Tesi sul tema "Mathematical thinking"
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Hart, Hilary. "Mathematics Vocabulary and English Learners: A Study of Students' Mathematical Thinking". BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2573.
Testo completoHannula, Markku. "Affect in mathematical thinking and learning /". Turku : University of Turku, 2004. http://kirjasto2.utu.fi/julkaisupalvelut/b/annaalit/B273.html.
Testo completoMonteleone, Chrissoula. "Critical mathematical thinking in young students". Phd thesis, Australian Catholic University, 2021. https://acuresearchbank.acu.edu.au/download/cb06753760247f43b88bfde14ea04bc78463c1734aa47d3ca60129d4d5e7c8ec/2879980/Monteleone_2021_Critical_mathematical_thinking_in_young_students.pdf.
Testo completoArgyle, Sean Francis. "Mathematical thinking: From cacophony to consensus". Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1337696397.
Testo completoLane, Catherine Pullin. "Mathematical Thinking and the Process of Specializing". University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1307441324.
Testo completoStillman, Gloria Ann. "Assessing higher order mathematical thinking through applications /". St. Lucia, Qld, 2001. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe16747.pdf.
Testo completoCardella, Monica E. "Engineering mathematics : an investigation of students' mathematical thinking from a cognitive engineering perspective /". Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/10692.
Testo completoTanner, 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.
Testo completoReyes-Santander, Pamela, David Aceituno e Pablo Cáceres. "Mathematical Thinking Styles of Students with Academic Talent". Pontificia Universidad Católica del Perú, 2017. http://repositorio.pucp.edu.pe/index/handle/123456789/123827.
Testo completoEl presente estudio establece el estilo de pensamiento matemático predominante que utilizan los estudiantes con talento académico en la resolución de problemas matemáticos. Los estilos de pensamiento son preferencias por parte de los sujetos en la forma de expresar las habilidades frente a una tarea matemática, en este caso, visual, formal e integrado. En el marco de un estudio ex post facto retrospectivo de grupo único, se evaluó a un total de 99 estudiantes pertenecientes a un programa académico de apoyo al talento con el cuestionario Estilos de Pensamiento Matemático de Borromeo-Ferri. Los resultados indican que los estudiantes declararon orientarse hacia el estilo de pensamiento integrado, que supone el uso de simbología y representaciones verbales junto con expresiones visuales en la resolución de los ejercicios matemáticos, así como una significativa orientación a abordar los problemas de modo combinado, que supone considerar los problemas como un todo.
La présente étude établit le style de pensée mathématique prédominant utilisé par les étudiants ayant un talent académique dans la résolution de problèmes mathématiques. Les styles de pensée sont des préférences de la part des sujets sous la forme d’exprimer les capacités face à une tâche mathématique, dans ce cas, visuelle, formelle et intégrée. Dans une étude rétrospective sur un seul groupe ex post facto, un total de 99 étudiants appartenant à un programme de soutien aux talents universitaires ont été évalués, à qui le questionnaire Styles de Pensée mathématique de Borromeo-Ferri a été appliqué et déterminé que ce type de sujets déclare principalement un style de pensée intégré, ce qui implique l’utilisation de la symbologie et des représentations verbales ainsi que des expressions visuelles dans la résolution des exercices mathématiques. En outre, ils montrent une forte orientation pour aborder les problèmes de manière combinée, ce qui implique de les considérer dans leur ensemble dans le même temps.
Este estudo estabelece o estilo predominante do pensamento matemático usado por os alunos com talento acadêmico na resolução de problemas matemáticos. Os estilos de pensamento são as preferências dos indivíduos sobre a forma para expressar as capacidades em uma tarefa matemática, neste caso, visual, formal e integrada. Como parte de um estudo ex post facto retrospectivo de grupo único, foram avaliados um total de 99 estudantes de um programa de talento acadêmico. Foram aplicados nos alunos o questionário “Estilos de Pensamento Matemático de Borromeo-Ferri” e determinou-se que a maioria dos participantes declararam um estilo de pensamento integrado, que envolve o uso de símbolos e representações verbais com resolução de expressões visuais de exercícios matemáticos. Eles mostram também uma forte orientação para resolver os problemas de modo combinado, o qual envolve a considerá-los como um todo de uma vez.
