1988. His first, and lowest, level is called naive empiricism. Typical for that level was that the student’s efforts to solve the problem just consisted of social interaction without any direction and structure. One reason can be that the students don’t recognize mathematical laws and general concepts well enough. Another problem is that they don’t check their results. Why they don’t do this is hard to say. Earlier results indicating that one reason can be that the students don’t take tasks in school as an intellectual challenge. The just consider it like something the must do.
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Marcou, Andri. "Teaching mathematical word-problem solving : can primary school students become self-regulated problem solvers?" Thesis, London South Bank University, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.478925.
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Yimer, Asmamaw Ellerton Nerida F. "Metacognitive and cognitive functioning of college students during mathematical problem solving." Normal, Ill. : Illinois State University, 2004. http://wwwlib.umi.com/cr/ilstu/fullcit?p3128290.
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Thesis (Ph. D.)--Illinois State University, 2004.Title from title page screen, viewed Dec. 9, 2004. Dissertation Committee: Nerida F. Ellerton (chair), Sherry L. Meier, Norma C. Presmeg, Beverly S. Rich. Includes bibliographical references (leaves 179-191) and abstract. Also available in print.
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Zheng, Xinhua. "Working memory components as predictors of children's mathematical word problem solving processes." Diss., UC access only, 2009. http://proquest.umi.com/pqdweb?did=1871874331&sid=1&Fmt=7&clientId=48051&RQT=309&VName=PQD.
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Thesis (Ph. D.)--University of California, Riverside, 2009.Includes abstract. Includes bibliographical references (leaves 83-98). Issued in print and online. Available via ProQuest Digital Dissertations.
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Zhang, Pingping. "Unpacking Mathematical Problem Solving through a Concept-Cognition-Metacognition Theoretical Lens." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1404764950.
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Heipcke, Susanne. "Combined modelling and problem solving in mathematical programming and constraint programming." Thesis, University of Buckingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297665.
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Armah, Prince Hamidu. "Teaching mathematical problem solving in Ghana : teacher beliefs, intentions and behaviour." Thesis, University of Aberdeen, 2015. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=228052.
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Recent curriculum reform agendas appear to exert pressure on teachers to incorporate Mathematical Problem Solving (MPS) meaningfully into their lessons, with the view to engaging pupils with real life problems, guessing, discovering, and making sense of mathematics. However, a comprehensive review of both government and academic literature indicate that understanding teachers' reform implementation decisions is largely unexplored, particularly within the Ghanaian context. The purpose of this mixed-methods sequential explanatory study was to identify factors contributing to teacher intentions to teach MPS by obtaining quantitative results from a survey of 375 primary teachers and then following up with six purposefully selected teachers to explore those results in more depth through interviews. Based on the Theory of Planned Behaviour (TPB), the quantitative phase of the study explored how certain different but interrelated belief variables such as attitudes towards the behaviour (AB), perceived norms (PN) and perceived behavioural control (PBC) lead to an explanation of teacher intentions to teach MPS, and an understanding of the contributions of relevant socio-demographic factors in defining these intentions in this context. In the follow up, qualitative phase, semi-structured interviews with six teachers were conducted to explore in depth the results from the statistical analyses. Results indicated that several beliefs about teaching MPS significantly contributed to AB, PN and PBC. Two factors, AB and PBC were found to have significant influences and accounted for 80% of the variance in the teachers' intent to teach MPS. Differences appeared to exist between private and public school teachers' for both intent and the three constructs (AB, PN, and PBC), whilst familiarity with the curriculum had an effect on teachers intentions only. In the qualitative phase, the study addressed some factors found to potentially influence teachers' intentions including MPS conceptions, past experience in mathematics, availability of resources, adequate classroom spaces and professional development opportunities. The quantitative and qualitative findings from the two phases of the study are discussed with reference to prior research. The results provide an understanding of the relevant social-cognitive processes which may influence a teacher's reform decisions, and in particular suggest strong implications for developing the capacity of schools to support teachers' intentions to implement curriculum reform policies.
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Craig, Tracy S. "Promoting understanding in mathematical problem-solving through writing : a Piagetian analysis." Doctoral thesis, University of Cape Town, 2007. http://hdl.handle.net/11427/4875.
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McCoy, Leah Paulette. "The effect of computer programming experience on mathematical problem solving ability." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/64669.
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Five component problem-solving skills (general strategy, planning, logical thinking, algebraic variables, and debugging) were identified as common elements of both computer programming and mathematical problem-solving. Based on the similarities of these general skills in specific contexts, a theory was generated that the skills would transfer and that experience in computer programming would cause an improvement in mathematical problem-solving achievement.
