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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
2
Ragonis, Noa. "Problem-solving strategies must be taught implicitly". Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6464/.
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Problem solving is one of the central activities performed by computer scientists as well as by computer science learners. Whereas the teaching of algorithms and programming languages is usually well structured within a curriculum, the development of learners’ problem-solving skills is largely implicit and less structured. Students at all levels often face difficulties in problem analysis and solution construction. The basic assumption of the workshop is that without some formal instruction on effective strategies, even the most inventive learner may resort to unproductive trial-and-error problemsolving processes. Hence, it is important to teach problem-solving strategies and to guide teachers on how to teach their pupils this cognitive tool. Computer science educators should be aware of the difficulties and acquire appropriate pedagogical tools to help their learners gain and experience problem-solving skills.
3
Lloyd, Lorraine Gladys. "The problem-solving strategies of grade two children : subtraction and division". Thesis, University of British Columbia, 1988. http://hdl.handle.net/2429/28106.
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This study was aimed at discovering the differences in how children responded to word problems involving an operation in which they had received formal instruction (subtraction) and word problems involving an operation in which they have not received formal instruction. Nineteen children were individually interviewed and were asked to attempt to solve 6 subtraction and 6 division word problems. Their solution strategies were recorded, and analysed with respect to whether or not they were appropriate, as to whether or not they modeled the structure of the problem, and as to how consistent the strategies were, within problem types.
It was found that children tended to model division problems more often than subtraction problems, and also that the same types of errors were made on problems of both operations. It was also found that children were more likely to keep the strategies for the different interpretations separate for the operation in which they had not been instructed (division) than for the operation in which they had been instructed (subtraction). For division problems, the strategies used to solve one type of problem were seldom, if ever used to solve the other type of problem. For subtraction problems, children had more of a tendency to use the strategies for the various interpretations interchangeably.
In addition, some differences in the way children deal with problems involving the solution of a basic fact, and those involving the subtraction of 2-digit numbers, were found. The 2-digit open addition problems were solved using modeling strategies about half as often as any other problem type. The same types of errors were made for both the basic fact and the 2-digit problems, but there were more counting errors and more inappropriate strategy errors for the 2-digit problems, and more incorrect operations for the basic fact problems.
Finally, some differences were noted in the problem-solving behaviour of children who performed well on the basic fact tests and those who did not. The children in the low group made more counting errors, used more modeling strategies, and used fewer incorrect operations than children in the high group.
These implications for instruction were stated: de-emphasize drill of the basic facts in the primary grades, delay the formal instruction of the operations until children have had a lot of exposure to word problem situations involving these concepts, use the problem situations to introduce the operations instead of the other way around, and leave comparison subtraction word problems until after the children are quite familiar with take away and open addition problems.Education, Faculty of
Curriculum and Pedagogy (EDCP), Department of
Graduate
4
Luk, Hok-wing. "Strategies in the teaching of problem solving skills in mathematics : a comparison between the experienced and the less-experienced teachers /". Hong Kong : University of Hong Kong, 1989. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18531520.
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Kavai, Portia. "The Use of animal organ dissection in problem-solving as a teaching strategy". Thesis, University of Pretoria, 2013. http://hdl.handle.net/2263/40228.
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The major purpose of this study was to investigate the effects of using animal organ
dissection in general, and its use specifically in problem-solving as a teaching strategy in
Grade 11 Life Sciences education. A multiple methods research design was used for this
study.
The data collection methods for the quantitative approach were the pre-test, post-test and a
questionnaire. The pre-test and post-test had predominantly problem-solving questions. The
questionnaire and the tests were administered to 224 learners from four Pretoria East
secondary schools from different environments. The data collection methods for the
qualitative approach were the interviews with the Grade 11 Life Sciences teachers of the
selected schools, lesson observations and relevant document analysis. The interviews were
conducted with six Grade 11 Life Sciences teachers teaching at the four selected schools.
Findings from both the quantitative and the qualitative approaches were integrated to give an
in-depth understanding of the study. The findings show that there were significant differences
between the means of the pre-test and the post-test for the total for the whole group of 224
learners. The variables in which the tests were categorised were the rote learning,
problem-solving and three learning outcomes of the National Curriculum Statement (NCS).
The way in which the learners answered the questions in terms of terminology they used, the
confidence they displayed, the level of answering and the explanations they gave when they
wrote the post-test were significantly different from when they wrote the pre-test. The
significant differences between the means of the pre-test and the post-test may possibly have
been due to the intervention. This showed the effectiveness of the intervention which was
animal organ dissection in problem-solving. The study also showed that most teachers are not
well-acquainted with problem-solving strategies which made it challenging for them to use
animal organ dissections to develop problem-solving skills in learners. The attitudes of the
teachers and learners towards animal organ dissection and its use in problem-solving as a
teaching strategy were predominantly positive with less than a quarter of the whole group
being negative due to a variety of reasons which include: moral values, religion, culture,
blood phobia, squeamishness and being vegetarian. The majority of learners acknowledged
the importance of animal organ dissections in developing skills like investigative, dissecting and problem-solving skills. This acknowledgement resulted in them being positive towards
the use of animal organ dissections in problem-solving.
One can conclude that animal organ dissections can be used in problem-solving as a teaching
strategy in Life Sciences education. The level of learner engagement with animal organ
dissections can determine the level of development of problem-solving skills as was
evidenced by the differences between the mean scores of the four schools. The study
recommended that the teachers should be encouraged to use animal organ dissections more
frequently where it is applicable to develop problem-solving skills in learners and not merely
let the learners cut, draw and label the organ. Teachers should also focus on problem-solving
in general and develop this as a prime strategy. All activities should be prepared by the
teacher and implemented in class to encourage and develop problem-solving skills.Thesis (PhD)--University of Pretoria, 2013.
gm2014
Science, Mathematics and Technology Education
restricted
6
Lam, Mau-kwan y 林謀坤. "Secondary three students' strategies in solving algebraic equations". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B3196025X.
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Luk, Hok-wing y 陸鶴榮. "Strategies in the teaching of problem solving skills in mathematics: a comparison between the experienced andthe less-experienced teachers". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B3195585X.
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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.
9
Bernstone, Helen. "The relationship between the beliefs of early childhood teachers and their use of scaffold, instruction and negotiation as teaching strategies". Thesis, Brunel University, 2007. http://bura.brunel.ac.uk/handle/2438/5179.
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This study investigates the relationship between the beliefs of early childhood education teachers and their use of the teaching strategies instruction and negotiation in relation to the scaffold process. Consideration of thinking skills and the ability to problem solve through the vehicle of play provided the background to the research focus. The research was undertaken in two differently structured early childhood education centres in New Zealand with a case study design framing the gathering of data through observations and interviews. It is a small qualitative study driven by socio-cultural theory and therefore considered from a social constructivist position. The main findings from observations and interviews revealed that not all teachers had congruency between their beliefs and practice, that instruction could be the only mediation within a scaffolding process and by considering the power relations in the learning and teaching situation, a model of how different teaching strategies could be related to different states of thinking. A key finding was that of a definition of negotiation as a teaching strategy.
10
Beyleveld, Mia. "The dynamics of active learning as a strategy in a private Higher Education Institution". Thesis, University of Pretoria, 2017. http://hdl.handle.net/2263/65466.