Coetzee, Carla. "Mathematical thinking skills needed by first year programming students". Diss., University of Pretoria, 2016. http://hdl.handle.net/2263/60991.
Testo completoDissertation (MEd)--University of Pretoria, 2016.
Science, Mathematics and Technology Education
MEd
Unrestricted
Groth, Randall E. Langrall Cynthia Willey Mooney Edward S. "Development of a high school statistical thinking framework". Normal, Ill. Illinois State University, 2003. http://wwwlib.umi.com/cr/ilstu/fullcit?p3087867.
Testo completoTitle from title page screen, viewed November 10, 2005. Dissertation Committee: Cynthia W. Langrall, Edward S. Mooney (co-chair), Beverly J. Hartter, Sharon S. McCrone. Includes bibliographical references (leaves 199-212) and abstract. Also available in print.
Calder, Nigel Stuart. "Processing mathematical thinking through digital pedagogical media the spreadsheet /". The University of Waikato, 2008. http://hdl.handle.net/10289/2662.
Testo completoOzdil, Utkun. "A Multilevel Structural Model Of Mathematical Thinking In Derivative Concept". Phd thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614000/index.pdf.
Testo completo(2) to investigate the extent of variation in the relationships among different mathematical thinking constructs at the within- and between-classroom levels
and (3) to examine the cross-level interactions among different types of mathematical thinking. Previous research was extended by investigating the factor structure of mathematical thinking in derivative at the within- and between-classroom levels, and further examining the direct, indirect, and cross-level relations among different types of mathematical thinking. Multilevel analyses of a cross-sectional dataset containing two independent samples of undergraduate students nested within classrooms showed that the within-structure of mathematical thinking includes enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking, whereas the between-structure contains formal-axiomatic, proceptual-symbolic, and conceptual-embodied thinking. Major findings from the two-level mathematical thinking model revealed that: (1) enactive, iconic, algebraic, and axiomatic thinking varied primarily as a function of formal and algorithmic thinking
(2) the strongest direct effect of formal-axiomatic thinking was on proceptual-symbolic thinking
(3) the nature of the relationships was cyclic at the between-classroom level
(4) the within-classroom mathematical thinking constructs significantly moderate the relationships among conceptual-embodied, proceptual-symbolic, and formal-axiomatic thinking
and (5) the between-classroom mathematical thinking constructs moderate the relationships among enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking. The challenges when using multilevel exploratory factor analysis, multilevel confirmatory factor analysis, and multilevel structural equation modeling with categorical variables are emphasized. Methodological and educational implications of findings are discussed.
Tan, Li-hua, e 陳麗華. "Primary school students' thinking processes when posing mathematical word problems". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31962592.
Testo completoTan, Li-hua. "Primary school students' thinking processes when posing mathematical word problems". Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk:8888/cgi-bin/hkuto%5Ftoc%5Fpdf?B23425155.
Testo completoGoggins, Lauren Lee. "Eliciting elementary preservice teachers' mathematical knowledge for teaching using instructional tasks that include children's mathematical thinking". Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 245 p, 2008. http://proquest.umi.com/pqdweb?did=1490070411&sid=13&Fmt=2&clientId=8331&RQT=309&VName=PQD.
Testo completoStone, Jason C. "The Formation of Self-Constructed Identity as Advanced Mathematical Thinker Among Some Female PhD Holders in Mathematics and the Relationship to the "Three-Worlds" Cognitive Model of Advanced Mathematical Thinking". Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1436975429.
Testo completoAizikovitsh, Einav, e Miriam Amit. "An innovative model for developing critical thinking skills through mathematical education". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79308.
Testo completoSpitzer, Sandy Margaret. "The role of graphing calculators in students' algebraic thinking". Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 135 p, 2008. http://proquest.umi.com/pqdweb?did=1601234511&sid=4&Fmt=2&clientId=8331&RQT=309&VName=PQD.
Testo completoOwens, Kay Dianne, e 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.
Testo completoQwillbard, Tony. "Less information, more thinking : How attentional behavior predicts learning in mathematics". Thesis, Umeå universitet, Institutionen för psykologi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-100999.