A path model was constructed to illustrate this hypothesized causal relationship between computer programming and mathematical problem-solving achievement. In order to control for other relevant variables, the model also included mathematics experience, access to a home computer, ability, socioeconomic status, and gender. The model was tested with a sample of 800 high school students in seven southwest Virginia high schools.
Results indicated that ability had the largest causal effect on mathematical problem-solving achievement. Three variables had a moderate effect: computer programming experience, mathematics experience, and gender. The other two variables in the model (access to a home computer and socioeconomic status) were only very slightly related to mathematical problem-solving achievement.
The conclusion of the study was that there was evidence to support the theory of transfer of skills from computer programming experience to mathematical problem-solving. Once ability and gender were controlled, computer programming experience and mathematics experience both had causal effects on mathematical problem-solving achievement. This suggests that to maximize mathematical problem-solving scores, a curriculum should include both mathematics and computer programming experiences.Ed. D.
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Rigelman, Nicole R. "Teaching Mathematical Problem Solving in the Context of Oregon's Educational Reform." PDXScholar, 2002. http://pdxscholar.library.pdx.edu/open_access_etds/1760.
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Implementation of Oregon’s Educational Reform Act (HB 3565 and HB 2991) provides the context for this inquiry as its emphasis on problem solving has impacted mathematics teaching and learning throughout the state. Even though all Oregon teachers are responding to the same policy, their goals in teaching problem solving vary. These goals and these practices are influenced by the way teachers view the role of problem solving in the curriculum. Further, their practice is influenced by their knowledge and beliefs about mathematics content, teaching, learning, and the reform policy. The questions addressed in this study are: (1) What do exemplary middle school math teachers do to engage students in mathematical problem solving? and (2) On what bases do these teachers make decisions about what to emphasize when teaching problem solving? how to teach problem solving?, and when to teach problem solving?
This qualitative study provides a fuller description of Standards-based classroom practice than presently represented in the literature by offering both examples of problem solving practice and the related influences on that practice. It considers the influences of policy, curriculum, professional development, administrators, and colleagues on teachers’ developing practice. The study also grounds the implementation of the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 2000) in the work of practicing middle school teachers. Finally, the study shows how, for these teachers, their curriculum has played a significant role in developing their perspectives on learning, teaching, and the nature of math, which has in turn, influenced their knowledge, beliefs, and instructional practice.
This study demonstrates that teachers are able to teach in ways consistent with the NCTM Standards when their knowledge and beliefs about practice align with the recommendations. Further, they teach in this manner when professional development experiences are geared toward understanding and developing Standards-based instructional practice, curriculum is consistent with this vision of practice, and administrators and school cultures are supportive of such practice. When these internal and external conditions exist within and for teachers, their students have the opportunity to learn to become “problem solvers,” not just “problem performers.”
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Carlsen, Martin. "Appropriating mathematical tools through problem solving in collaborative small-group settings /." Kristiansand : University of Agder, Faculty of Engineering and Science, 2008. http://www.uia.no/no/portaler/aktuelt/nyhetsarkivet/disputas_elevsamarbeid_gir_matematikklaering.
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Vincent, Jill. "Mechanical linkages, dynamic geometry software, and argumentation : supporting a classroom culture of mathematical proof /." Connect to thesis, 2002. http://eprints.unimelb.edu.au/archive/00001399.
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Lehmann, Timothy H. "Teaching area measurement and subgoals through problem solving." Thesis, Queensland University of Technology, 2018. https://eprints.qut.edu.au/117668/1/Timothy_Lehmann_Thesis.pdf.
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This thesis examined the teaching and learning of area measurement and the subgoals strategy through problem solving. A pedagogical model was developed to show how students' conceptual understanding of a mathematical concept and their strategic competence can develop simultaneously through problem solving.
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Edwards, Belinda Pickett. "The Interplay among Prospective Secondary Mathematics Teachers' Affect, Metacognition, and Mathematical Cognition in a Problem-Solving Context." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/msit_diss/63.