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In South Africa, the Department of Education (DOE) via its South African Qualifications Authority (SAQA) mandates lecturers particularly at higher education level to deliver students that should be able to think critically and solve problems by the end of their undergraduate journey at any Higher Education Institution (HEI), whether public or private. HEIs have each taken their own approach on how to develop these competencies in their undergraduate students. This qualitative inductive case study focuses on understanding how eleven lecturers teaching at a private HEI in Midrand South Africa facilitate Active Learning in their classes, how they measure the success of Active Learning strategies and the support they have available to them by using semi-structured interviews and class observation data. Some of the findings highlight that these lecturers know exactly what Active Learning is even though most have never been officially trained. Six groups of different Active Learning strategies were identified including different questioning techniques, engagement via reading, engagement via writing, hands-on activities, use of technology and interaction with peers. Even though lecturers believed in Active Learning, evidence substantiating the effectiveness of their teaching methodology was mostly subjective. It was also found that lecturers had more support requirements than current support available and that the majority of current support was in the form of the immediate lecturer community.Thesis (PhD)--University of Pretoria, 2017.
Science, Mathematics and Technology Education
PhD
Unrestricted
11
Dirks, Denise. "Mediation and a Problem Solving Approach to Junior Primary Mathematics". University of the Western Cape, 1996. http://hdl.handle.net/11394/8379.
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Magister Educationis - MEdThis study argues that not all children in the Junior Primary phase benefit from the Problem Centred Approach in mathematics that was adapted by the Research, Unit for Mathematics at the University of Stellenbosch (RUMEUS). \One of the reasons could be that not all pupils can construct their own knowledge and methods. There are the highly capable pupils who cope well with this approach. These pupils are able to solve mathematical problems with little or no teacher interaction. Then there are the average and weaker pupils who cannot solve a mathematical problem on their own. These pupils need strategies and skills to solve problems and they need the teacher to mediate these strategies and skills to them, which will help these pupils to become autonomous problem solvers. ,Working in groups can, to some extent, supplement mediation or teacher interaction. Peer group teaching can be effective, whereby pupils are placed in groups so that the more capable pupils can teach concepts or make concepts clearer to the average or weaker pupils). There is, however, the possibility that when pupils of mixed abilities are placed in groups of four there might be one pupil who might refuse to work with the group. This pupil will work on her own and will not share ideas with the other members of the group. If this happens, mediation is necessary for those pupils who cannot solve a mathematical problem on their own. The purpose of this study is to investigate how exposure to mediation can improve pupils' problem solving abilities. As directions for my research I've chosen the first six criteria of Feuerstein's Mediated Learning Experiences (MLE). The first three parameters: intentionality and reciprocity, mediation of transcendence and mediation of meaning _are conditions for an interaction to qualify as MLE. Mediation of competence and regulation of behaviour are functions of specific experiences that combine with the first three to make an adult-child interaction one of mediated learning. Mediation of sharing behaviour . can be added. Here the child and the mediator are engaged in a shared quest for structural change in the child. In addition to this, the five mechanisms of mediational teaching, i.e. process questioning; challenging or asking reasons; bridging; teaching about rules; and emphasising order, predictability, system, sequence and strategy are also used in the implementation of mediation as described by Haywood. Two methods of investigation were chosen. The pupils' problem solving abilities were studied by means of eight word sums, of which the first four word sums were done in the pre-test and the other four word sums in the post-test. After the pre-test and before the post-test there was a period of mediational teaching for the experimental group. During this period and during the post-test the control group was denied mediation. After this research, mediation was also available for the control group. Two pupils from the experimental group were then chosen for further in-depth, think-aloud, person-to-person interviews. The aim of the interviews was to determine why these pupils could not solve the problem in the pre-test, but could successfully solve the post-test question. The results of the word sums in the pre-test and the post-test were compared. The role of strategies and thinking skills is concentrated on in the results. Mediation was not equally successful in all of the four different types of problem sums. Questions one and five contained two or more numbers and here pupils tended to either plus or minus these numbers. Questions two and six also contained numbers, but this is a problem situated in a real life situation. Questions three and seven contained no numbers and questions four and eight compelled pupils to first work out a plan. Mediation was most successful in problem sums situated in a real life situation, followed by problem sums which compelled pupils to first work out a plan, and then by problem sums where there were no numbers. Mediation was least; successful in problem sums that contained two or more numbers. Analysis of these results shows that with mediation there is an improvement in the pupils' problem solving abilities; Mediation can be viewed as S-H-O-H-R, in which the human mediator (H) is interposed between the stimulus (S) and the organism (0), and between the organism and the response (R). We can argue that the Problem Centred Approach without mediation can produce individuals who are little, if at all, affected by their encounter and interaction with new situations. Due to the lack of support in the Problem Centred Approach to Mathematics, it is the aim of this mini-thesis to propose mediation as an essential component in the Problem Centred Approach to Mathematics in the Junior Primary phase.
12
Cheng, Wing-kin y 鄭永健. "A comparative study of form 4 students' problem solving strategies with or without using geometer's sketchpad". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B31963365.
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Van, der Sandt Suriza. "An analysis of geometry learning in a problem solving context from a social cognitive perspective / Suriza van der Sandt". Thesis, Potchefstroom University for Christian Higher Education, 2000. http://hdl.handle.net/10394/48.
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Traditionally, geometry at school starts on a formal level, largely ignoring prerequisite
skills needed for formal spatial reasoning. Ignoring that geometry has a sequential and
hierarchical nature causes ineffective teaching and learning.
The Van Hiele theory postulates learner progression through levels of geometry
thinking, from a Gestalt-like visual level through increasing sophisticated levels of
description, analysis, abstraction, and proof. Progression from one level to the next
does not depend on biolog~caml aturation or development only, but also on appropriate
teachingllearning experiences. A higher thinking level is achieved through the
application of a series of learning phases, consisting of suitable learning activities. The
teacher plays an important facilitating role during this process.
In accordance with the social cognitive learning perspective on self-regulated learning,
geometry learners must direct their thoughts and actions while completing activities in
order for effective learning to take place. Learners can be described as being selfregulated
to the degree that they are metacognitively, motivationally, and behaviorally
active in their own learning. The social cognitive theory assumes that students enter
learning activities to acquire knowledge, learning how to solve' problems and
completing learning activities. Self-regulated learners are aware of strategic relations
between self-regulatory processes and learning outcomes and feel self-efficacious
about using strategies. Self-regulation is similar to metacognitive awareness, which
includes task and personal knowledge. Self-regulated learning requires that learners
understand task demands, their personal qualities, and strategies for completing a task. A Van Hiele-based geometry learning and teaching program was designed (with a
problem solving context in mind) and implemented in four Grade 7 classes (133
learners) at two schools. The study investigated factors and conditions influencing the
effective learning and teaching of spatial concepts, processes and skills in different
contexts.
Results suggest that the implementation of a Van Hiele based geometry learning and
teaching program in a problem solving context had a positive effect on the learners'
concentration, when working on academic tasks, and level of geometric thought. The
higher levels of geometric thought included higher categories of thought within these
levels. Learners who completed the program reasoned on a higher level, ,gave more
complete answers, demonstrated less confusion, and generally exhibited higher order
thinking skills than their counterparts who did not take part in the program. The only
prerequisite' is that the teacher should consistently teach from a learner-centered
approach as the program will deliver little or no advantages if the program is presented
in a teacher-centered content-based context.Thesis (M.Ed.)--Potchefstroom University for Christian Higher Education, 2000.