Testo completoExperiment har visat att en undervisningsmetod i vilken elever uppmuntras att själva komma på lösningsmetoder till matematiska problem (creative mathematically founded reasoning, CMR) resulterar i bättre inlärning och färdighet än en metod i vilken eleverna ges en färdig en lösningsmetod att öva på genom repetition (algorithmic reasoning, AR). Denna studie undersöker om elever under en AR-träningsbetingelse ägnar mindre uppmärksamhet åt information som är relevant för matematisk problemlösning än vad elever under en CMR-träningsbetingelse gör. För att testa detta mättes elevernas uppmärksamhetsbeteende under träning med hjälp av ögonrörelsekamera. Måtten ställdes sedan i relation till uppgiftsfärdighet i ett uppföljningstest en vecka efter träningssessionen. Resultaten stödjer teorin och bekräftar tidigare studier som visat att CMR leder till bättre prestation i uppföljningstestet. Resultaten tyder även på att de elever under CMR-betingelsen som fokuserar minst på ovidkommande information presterar bättre.
Venter, Dalene. "Three-dimensional thinking in radiography". Thesis, Cape Peninsula University of Technology, 2008. http://hdl.handle.net/20.500.11838/1564.
Testo completoIntroduction Research to date has not been able to agree whether spatial abilities can be developed by practice. According to some researchers spatial ability is an inherited cognitive ability, compared to spatial skills that are task specific and can be acquired through formal training. It is commonly assumed that radiographers require general cognitive spatial abilities to interpret complex radiographic images. This research was conducted to investigate second year radiography students’ three-dimensional thinking skills pertaining to film-viewing assessments. Materials and methods The experimental research strategy was mainly applied together with correlation research. Two trials were run (in 2005 and 2006). The sample group consisted of fifteen second year diagnostic radiography students in 2005 and twenty-three second year diagnostic radiography students, of the same institution, in 2006. Each year group was randomly divided into a control group and an intervention group. Two instruments were used, that is a film-viewing assessment and a three-dimensional test, Academic Aptitude Test (University) (AAT) nr. nine: Spatial Perception (3-D). The whole class completed this basic spatial aptitude test, as well as a base-line film viewing assessment, which focused on the evaluation of technique/anatomy of second year specialised radiographic projections. The marks that the students achieved in the fore-mentioned tests were compared, to determine if there was any correlation between their performances in the different tests. A curricular intervention, which was intended to improve applied three-dimensional skills, was subsequently applied. The students executed certain modified radiographic projections on parts of a human skeleton. For each radiographic projection, the students had to draw the relation of the X-ray beam to the specific anatomical structures, as well as the relation of these structures to the film. The related images of these projections were also drawn. With each of the following sessions, films including images of the previous session were discussed with each student. After the intervention, the whole class wrote a second film-viewing assessment. The marks achieved in this assessment were compared to the marks of the initial film-viewing assessment to determine the influence of the intervention on the performance of the intervention group. Following this assessment, for ethical reasons, the same intervention took place with the control group. A third film-viewing assessment was then written by all the diagnostic second year students to evaluate the overall impact of the intervention on the applied three-dimensional skills of the class. The marks of both the 2005 and 2006 classes (intervention classes) were compared to the marks achieved by former classes from 2000 to 2004 (control classes), in film-viewing assessments to evaluate the role of the curricular intervention over the years. The students again completed the three-dimensional test, Spatial Perception (3-D) to evaluate the impact of the intervention on students’ general three-dimensional cognitive abilities. These marks were also compared to the marks of the third filmviewing assessment, to determine if there was any correlation between the students’ performances in the different tests. Results The intervention groups did not perform significantly better in film-viewing assessments after the intervention, compared to the control groups, but reasonable differences, favouring the intervention group, were achieved. Statistical significance was achieved in film-viewing assessments with both year groups after the whole class had the intervention. The intervention year groups also performed significantly better than the previous year groups (without the intervention) in film-viewing assessments. The performance in general three-dimensional cognitive abilities of the group of 2006 improved significantly after the intervention, but on the contrary, the performance of the group of 2005 declined. There was a small intervention effect on the performance of the group of 2006. Only a weak to moderate correlation between the marks of the students achieved in the three-dimensional tests and the marks achieved in the film-viewing assessments, was found. Conclusion The contrasting evidence between the data of the two groups (2005 and 2006) in the three-dimensional tests and the small intervention effect on the performance of the group of 2006, makes the intervention not applicable for the increase of general spatial abilities. The results of this research show that the applied three-dimensional skills of radiography students in interpreting specialised and modified projections can be improved by intensive practice, independent of their inherited spatial abilities.