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The purpose of this grounded theory study was to explore the interplay of prospective secondary mathematics teachers’ affect, metacognition, and mathematical cognition in a problem-solving context. From a social constructivist epistemological paradigm and using a constructivist grounded theory approach, the main research question guiding the study was: What is the characterization of the interplay among prospective teachers’ mathematical beliefs, mathematical behavior, and mathematical knowledge in the context of solving mathematics problems? I conducted four interviews with four prospective secondary mathematics teachers enrolled in an undergraduate mathematics course. Participant artifacts, observations, and researcher reflections were regularly recorded and included as part of the data collection. The theory that emerged from the study is grounded in the participants’ mathematics problem-solving experiences and it depicts the interplay among affect, metacognition, and mathematical cognition as meta-affect, persistence and autonomy, and meta-strategic knowledge. For the participants, “Knowing How and Knowing Why” mathematics procedures work and having the ability to justify their reasoning and problem solutions represented mathematics knowledge and understanding that could empower them to become productive problem-solvers and effective secondary mathematics teachers. The results of the study also indicated that the participants interpreted their experiences with difficult, challenging problem-solving situations as opportunities to learn and understand mathematics deeply. Although they experienced fear, frustration, and disappointment in difficult problem-solving and mathematics-learning situations, they viewed such difficulty with the expectation that feelings of satisfaction, joy, pride, and confidence would occur because of their mathematical understanding. In problem-solving situations, affect, metacognition, and mathematics cognition interacted in a way that resulted in mathematics understanding that was productive and empowering for these prospective teachers. The theory resulting from this study has implications for prospective teachers, teacher education, curriculum development, and mathematics education research.
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Chiu, Mei-Shiu. "Children's emotional responses to mathematical problem-solving : the roles of teaching methods and problem types." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597616.
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The aim of the thesis is to investigate children’s emotional responses to mathematical problem solving, based on the concern that children in Taiwanese mathematical classrooms are experiencing a significant change in teaching methods and problem types from the ‘traditional mathematics’ to ‘constructivist mathematics’. The focused emotional variables include disposition toward teaching, liberal thinking styles, conservative styles, deep approaches, surface approaches, self-efficacy of effort and mistake anxiety. The research participants were 116 Year 5 (aged 9-10) children and their respective four mathematics teachers. Fraction and coordinates topics were chosen as two focused topics, in which a number of typical ill- and well-structured problems were chosen as focused problems from the participants’ textbooks. There are three main research findings. First, teaching methods revealed impacts on children’s emotional response. Second, there were four distinct patterns of children’s emotional and motivational responses to mathematical problem solving, with differential development processes in terms of emotional variables and preferred problem types. Third, the best determinants of children’s attainments in mathematics were self-efficacy, thinking styles and learning approaches, which however varied with genders, teaching methods and problem types. Chapter 1 explains the background and situation of mathematics education in Taiwan and outlines the goals of the thesis. Chapter 2 is concerned with the literature on emotional issues in mathematical learning, teaching styles, problem types, genders and achievement in mathematics, based on which, the research questions are proposed. In Chapter 3, an initial model is posited in order to answer the research questions and develop a research design, involving both quantitative and qualitative research methods. Chapter 4 explores the impact of teaching methods on children’s emotional responses to mathematical problem solving by analysing data of systematic and narrative classroom observations, teacher interviews, child interviews and children’s responses to the questionnaires. Chapter 5 investigates factors and patterns of children’s emotional responses to mathematical problem solving by a factor analysis, cluster analysis, discriminant analysis and analysis of data from child interview with a repertory grid technique. Chapter 6 examines the determinants of mathematics attainments in terms of genders, teaching method and emotional responses to problem solving by ANOVAs and correlation analyses. Chapter 7 focuses on discussion and conclusions.
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Brown, Leonard Dale. "The effects of alternative reading and math strategy treatments on word problem-solving." Oxford, Ohio : Miami University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=miami1272846865.
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Lo, Man-Hon. "Evolution optimization : solving crypto-arithmetic problems and the knapsack problem using adaptive genetic algorithms /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202003%20LO.
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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.Includes bibliographical references (leaves 69-70). Also available in electronic version. Access restricted to campus users.
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Hart, Janelle Marie. "Contextualized Motivation Theory (CMT) : intellectual passion, mathematical need, social responsibility, and personal agency in learning Mathematics /." Diss., CLICK HERE for online access, 2010. http://contentdm.lib.byu.edu/ETD/image/etd3393.pdf.
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Green, Alison Julia Katherine. "Statistical computing : individual differences in the acquisition of a cognitive skill." Thesis, University of Aberdeen, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.277291.
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The rate at which individuals acquire new cognitive skills may vary quite substantially, some acquiring a new skill more rapidly and efficiently than others. It has been shown through the analysis of think aloud protocols that learning performance on a map learning task, for instance, is associated with the use of certain learning procedures. In the domain of mathematical problem solving, it has also been shown that performance is associated with strategic as opposed to tactical decision making. Previous research on learning and problem solving has tended to focus on tactical processes, ignoring the role of strategic processes in learning and problem solving. There is clearly a need to examine the role of strategic processes in learning and to determine whether they might be an important source of individual differences in learning performance. A related question concerns teaching thinking skills. If it is possible to determine those learning procedures that differentiate good from poor learners, is it then possible to teach the effective procedures to a group of novice students in order to enhance the rate of skill acquisition? Results from the experiments reported here show that novices differ, and that learning performance is related to the use of certain learning procedures, as revealed by subjects' think aloud protocols. A follow-up study showed that novices taught to use the procedures differentiating good from poor learners performed at a higher level than two control groups of novices. A coding scheme was developed to explicitly examine learning at macroscopic and microscopic levels, and to contrast tactical with strategic processes. Discriminant function analysis was used to examine differences between good and poor learners. It was shown that good learners more frequently use executive processes in learning episodes. A study of the same subjects learning to use statistical packages on a microcomputer corroborate these findings. Thus, results extend those obtained from the first study. A study of the knowledge structures possessed by novices was complicated by differences in levels of statistical knowledge. Multidimensional scaling techniques revealed differences between novices with three statistical courses behind them, but not among those with only two statistical courses behind them. Among those novices with three statistical courses behind them, faster learners' knowledge structures more closely resembled those of experienced users of statistical packages than did those of slower learners.