14
Maxfield, Marian Belle. "The Effects of Small Group Cooperation Methods and Question Strategies on Problem Solving Skills, Achievement, and Attitude during Problem-Based Learning". Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1301113251.
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Gosnell, Susan. "Teaching and Assessing Critical Thinking in Radiologic Technology Students". Doctoral diss., University of Central Florida, 2010. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3594.
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The purpose of this study was primarily to explore the conceptualization of critical thinking development in radiologic science students by radiography program directors. Seven research questions framed three overriding themes including 1) perceived definition of and skills associated with critical thinking; 2) effectiveness and utilization of teaching strategies for the development of critical thinking; and 3) appropriateness and utilization of specific assessment measures for documenting critical thinking development. The population for this study included program directors for all JRCERT accredited radiography programs in the United States. Questionnaires were distributed via Survey Monkey©, a commercial on-line survey tool to 620 programs. A forty-seven percent (n = 295) response rate was achieved and included good representation from each of the three recognized program levels (AS, BS and certificate). Statistical analyses performed on the collected data included descriptive analyses (median, mean and standard deviation) to ascertain overall perceptions of the definition of critical thinking; levels of agreement regarding the effectiveness of listed teaching strategies and assessment measures; and the degree of utilization of the same teaching strategies and assessment measures. Chi squared analyses were conducted to identify differences within each of these themes between various program levels and/or between program directors with various levels of educational preparation as defined by the highest degree earned. Results showed that program directors had a broad and somewhat ambiguous perception of the definition of critical thinking, which included many related cognitive processes that were not always classified as attributes of critical thinking according to the literature, but were consistent with definitions and attributes identified as critical thinking by other allied health professions. These common attributes included creative thinking, decision making, problem solving and clinical reasoning as well as other high-order thinking activities such as reflection, judging and reasoning deductively and inductively. Statistically significant differences were identified for some items based on program level and for one item based on program director highest degree. There was general agreement regarding the appropriateness of specific teaching strategies also supported by the literature with the exception of on-line discussions and portfolios. The most highly used teaching strategies reported were not completely congruent with the literature and included traditional lectures with in-class discussions and high-order multiple choice test items. Significant differences between program levels were identified for only two items. The most highly used assessment measures included clinical competency results, employer surveys, image critique performance, specific course assignments, student surveys and ARRT exam results. Only one variable showed significant differences between programs at various academic levels.Ed.D.
Department of Educational and Human Sciences
Education
Education EdD
16
Raoano, Malesela Joel. "Improving learners Mathematics problem solving skills and strategies in the intermediate phase : a case study of primary school in Lebopo Circuit". Thesis, University of Limpopo, 2016. http://hdl.handle.net/10386/1761.
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Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2016.The purpose of this study was to examine learners’ mathematical word problem solving skills and strategies in Intermediate Phase. The study was prompted by Grade 6 learners’ poor performance in the cognitive area, non-routine mathematical word problems, as revealed in Annual National Assessment reports of 2011, 2012, 2013 and 2014. The study followed action research collaborative method involving 26 Grade 6 learners and their mathematics educator. The school is a rural primary school categorised under quintile two. Problem solving theory by Polya (1957) guided the study in answering three research questions: What are the challenges faced by Grade 6 learners in solving word problems? What are Grade 6 learners’ strategies in solving word problems? How can learners’ problem solving skills and strategies focusing on word problems be improved? Data were collected in a routine structured process: pre-intervention phase, intervention phase and post-intervention phase. Analysis was made through the development of a system of categorisation of learners’ responses. The four principles of problem solving by Polya (1957) namely, the way learners understand the problem, how they devise the plan, how they carry out the plan and the manner in which they look back guided the analysis. The findings of the study revealed that the strategies introduced assisted learners in making sense of the word problems and finally proceeding towards an adequate solution. It was also found out that the learners lacked the ability to read with understanding; the problem being their lack of competence in the language of learning and teaching. The skills which learners also lacked when solving word problems were identified as arithmetic skills and reflective skills.
17
Karlsson, Hanna y Ellen Bååth. "Undervisningsmetoder i problemlösning : Hur olika undervisningsmetoder i problemlösning påverkar elevers matematiska kunskaper". Thesis, Linköpings universitet, Pedagogik och didaktik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-156141.
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Denna studie behandlar problemlösning med fokus på lärarens val av undervisningsmetod i syfte att utveckla elevers matematiska kunskaper. Vi har uppmärksammat brister i nyttjandet av strategier i problemlösning hos elever i årskurs F-3. Studiens syfte är därför att bidra med vad tidigare forskning om problemlösningsundervisning har resulterat i och jämföra dessa resultat med varandra. För att undersöka detta har tidigare forskning granskats genom en systematisk litteraturstudie. De databaser som använts för att finna tidigare forskningsstudier är ERIC, UniSearch samt SwePub. Resultatet av studien visar att en väl genomtänkt undervisningsmetod i problemlösning är av stor vikt för elevers kunskaper i matematik. Genom resultatet framkommer även att en god problemlösningsförmåga underlättar för elevers fortsatta matematikutveckling.
18
Graaff, Magda. "Probleemoplossing en die onderrig en leer van wiskunde in graad 4 / deur Magda Graaff". Thesis, North-West University, 2005. http://hdl.handle.net/10394/785.
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The objective with this research was to establish the correlation between
problem solving and the teaching and learning of mathematics in grade 4.
The results of the Third International Mathematics and Science Study (TIMSS)
showed that South Africa is behind other countries in terms of the teaching
and learning of mathematics, especially with regard to problem solving.
Because problem solving is an integral part of the teaching and learning of
mathematics, a literature study was conducted (1) to investigate the learning
of school mathematics and (2) to describe the manner in which problem
solving can take place in the classroom.
The learning of school mathematics was studied by focusing on different
approaches to the learning of mathematics. The constructionist approach to
learning was identified as the appropriate approach towards learning, which
correlates with outcomes-based education (OBE) and with the approach
currently taught in South African schools. Factors which contribute towards
the meaningful learning of school mathematics, namely mathematical
knowledge and skills, meta-cognition, learning strategies and tasks and
assignments in mathematics, have been discussed. The role of problem
solving in the learning of mathematics was studied by means of a possible
problem-solving model which may be developed together with the learners.
The teaching of problem solving was investigated by referring to the planning
of a problem-based lesson and attention was paid to the learning content of
the lesson and the planning of the teaching-learning activities. Together with
the learners a problem-solving model was developed for the teaching of
problem solving. The implementation of the teaching of problem solving was
described with reference to the use of big-group presentations as well as
problem solving in small groups. Attention was also paid to problem solving,
and the use of different assessment techniques was discussed.
The empirical investigation was done by means of a case study, and the focus
was firstly on the influence of problem solving on the learning of mathematics,
and secondly on the manner in which problem solving may be taught.
Information was collected during the qualitative investigation by using a
questionnaire which was completed by the learners, as well as an interview
and observation schedule. The class work, homework and group work books
of the learners were studied and transcribed. Video recordings were made of
the learners' participation in the big group, small groups and written work, and
the transcribed information was used to make deductions about the teaching
of problem solving to the learners.
From the empirical investigation it became clear that there is a correlation
between problem solving and the teaching and learning of mathematics.