Rahman, Roselainy Abdul. "Changing my own and my students' attitudes to calculus through working on Mathematical Thinking". Thesis, Open University, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.518366.
Testo completoDumitraşcu, Gabriela Georgeta. "Generalization: Developing Mathematical Practices in Elementary School". Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/556959.
Testo completoLealdino, Pedro. "Didactic Situations for the Development of Creative Mathematical Thinking : A study on Functions and Algorithms". Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1254/document.
Testo completoCreativity is considered as a crucial skill for the contemporary world. The research described in this thesis had the Project MC Squared as the main context. Carried out between October 2013 and September 2016. The objective of the project was to develop a digital platform for the development of C-books for teaching mathematics in a way that develops Creative Mathematical Thinking both in the students and the authors. This thesis, entitled: Didactic Situations for the Development of Creative Mathematical Thinking proposes an analysis of the design, development, implementation, and testing of digital and non-digital activities with the aim of improving and fostering Creative Mathematical Thinking having Functions and Algorithms as mathematical objects to analyze. The following research questions raised from the problem: • How to operationalize and revise existing definitions of Creative Mathematical Thinking? • How can we assess the progress of a process involving Creative Mathematical Thinking? • How the "Diamond of Creativity" model is an useful analytic tool to map the Creative Process path? To answer such questions, the research followed a methodology based on an agile Design-Based Research. Four activities were cyclically developed. The first one, called: "Function Hero," is a digital game that uses body movements of the player to evaluate recognizability of functions. Three other activities called "Binary Code," "FakeBinary Code" and "Op’Art", aimed at the development of Computational Thinking. The main constructs of this thesis are: (a) the "Diamond of Creativity" model to map the process of solving problems found in each activity, evaluating the process and the products derived from the students’ work. (b) The digital game: "Function Hero". To validate the research hypotheses, we collected data from each activity and analyzed them quantitatively and qualitatively. The results show that developed activities have awakened and engaged students into problem-solving and that the "Diamond of Creativity" model can help in identifying and labeling specific points in the creative process
Harris, Carolina. "Hur tänker elever? : Elevintervjuer som metod för att kartlägga elevers tankar kring matematikundervisning". Thesis, Södertörn University College, Lärarutbildningen, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-843.
Testo completoDuring my time as a student of education I have learnt that it is my responsibility, as a teacher, to adjust the ways in which I teach to the needs, abilities, experiences, and thoughts of each individual child. What I have not yet gained much knowledge on is how to go about finding the children’s thoughts.
In this thesis I investigate the interview as a method of finding out how sixth graders think about their mathematics education. Four children were interviewed. In addition to these inter-views, as a means of giving a broader perspective to and a greater understanding of the chil-dren’s answers, one math lesson was filmed and the math teacher was interview on two sepa-rate occasions.
What I found was that a number of factors seemed to influence the children’s thoughts and answers, and that their answers were most likely not always a mirror of their thoughts. From this follows that we, as teachers, must be careful and not assume that we know about a child’s thoughts when, in fact, what we know is what the child chooses to communicate about his or her thoughts. I also found that the children seemed unaccustomed to speaking about mathe-matics in the way that I wanted them to. One reason for this seemed to be the way in which their teacher organized the lessons.
Lemon, Travis L. "Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections". BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2292.
Testo completoEspinoza, Eduardo. "Elevers utveckling i den matematiska tänkande : Exempel från en fristående skolan profilerad i matematik". Thesis, Södertörn University College, Lärarutbildningen, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-848.
Testo completoThe primordial purpose of our studies has been carrying out a detailed research to describe methods or work procedures in the teaching and application of the mathematics, at a school based or alignment on the mathematics instruction. To be able to study the pupils in their development of the mathematical thinking.
We have carried out a detailed investigation, in the previously mentioned school using the ethnography observation methods directly in the place of the facts. Where it was possible to verify that the mathematics lessons were a consequences of the methods or work procedures which made us deduce that this school did every possible effort to stimulate all the pupils to be better and particularly talented pupils individually to develop one’s talent by means of the following results:
· Develop the logical thinking
· The self-critical ability
· The attitude of the teacher/communication
· A positive work atmosphere
· Organization of the school and the class
· Formation of the theoretical knowledge
Keywords
Mathematical thinking.