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Kanevsky, Inna Glaz. "Role of rules in transfer of mathematical word problems." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3223010.
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Thesis (Ph. D.)--University of California, San Diego, 2006.Title from first page of PDF file (viewed September 21, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 86-90).
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BaldwinDouglas, Crystal Yvette. "Teachers' Perceptions About Instructing Underachieving K-5 Students on Mathematical Word Problem-Solving." ScholarWorks, 2019. https://scholarworks.waldenu.edu/dissertations/6395.
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The state of Maryland has implemented the Common Core State Standards for Mathematics (CCSSM) operations & algebraic thinking and number & operations-fractions with emphasis on students in Grades K-5 acquiring the ability to solve word problems for state and curriculum math assessments. However, since the implementation of CCSSM, 30% of elementary students in a Maryland school district have demonstrated underachievement (basic or below basic level) on problem-solving sections of the state and school standardized tests. This qualitative case study, guided by Polya's model of the four phases of mathematical problem-solving, was conducted to address this problem. The research questions addressed teachers' perceptions of how they teach underachieving students' word problem-solving skills, how prepared they feel, the challenges they experience when teaching word problem-solving skills, and the resources for instructing underachieving students on mathematical word problem-solving. Semi-structured interviews were conducted with 8 certified elementary classroom teachers. Data from the teacher interviews were analyzed using pattern coding and thematic analysis. The findings indicated that teachers are not fully prepared to teach the CCSSM, teachers need assistance in creating standards-based detailed lesson plans, and teachers need help with the development of pedagogical strategies that enhance students' math vocabulary. Findings may lead to positive social change by informing the design of professional development and increasing the number of students who achieve proficiency in mathematical word problem-solving.
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Owens, Kay Dianne, and mikewood@deakin edu au. "Spatial thinking processes employed by primary school students engaged in mathematical problem solving." Deakin University, 1993. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20050826.100440.
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This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving.
The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasionsbefore, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a control group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups.
The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest.
The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.
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Raggi, Daniel. "Searching the space of representations : reasoning through transformations for mathematical problem solving." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/22936.
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The role of representation in reasoning has been long and widely regarded as crucial. It has remained one of the fundamental considerations in the design of information-processing systems and, in particular, for computer systems that reason. However, the process of change and choice of representation has struggled to achieve a status as a task for the systems themselves. Instead, it has mostly remained a responsibility for the human designers and programmers. Many mathematical problems have the characteristic of being easy to solve only after a unique choice of representation has been made. In this thesis we examine two classes of problems in discrete mathematics which follow this pattern, in the light of automated and interactive mechanical theorem provers. We present a general notion of structural transformation, which accounts for the changes of representation seen in such problems, and link this notion to the existing Transfer mechanism in the interactive theorem prover Isabelle/HOL. We present our mechanisation in Isabelle/HOL of some specific transformations identified as key in the solutions of the aforementioned mathematical problems. Furthermore, we present some tools that we developed to extend the functionalities of the Transfer mechanism, designed with the specific purpose of searching efficiently the space of representations using our set of transformations. We describe some experiments that we carried out using these tools, and analyse these results in terms of how close the tools lead us to a solution, and how desirable these solutions are. The thorough qualitative analysis we present in this thesis reveals some promise as well as some challenges for the far-reaching problem of representation in reasoning, and the automation of the processes of change and choice of representation.
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Wares, Arsalan Jones Graham A. Cottrill James F. "Middle school students' construction of mathematical models." Normal, Ill. Illinois State University, 2001. http://wwwlib.umi.com/cr/ilstu/fullcit?p3064487.
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Thesis (Ph. D.)--Illinois State University, 2001.Title from title page screen, viewed March 30, 2006. Dissertation Committee: Graham A. Jones, James Cottrill (co-chairs), Linnea Sennott. Includes bibliographical references (leaves 107-111) and abstract. Also available in print.