Problem solving may be taught to learners by means of a problem-solving
model, although this does not necessarily result in successful problem solving
by all learners. While learners are solving problems, they are also learning
mathematical concepts and acquiring and applying mathematical skills.Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2005.
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Sonnenburg, Edith M. "Pre-writing rhetorical strategies which activate both hemispheres of the brain". CSUSB ScholarWorks, 1985. https://scholarworks.lib.csusb.edu/etd-project/349.
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Lavado, Anabela de Jesus Machado. "O contributo do GeoGebra no desenvolvimento da capacidade de resolução de problemas de alunos do 8º ano do ensino básico". Master's thesis, Universidade de Évora, 2012. http://hdl.handle.net/10174/11859.
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O presente estudo tem como objetivo compreender como pode um contexto de sala de aula apoiado pelo GeoGebra contribuir para promover o desenvolvimento da capacidade de resolução de problemas de alunos do 8.º ano do Ensino Básico. Esta capacidade transversal é especialmente importante nas atuais orientações curriculares.
O estudo, pelos objetivos definidos e natureza dos dados recolhidos, constitui uma investigação qualitativa, concretizada pela modalidade de estudo de caso de uma turma participante numa intervenção didática centrada na resolução de problemas geométricos.
Conclui-se que as resoluções dos problemas apresentadas pelos alunos com o Geogebra são, na maioria, adequadas e rigorosas mas não apresentam robustez. Em relação às estratégias de resolução, as duas mais utilizadas pelos alunos foram Fazer um diagrama ou esquema e Fazer tentativa mas alguns conciliaram diversas estratégias. Em relação à formulação de problemas, a maioria optou por fazer variações dos problemas iniciais, variando o contexto ou os dados; ### Abstract:
GeoGebra contribution to the development of problem solving abilities in 8th grade students
The objective of this study is to determine how GeoGebra, used in classroom situations, can contribute to the development of problem solving abilities in 8th grade students. This ability is specially important in current curricula guidelines and it is present in mathematics syllabus for basic school.
Due to the nature of its objectives and collected data, this study is a qualitative investigation, a case study of a class that was involved in a didactic intervention based on geometric problem solving.
We conclude that the resolutions presented by students to problems in GeoGebra are for the most part adequate and rigorous but lacking robustness. As for problem solving strategies, the most used were How to make a diagram and Making Tries. However, some students used a combination of several strategies. Considering problem formulation, most students preferred to use initial problem variations, changing context or data.
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Larsson, Hanna-Sofia y Josefine Sillén. "Problem är till för att lösas : En kvalitativ intervjustudie som undersöker hur grundskolelärares uppfattning om problemlösning i de yngre åldrarnas matematikundervisning stämmer överens med hur forskning och styrdokument ser på problemlösning". Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-42709.
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Syftet med studien är att undersöka hur grundskolelärares uppfattning om problemlösning stämmer överens med hur forskning och styrdokument och ser på problemlösning. Undersökningen genomfördes med en kvalitativ forskningsmetod. Genom lärar-observationer och semistrukturerade intervjuer studerade lärares syn på problemlösning och hur de arbetar med problemlösning. Efter genomförandet analyserades lärarnas syn på problemlösning, lärares uppfattningar om syftet, hur de arbetade samt lärarnas roll i arbetet med problemlösning. Resultatet visar att grundskolelärarna arbetar med problemlösning men att det kan finnas en osäkerhet kring begreppets innebörd och betydelse. Slutsatsen blev att grundskolelärarna till viss del arbetar med vad forskning anser är problemlösning.The aim of the study is to examine how teachers’ perception of problem solving are consistent with that of which is concluded in both research and the curriculum. The investigation was conducted with a qualitative method. Through teacher observations and semi-structured interviews, we studied teachers' views on problem solving and how they work with problem solving. After the implementation an analysis was made containing teachers' views on problem solving, their perceptions about the aim, how they work and their place in the work on problem solving. The result shows that primary school teachers work with problem solving, but that there may be uncertainty about the meaning and significance of the concept. The conclusion, based on the results, shows that elementary school teachers work to some extent of what science considers problem solving. However, the result also shows that the lack of basic knowledge in the matter has lead to a deficient education in solving problem.
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Pinto, Viviane Damasceno. "Funções exponenciais, logarítmicas via resolução de problemas". Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/7664.
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Experience shows that exponentials and logarithms are two themes seen by our students as extremely complex. On the other hand, the teaching and learning of such contents are of great importance and significance, as well as being used in several areas of knowledge as a tool for solving problems. We present a proposal of teaching Exponential functions with their definitions, theorems and properties, but with an approach that aims at the applicability of the concepts acquired in solving significant problems, involving several areas of knowledge. We believe that approaching the theme with this new look will facilitate and enrich teaching and learning, often impoverished, when it occurs only through conceptualizations, theorems and operative properties. The Problem-Based Learning method guided this work and was used to guide the proposed methodology of starting the content of exponential functions, starting from simple and significant problems and, later, enabling the teacher to work with the operative properties of exponentials and logarithms as tools to resolve them.
A experiência mostra que exponenciais e logaritmos são dois temas vistos por nossos alunos como extremamente complexos. Por outro lado, o ensino e aprendizagem de tais conteúdos são de grande importância e significado, além de serem usados em diversas áreas do conhecimento como ferramenta para solução de problemas. Apresentamos uma proposta de ensino de funções Exponenciais com suas definições, teoremas e propriedades, mas com uma abordagem que visa a aplicabilidade dos conceitos adquiridos na resolução de problemas significativos, envolvendo diversas áreas do conhecimento. Acreditamos que a abordagem do tema com esse novo olhar, venha facilitar e enriquecer o ensino e aprendizagem, muitas vezes empobrecido, quando se dá somente através de conceituações, teoremas e propriedades operatórias. O método de Aprendizagem Baseada em Problemas orientou esse trabalho e foi usado para nortear a metodologia proposta de iniciar o conteúdo de funções exponenciais, partindo de problemas simples e significativos e, posteriormente, possibilitando ao professor trabalhar com as propriedades operatórias de exponenciais e logaritmos como ferramentas para resolução dos mesmos.
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Mendes, Marco Miguel da Silva. "Estratégias de resolução de problemas: construção de conhecimento matemático por alunos de currículos alternativos". Master's thesis, Universidade de Évora, 2007. http://hdl.handle.net/10174/16190.
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Este trabalho procurou analisar/compreender se o aluno, que frequenta uma turma onde se desenvolve um currículo alternativo de Matemática, poderia, com base numa prática letiva assente na resolução de problemas, criar e/ou utilizar estratégias de resolução que levassem à construção de conhecimento matemático e à sua efetiva utilização. Procurou, igualmente, compreender em que medida essa prática, poderia constituir um fator influente na melhoria da aprendizagem e também no sentido de influenciar a sua relação coma Matemática. As questões orientadoras do estudo foram as seguintes: a) As estratégias de resolução criadas e/ou utilizadas pelos alunos para resolverem problemas evidenciam alguma prática regular? b) As diferentes estratégias de resolução utilizadas pelos alunos na resolução de problemas permitem a construção de conhecimento matemático? c) Em que medida a prática letiva com base na resolução de problemas pode ser fator influente na melhoria da aprendizagem matemática de alunos que frequentam uma turma onde se desenvolve um currículo alternativo? d) De que modo essa prática pode influenciar a relação com a Matemática de alunos inseridos numa turma onde se desenvolve um currículo alternativo? Metodologicamente, o estudo" seguiu uma abordagem de investigação qualitativa e interpretativa, assente em dois estudos de caso qualitativo e analítico. O investigador assume os papéis de investigador-instrumento e observador-participante. Foram recolhidos dados através de entrevistas, observação direta do trabalho dos alunos e documentos escritos das resoluções dos problemas elaborados pelos alunos. “ A análise de dados permite concluir que os alunos evoluíram no que se refere à sua capacidade de resolução de problemas, observando-se uma maior facilidade na compreensão e utilização de estratégias de resolução de problemas. A autonomia e persistência dos alunos na realização deste tipo de tarefas matemáticas foram algo notório ao longo do estudo, melhorando significativamente a relação com a Matemática. Estas conclusões reforçam a ideia da importância em assumir a resolução de problemas, como uma linha de força que, “atravessando” todo o currículo, oriente a definição de objetivos, de metodologias e de conteúdos significativos. /ABSTRACT - This work tried to analise/understand whether a student, attending a class with an alternative Mathematics' curriculum, could, in a problem-solving teaching environment, create and/or use strategies that Would converge in the building of Math comprehension and its use. It seeks to understand in what way this strategy influences not only as learning’ improvement but also the students' attitude towards this subject. The study’s guiding questions were: a) Are the resolution strategies, used by the students, evidence of a standard practice? b) Do the different problem-solving strategies, .used by the students, allow the building of Mathematics' comprehension? c) In what way can a problem-solving teaching environment influence these students in -the development of Math learning skills? d) In what way can this teaching influence their attitude towards Math? Methodologically, this study has followed a qualitative and interpretative investigation approach, based on two qualitative and analytical case studies. The investigator undertook both the role of investigator-instrument and observer-participant. The information was collected through interviews, direct observation and the gathering of Students’ Works. According to the data analyzed, the students acquired new problem-solving abilities, gaining a new sense of comprehension and being able to use problem-solving strategies. It was evident throughout the study that these students became more involved with Mathematics, solving its problems with a new independent and persistent attitude. These finding-s reinforce the notion of assuming problem-solving as a guiding line .throughout Math’s curriculum, helping defining goals, methods and significant contents.
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Pinto, Maria Elisa Calado. "O papel das representações na resolução de problemas de Matemática: um estudo no 1º ano de escolaridade". Master's thesis, Universidade de Évora, 2009. http://hdl.handle.net/10174/18507.
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Este estudo tem como objectivo investigar o papel que as representações, construídas por alunos do 1.o ano de escolaridade, desempenham na resolução de problemas de Matemática. Mais concretamente, a presente investigação procura responder às seguintes questões: Que representações preferenciais utilizam os alunos para resolver problemas? De que forma é que as diferentes representações são influenciadas pelas estratégias de resolução de problemas utilizadas pelos alunos? Que papéis têm os diferentes tipos de representação na resolução dos problemas? Nesta investigação assume-se que a resolução de problemas constitui uma actividade muito importante na aprendizagem da Matemática no 1.o Ciclo do Ensino Básico. Os problemas devem ser variados, apelar a estratégias diversificadas de resolução e permitir diferentes representações por parte dos alunos. As representações cativas, icónicas e simbólicas constituem importantes ferramentas para os alunos organizarem, registarem e comunicarem as suas ideias matemáticas, nomeadamente no âmbito da resolução de problemas, servindo igualmente de apoio à compreensão de conceitos e relações matemáticas. A metodologia de investigação segue uma abordagem interpretativa tomando por design o estudo de caso. Trata-se simultaneamente de uma investigação sobre a própria prática, correspondendo os quatro estudos de caso a quatro alunos da turma de 1.0 ano de escolaridade da investigadora. A recolha de dados teve lugar durante o ano lectivo 2007/2008 e recorreu à observação, à análise de documentos, a diários, a registos áudio/vídeo e ainda a conversas com os alunos. A análise de dados que, numa primeira fase, acompanhou a recolha de dados, teve como base o problema e as questões da investigação bem como o referencial teórico que serviu de suporte à investigação. Com base no referencial teórico e durante o início do processo de análise, foram definidas as categorias de análise principais, sujeitas posteriormente a um processo de adequação e refinamento no decorrer da análise e tratamento dos dados recolhidos -com vista à construção dos casos em estudo. Os resultados desta investigação apontam as representações do tipo icónico e as do tipo simbólico como as representações preferenciais dos alunos, embora sejam utilizadas de formas diferentes, com funções distintas e em contextos diversos. Os elementos simbólicos apoiam-se frequentemente em elementos icónicos, sendo estes últimos que ajudam os alunos a descompactar o problema e a interpretá-lo. Nas representações icónicas enfatiza-se o papel do diagrama, o qual constitui uma preciosa ferramenta de apoio ao raciocínio matemático. Conclui-se ainda que enquanto as representações activas dão mais apoio a estratégias de resolução que envolvem simulação, as representações icónicas e simbólicas são utilizadas com estratégias diversificadas. As representações construídas, com papéis e funções diferentes entre si, e que desempenham um papel crucial na correcta interpretação e resolução dos problemas, parecem estar directamente relacionadas com as caraterísticas da tarefa proposta no que diz respeito às estruturas matemáticas envolvidas. ABSTRACT; The objective of the present study is to investigate the role of the representations constructed by 1st grade students in mathematical problem solving. More specifically, this research is oriented by the following questions: Which representations are preferably used by students to solve problems? ln which way the strategies adopted by the students in problem solving influence those distinct representations? What is the role of the distinct types of representation in the problems solving process? ln this research it is assumed that the resolution of problems is a very important activity in the Mathematics learning at the first cycle of basic education. The problems must be varied, appealing to diverse strategies of resolution and allow students to construct distinct representations. The active, iconic and symbolic representations are important tools for students to organize, to record and to communicate their mathematical ideas, particularly in problem solving context, as well as supporting the understanding of mathematical concepts and relationships. The adopted research methodology follows an interpretative approach, and was developed in the context of the researcher classroom, originating four case studies corresponding to four 1 st grade students of the researcher's class. Data collection was carried out during the academic year of 2007/2008 and was based on observation, analysis of documents, diaries, audio and video records and informal conversations with students. The initial data analysis was based on the problems and issues of research, as well in the theoretical framework that supports it. The main categories of analysis were defined based on the theoretical framework, and were subjected to a process of adaptation and refining during data processing and analysis aiming the -case studies construction. The results show that student's preferential representations are the iconic and the symbolic, although these types of representations are used in different ways, with different functions and in different contexts. The symbolic elements are often supported by iconic elements, the latter helping students to unpack the problem and interpret it. ln the iconic representations the role of the diagrams is emphasized, consisting in a valuable tool to support the mathematical reasoning. One can also conclude that while the active representations give more support to the resolution strategies involving simulation, the iconic and symbolic representations are preferably used with different strategies. The representations constructed with distinct roles and functions, are crucial in the proper interpretation and resolution of problems, and seem to be directly related to the characteristics of the proposed task with regard to the mathematical structures involved.
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Mazorodze, R. "The impact on students' self-efficacy and attainment of the explicit teaching of cognitive and metacognitive problem solving strategies in post-16 physics. The case for a GCE A-level physics course in an inner London Academy". Thesis, University College London (University of London), 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.711893.
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Problem solving plays a pivotal role in the physics curriculum at all levels, as a summative assessment tool or a pedagogic barometer to gauge transfer of acquired physics knowledge and skills. However, evidence shows that students’ performance in problem solving remains limited to basic routine problems, with evidence of poor performance in solving problems that go beyond basic equation retrieval and substitution. Research into physics problem solving, with very little literature existent for the UK, has advocated for explicit teaching of problem-solving strategies but with little impact of these studies on the actual learning-teaching process of physics. In heeding the call by most researchers to extend research on physics problem to real classrooms situations, an action research methodology, consisting of two cycles, was adopted. This action research study attempted to bridge the `research-practical divide´ by explicitly teaching physics problem-solving strategies through collaborative group problem-solving sessions embedded within the curriculum. The target group was a GCE-A level cohort in the AS course, the only course cohort at this inner London academy. The objective was to trigger the generative mechanisms identified within the information processing, sociocultural theory and social cognitive theories. These mechanisms were viewed as possessing causal powers to enable an improvement in physics problem-solving competence. Data were collected using external assessments and video recordings of individual and collaborative group problem-solving sessions. The data analysis revealed a general positive shift in the students’ problem-solving patterns, both at group and individual level. All four students demonstrated a deliberate, well-planned deployment of the taught strategies. The marked positive shifts in collaborative competences, cognitive competences, metacognitive processing and increased self-efficacy are positively correlated with attainment in problem solving in physics. However, this shift proved to be due to different mechanisms triggered in the different students.
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Coskun, Sirin. "A multiple case study investigating the effects of technology on students' visual and nonvisual thinking preferences comparing paper-pencil and dynamic software based strategies of algebra word problems". Doctoral diss., University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4874.
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In this multiple-case study, I developed cases describing three students' (Mary, Ryan and David) solution methods for algebra word problems and investigated the effect of technology on their solution methods by making inferences about their preferences for visual or nonvisual solutions. Furthermore, I examined the students' solution methods when presented with virtual physical representations of the situations described in the problems and attempted to explain the effect of those representations on students' thinking preferences. In this study, the use of technology referred to the use of the dynamic software program Geogebra. Suwarsono's (1982) Mathematical Processing Instrument (MPI) was administered to determine their preferences for visual and nonvisual thinking. During the interviews, students were presented with paper-and-pencil-based tasks (PBTs), Geogebra-based tasks (GBTs) and Geogebra-based tasks with virtual physical representations (GBT-VPRs). Each category included 10 algebra word problems, with similar problems across categories. (i.e., PBT 9, GBT 9 and GBT-VPR 9 were similar). By investigating students' methods of solution and their use of representations in solving those tasks, I compared and contrasted their preferences for visual and nonvisual methods when solving problems with and without technology. The comparison between their solutions of PBTs and GBTs revealed how dynamic software influenced their method of solution. Regardless of students' preferences for visual and nonvisual solutions, with the use of dynamic software students employed more visual methods when presented with GBTs. When visual methods were as accessible and easy to use as nonvisual methods, students preferred to use them, thus demonstrating that they possessed a more complete knowledge of problem-solving with dynamic software than their work on the PBTs.; Nowadays, we can construct virtual physical representations of the problems in technology environments that will help students explore the relationships and look for patterns that can be used to solve the problem. Unlike GBTs, GBT-VPRs did not influence students' preferences for visual or nonvisual methods. Students continued to rely on methods that they preferred since their preferences for visual or nonvisual solutions regarding GBT-PRs were similar to their solution preferences for the problems on MPI that was administered to them to determine their preferences for visual or nonvisual methods. Mary, whose MPI score suggested that she preferred to solve mathematics problems using nonvisual methods, solved GBT-VPRs with nonvisual methods. Ryan, whose MPI score suggested that he preferred to solve mathematics problems using visual methods, solved GBT-VPRs with visual methods. David, whose MPI score suggested that he preferred to solve mathematics problems using both visual and nonvisual methods, solved GBT-VPRs with both visual and nonvisual methods.ID: 030422900; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (Ph.D.)--University of Central Florida, 2011.; Includes bibliographical references (p. 293-303).
Ph.D.
Doctorate
Education
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Lam, Siu-Yuk Rebecca. "Acupuncturists' clinical problem-solving strategies". Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28477.
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This study investigates the clinical problem-solving among Western-trained and traditionally trained acupuncturists. Fifty-six subjects with varying clinical experience were divided into four groups: physicians without acupuncture training (control), physician-acupuncturists, non-licensed physician-acupuncturists, and traditionally trained acupuncturists. Three clinical cases (two routine and one non-routine), were given to the subjects to provide diagnostic and treatment plans. The data were quantitatively and qualitatively analyzed. Subjects' diagnostic and treatment plans were evaluated against reference models for Western medicine and traditional Chinese medicine (TCM).The results indicate that acupuncturists were influenced by their initial medical training. Physician-acupuncturists and non-licensed physician-acupuncturists' practices were greatly influenced by the training in Western medicine, regardless of their exposure to traditional Chinese medicine. The traditionally trained practitioners outperformed the other groups of subjects in the non-routine case. Accuracy in diagnoses and treatments for the non-routine case was also positively related to the length of clinical experience. The findings support theories of expertise that experts use forward reasoning when coping with familiar cases, and backward reasoning when encountering difficult cases.
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Newman, Victor. "Teaching problem-solving in teams". Thesis, University of Bath, 1988. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760587.
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Yuen, Gary. "Problem solving strategies students use when solving combinatorial problems". Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/5535.
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This research is a case study that examines the strategies that three grade 11 students use
to manoeuvre through a series of three combinatorial problems. Grade 11 students were chosen
as participants because they have had no formal training in solving this class of math problems.
Data includes video recordings of each participant’s problem solving sessions along with each
participant’s written work. Through analysis of this data, several themes related to problem
solving strategies were identified. First, students tend to rely on algebraic representation and
methods as they approach a problem. Second, students use the term “guess and check” to
describe any strategy where the steps to a solution are not clearly defined. Thirdly, as students
negotiate problems, they tend to search for patterns that will streamline their methods. Fourthly,
students approach complicated problems by breaking up the problem into smaller parts. Finally,
students who verify their work throughout the problems solving process tend to experience more
success than those who do not. From these findings, I suggest that mathematics teachers need to
ensure that they are not over-emphasizing algebraic strategies in the classroom. In addition,
students need to be given the opportunity to explore various solution strategies to a given
problem. Finally, students should be taught how to verify their work, and be encouraged to
perform this step throughout the problem solving process.
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Poon, Oi-yee Teresa y 潘藹怡. "The problem-solving strategies of adolescents". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31959763.
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Poon, Oi-yee Teresa. "The problem-solving strategies of adolescents". Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18811930.
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Doty, Mary P. "Teaching arithmetic understanding through problem solving /". Abstract Full Text (HTML) Full Text (PDF), 2008. http://eprints.ccsu.edu/archive/00000521/02/1070FT.htm.
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Thesis (M.S .) -- Central Connecticut State University, 2008.Statement of responsibility from accompanying documentation. Thesis advisor: Philip Halloran "... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 50-59). Also available via the World Wide Web.
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Toy, Serkan. "Online ill-structured problem-solving strategies and their influence on problem-solving performance". [Ames, Iowa : Iowa State University], 2007.
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Welsh, Kimberly D. "Individuals solving problems : the effects of problem solving strategies and problem solving technologies on generating solutions". Virtual Press, 1997. http://liblink.bsu.edu/uhtbin/catkey/1045625.
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This experiment was designed to compare two problem solving strategies, brainstorming and the hierarchical technique, and two problem solving technologies, computer software and pencil and paper. The first purpose of this study was to explore what effects computer software and pencil and paper have on the facilitation of solutions for individual problem solvers. Subjects generated solutions by either recording ideas on a computer or by writing ideas down on paper. The second purpose of this study was to examine how individuals evaluate solutions they have generated.Specifically, we were looking for solution evaluations to differ according to which problem solving strategy subjects received training on, brainstorming or the hierarchical technique. Solutions were rated on overall quality, practicality, and originality on a scale ranging from 0 (being the lowest possible score) to 4 (being the highest possible score).Subjects who used a computer to record ideas generated significantly more solutions than those subjects recording ideas on paper. Subjects trained with the hierarchical technique generated ideas higher in quality than those trained with brainstorming. Subjects trained with brainstorming generated more original ideas than those trained with the hierarchical technique. Finally, subjects rating of practicality did not differ according to problem solving strategy.Department of Psychological Science
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Scanlon, Eileen. "Modelling physics problem solving". Thesis, Open University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.277276.
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Silva, Carina Brunehilde Pinto da. "Combinatorial analysis: focusing on teaching problem solving". Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10084.
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A AnÃlise CombinatÃria à o conjunto de tÃcnicas para a resoluÃÃo de problemas de contagem. à usada quando à preciso conhecer a quantidade de elementos de um conjunto finito, sem necessidade de elencar cada um. Neste trabalho, discute-se a maneira como este assunto tÃo importante à apresentado para os alunos que cursam o Ensino MÃdio, a fim de aprimorÃ-la. Ao final do trabalho, à sugerido um software educacional, de prÃpria autoria, capaz de resolver problemas de contagem, com a finalidade de auxiliar e dinamizar o desempenho do professor em sala de aula.The Combinatory Analysis is the technical set used to solve counting problems. It's useful when is necessary to know how much elements are in a set finite, without the need to list each one. In this work, let's discuss the way in which this important matter is taught to high school students, and give suggestions to make it better. At the end, is suggested an educational software, of our own authorship, which is able to solve counting problems. It was developed to help and to stimulate the teacher performance during the classes.
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Sullivan, Gary E. (Gary Eugene). "The Impact of Student Thinking Journals and Generic Problem Solving Software on Problem Solving Performance and Transfer of Problem Solving Skills". Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc278982/.
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This study examined the effects of specially designed thinking journal activities that have been attributed with encouraging reflective thinking, on instruction using generic, or content-free problem solving software. Sixty-three fourth grade students participated in four instructional sessions using a software package called Moptown Hotel. Students completed separate posttests that measured (1) performance on problems of the same kind as those used in instruction, and (2) transfer of skills to other kinds of problems. Scores of students who wrote thinking journals prior to testing were compared with scores of students who did not. Results indicate that students who wrote thinking journals performed the same as students who did not when tested on problems similar to those practiced in class. Tests in which students transferred their skills to word problems, however, produced significant differences. There was no significant difference between scores when averaged over all four weekly occasions. However, for the final session alone, students who wrote thinking journals scored higher on tests of problem solving transfer than students who did not (p < .01). The study also examined the relationship between the degree of metacognitive thought displayed in students' journal entries, and their measured problem solving ability. Results indicate that students who had higher average reflectivity scores also had higher average problem solving performance and transfer scores (p < .05). It was also noted that the significant relationship between reflectivity and scores of problem solving ability was only observed in male students. It was concluded that under the right conditions, and for the right kinds of problems, thinking journal writing can help students understand their own thinking processes, resulting in improved problem solving behavior. The study also raises the question of whether there are differences between the ways that male and female students apply metacognitive awareness gained through journal writing experiences.
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Will, Sean. "Increasing Problem Solving in a Special Education Class by Teaching Talk Aloud Problem Solving (TAPS)". Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011828/.
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Although there is extensive research demonstrating the benefits of teaching problem solving repertoires to typically developing individuals, there is little research on the effectiveness of these kinds of procedures with individuals with special needs. In this study, a group of special education students in a public school were taught problem solving skills using a curriculum called Talk Aloud Problem Solving (TAPS), which was developed by Robbins (2014). TAPS teaches students five problem solving skills and five active listening skills. This study utilized a multiple baseline design to examine whether training in TAPS would change the way that students solve problems and increase their accuracy when solving problems. In addition, a reversal design was used for each participant, consisting of the presence and the removal of the active listener during different stages of the study. After TAPS training and guided practice sessions, all students demonstrated new problem solving repertoires and their accuracy improved. For some students, having an audience (an active listener) was necessary to maintain their behavior. Further research is needed to determine how to teach students to be their own active listener.
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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.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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Al-Nashwan, Ahmed Mohammed. "Writing competence in Arabic : AFL/ASL problem solving strategies". Thesis, University of Leeds, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.399867.
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Snyder, Brian Lyn. "A study of pedagogical approaches to teaching problem solving". Thesis, Kansas State University, 1985. http://hdl.handle.net/2097/9880.
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Jensen-Hole, Catherine. "Experiencing the interdependent nature of musicianship and educatorship as defined by David J. Elliott in the context of the collegiate level vocal jazz ensemble". Thesis, connect to online resource, 2005. http://www.unt.edu/etd/all/Aug2005/jensen-hole%5Fcatherine%5Fmary/index.htm.
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Wong, Man-on y 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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Raynor, Barbara Jean. "Fostering critical thinking through problem solving in home economics". Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29059.
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This study investigated whether critical thinking can be fostered in home economics through teaching a problem solving approach in Family Management. Secondarily, it investigated teacher behaviours which may foster critical thinking abilities, the moral and ethical issues which the teaching of critical thinking addresses, and whether the students were able to use problem solving in real life situations.
The research involved the students and teacher in a Family Management eleven class in rural British Columbia. All students in the class chose to participate in the study. The study was conducted during twenty-six classroom hours.
The study used action research as the research methodology. The research included action/research cycles with time between for analysis and reflection. The phase of data analysis and reflection was called the reconnaissance. Data was collected through audio tapes of the classes, entries in the teacher's journal, a checklist, and collected student work. The data collected in the first reconnaissance phase established a description which served as a point of reference for comparing and analyzing later observations.
Two cycles of action/research followed. Observations were made and data collected as the critical thinking concepts were introduced. The introduction of the macro-thinking skill of problem solving was combined with the micro-
thinking skills of avoiding fallacies, observing, reporting and summarizing.
The research found that there was an increase in critical thinking activities at the end of the study. Factors that were found to have effected this change were: the teaching of a problem solving process, the teaching of micro-thinking skills, certain teacher behaviours, and the classroom atmosphere. Home economics was found to play a unique role in providing practice in real life problem solving.
Further research is needed to determine if the skills the students learned while problem solving in Family Management will carry over to everyday life.Education, Faculty of
Curriculum and Pedagogy (EDCP), Department of
Graduate
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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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Jacobi, Ian Campbell. "Dynamic application of problem solving strategies : dependency-based flow control". Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/84718.
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Thesis (Elec. E. in Computer Science)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student submitted PDF version of thesis.
Includes bibliographical references (pages 105-107).
While humans may solve problems by applying any one of a number of different problem solving strategies, computerized problem solving is typically brittle, limited in the number of available strategies and ways of combining them to solve a problem. In this thesis, I present a method to flexibly select and combine problem solving strategies by using a constraint-propagation network, informed by higher-order knowledge about goals and what is known, to selectively control the activity of underlying problem solvers. Knowledge within each problem solver as well as the constraint-propagation network are represented as a network of explicit propositions, each described with respect to five interrelated axes of concrete and abstract knowledge about each proposition. Knowledge within each axis is supported by a set of dependencies that allow for both the adjustment of belief based on modifying supports for solutions and the production of justifications of that belief. I show that this method may be used to solve a variety of real-world problems and provide meaningful justifications for solutions to these problems, including decision-making based on numerical evaluation of risk and the evaluation of whether or not a document may be legally sent to a recipient in accordance with a policy controlling its dissemination.
by Ian Campbell Jacobi.
Elec.E.in Computer Science
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Jonklass, Raymond. "Learners' strategies for solving linear equations". Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52915.
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Thesis (MEd)--University of Stellenbosch, 2002.ENGLISH ABSTRACT: Algebra deals amongst others with the relationship between variables. It differs from Arithmetic amongst others as there is not always a numerical solution to the problem. An algebraic expression can even be the solution to the problem in Algebra. The variables found in Algebra are often represented by letters such as X, y, etc. Equations are an integral part of Algebra. To solve an equation, the value of an unknown must be determined so that the left hand side of the equation is equal to the right hand side. There are various ways in which the solving of equations can be taught. The purpose of this study is to determine the existence of a cognitive gap as described by Herseovies & Linchevski (1994) in relation to solving linear equations. When solving linear equations, an arithmetical approach is not always effective. A new way of structural thinking is needed when solving linear equations in their different forms. In this study, learners' intuitive, informal ways of solving linear equations were examined prior to any formal instruction and before the introduction of algebraic symbols and notation. This information could help educators to identify the difficulties learners have when moving from solving arithmetical equations to algebraic equations. The learners' errors could help educators plan effective ways of teaching strategies when solving linear equations. The research strategy for this study was both quantitative and qualitative. Forty-two Grade 8 learners were chosen to individually do assignments involving different types of linear equations. Their responses were recorded, coded and summarised. Thereafter the learners' responses were interpreted, evaluated and analysed. Then a representative sample of fourteen learners was chosen randomly from the same class and semi-structured interviews were conducted with them From these interviews the learners' ways of thinking when solving linear equations, were probed. This study concludes that a cognitive gap does exist in the context of the investigation. Moving from arithmetical thinking to algebraic thinking requires a paradigm shift. To make adequate provision for this change in thinking, careful curriculum planning is required.
AFRIKAANSE OPSOMMING: Algebra behels onder andere die verwantskap tussen veranderlikes. Algebra verskil van Rekenkunde onder andere omdat daar in Algebra nie altyd 'n numeriese oplossing vir die probleem is nie. InAlgebra kan 'n algebraïese uitdrukking somtyds die oplossing van 'n probleem wees. Die veranderlikes in Algebra word dikwels deur letters soos x, y, ens. voorgestel. Vergelykings is 'n integrale deel van Algebra. Om vergelykings op te los, moet 'n onbekende se waarde bepaal word, om die linkerkant van die vergelyking gelyk te maak aan die regterkant. Daar is verskillende maniere om die oplossing van algebraïese vergelykings te onderrig. Die doel van hierdie studie is om die bestaan van 'n sogenaamde "kognitiewe gaping" soos beskryf deur Herseovies & Linchevski (1994), met die klem op lineêre vergelykings, te ondersoek. Wanneer die oplossing van 'n linêere vergelyking bepaal word, is 'n rekenkundige benadering nie altyd effektiefnie. 'n Heel nuwe, strukturele manier van denke word benodig wanneer verskillende tipes linêere vergelykings opgelos word. In hierdie studie word leerders se intuitiewe, informele metodes ondersoek wanneer hulle lineêre vergelykings oplos, voordat hulle enige formele metodes onderrig is en voordat hulle kennis gemaak het met algebraïese simbole en notasie. Hierdie inligting kan opvoeders help om leerders se kognitiewe probleme in verband met die verskil tussen rekenkundige en algebraïese metodes te identifiseer.Die foute wat leerders maak, kan opvoeders ook help om effektiewe onderrigmetodes te beplan, wanneer hulle lineêre vergelykings onderrig. As leerders eers die skuif van rekenkundige metodes na algebrarese metodes gemaak het, kan hulle besef dat hul primitiewe metodes nie altyd effektief is nie. Die navorsingstrategie wat in hierdie studie aangewend is, is kwalitatief en kwantitatief Twee-en-veertig Graad 8 leerders is gekies om verskillende tipes lineêre vergelykings individueel op te los. Hul antwoorde is daarna geïnterpreteer, geëvalueer en geanaliseer. Daarna is veertien leerders uit hierdie groep gekies en semigestruktureerde onderhoude is met hulle gevoer. Vanuit die onderhoude kon 'n dieper studie van die leerders se informele metodes van oplossing gemaak word. Die gevolgtrekking wat in hierdie studie gemaak word, is dat daar wel 'n kognitiewe gaping bestaan in die konteks van die studie. Leerders moet 'n paradigmaskuif maak wanneer hulle van rekenkundige metodes na algebraïese metodes beweeg. Hierdie klemverskuiwing vereis deeglike kurrikulumbeplanning.
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Alias, Maizam. "Spatial visualisation ability and problem solving in civil engineering". Thesis, Online version, 2000. http://ethos.bl.uk/OrderDetails.do?did=1&uin=uk.bl.ethos.325666.
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Almazedi, A. K. R. "A study of learner control programs for teaching problem solving". Thesis, University of Leeds, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.354432.
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Johns, Erin Shae. "Teaching Problem-Solving to Improve Family Functioning and Decrease Suicidality". NSUWorks, 2009. http://nsuworks.nova.edu/cps_stuetd/40.
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Suicide is a leading cause of death among adolescents and young adults. Numerous risk factors have been identified in the literature, including poor problem-solving skills, poor family functioning, excessive risk-taking behaviors, legal difficulties, and school difficulties. Deficits in problem-solving skills and poor family functioning are typically reported together, indicating a relationship between the two. However, no previous studies have identified this relationship. The purpose of this study was to identify possible relationships between two known risk factors and suicidal ideation, to determine whether problem-solving skills taught in the experimental groups reduce suicidal ideation and improve perceptions of family relationships, and to establish if knowledge of problem-solving skills acts as a mediator between family functioning and suicidal ideation. Archival data of 285 adolescents who participated in up to 10 sessions dedicated to teaching the process of solving problems were analyzed. There was an unusually high attrition rate (64%), and so in some analyses, only data from 85 adolescents was reported. One empirically-validated questionnaire and three additional questionnaires were utilized to assess suicidal ideation, perception of family functioning, risky behaviors, and knowledge of steps in problem-solving. Knowledge of the problem solving process was shown to significantly improve over the course of the group. Although there were not significant improvements in suicidal ideation or family functioning, the change in scores was in the predicted direction. The results also found significant correlations between family functioning and problem solving and family functioning and suicidal ideation; however, no significant relationship was found between problem solving and suicidal ideation. Additionally, there were many significant correlations found between the outcome measures and many of the risk factors for suicide. Lastly, a mediator effect of problem-solving on the relationship between family functioning and suicidal ideation was found at pre-test only.