Pupils
Independent school
Basaran, Seren. "An Exploration Of Affective And Demographic Factors That Are Related To Mathematical Thinking And Reasoning Of University Students". Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613422/index.pdf.
Testo completoapproaches to studying, self-efficacy in mathematics, problem solving strategies, demographic profile, mathematical thinking and reasoning competencies were identified through the adopted survey and the competency test which was designed by the researcher. These scales were administered to 431 undergraduate students of mathematics, elementary and secondary mathematics education in Ankara and in Northern Cyprus and to prospective teachers of classroom teacher and early childhood education of teacher training academy in Northern Cyprus. Secondly, three structural models were proposed to explore the interrelationships among idenitified factors. Thirdly, among three models, the model yielding best fit to data was selected to evaluate the equality of the factor structure across Ankara and Northern Cyprus regions. Lastly, differences regarding pre-identified factors with respect to gender, region and grade level separately and dual, triple interaction effects were investigated through two two-way MANOVA and a three-way ANOVA analyses. Exploratory and confirmatory factor analyses were employed to determine the factors
meaning orientation, mathematics self-efficacy, motivation, disorganized study methods and surface approach for the survey and &lsquo
expressing, extracting and computing mathematically&rsquo
(fundamental skills) and &lsquo
logical inferencing and evaluating conditional statements in real life situations&rsquo
(elaborate skills) for the test. The three models commonly revealed that while mathematics self-efficacy has a significant positive effect on both fundamental and elaborate skills, motivation which is a combination of intrinsic, extrinsic and achievement motivational items was found to have a negative direct impact on fundamental skills and has a negative indirect contribution upon elaborate skills. The results generally support the invariance of the tested factor structure across two regions with some evidence of differences. Ankara region sample yielded similar factor structure to that of the entire sample&rsquo
s results whereas
no significant relationships were observed for Northern Cyprus region sample. Results of gender, grade level and region related differences in the factors of the survey and the test and on the total test indicated that, females are more meaning oriented than males. &lsquo
Fourth and fifth (senior)&rsquo
and third year university students use disorganized study methods more often than second year undergraduate students. In addition, senior students are more competent than second and third year undergraduate students in terms of both skills. Freshmen students outscored sophomore students in the elaborate skills. Students from Ankara region are more competent in terms of both skills than students from Northern Cyprus region. This last inference is also valid on the total test score for both regions. Males performed better on the total test than females. Moreover, there exist region and grade level interaction effect upon both skills. Additionally, significant interaction effects of &lsquo
region and gender&rsquo
, &lsquo
region and grade level&rsquo
, &lsquo
gender and grade level&rsquo
and &lsquo
region and gender and grade level&rsquo
were detected upon the total test score.
Munlo, Isaac. "Critical systems thinking, theory and practice : a case study of an intervention in two British local authorities". Thesis, University of Hull, 1997. http://hydra.hull.ac.uk/resources/hull:5718.
Testo completoFarlow, Brian. "Square Peg Thinking, Round Hole Problems: An Investigation of Student Thinking About and Mathematical Preparation for Vector Concepts in Cartesian and Non-Cartesian Coordinates Used in Upper-Division Physics". Diss., North Dakota State University, 2019. https://hdl.handle.net/10365/31479.
Testo completoSerbin, Kaitlyn Stephens. "Prospective Teachers' Knowledge of Secondary and Abstract Algebra and their Use of this Knowledge while Noticing Students' Mathematical Thinking". Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/104563.
Testo completoDoctor of Philosophy
Once future mathematics teachers learn about how advanced mathematics content is related to high school algebra content, they can better understand the algebra content they may teach. The future teachers in this study took a Mathematics for Secondary Teachers course during their senior year of college. This course gave them opportunities to make connections between advanced mathematics and high school mathematics. After this course, they better understood the mathematical properties that people use while equation solving, and they improved their teaching practice of making sense of high school students' mathematical thinking about inverses and equation solving. Overall, making connections between the advanced mathematics content they learned during college and the algebra content related to inverses and equation solving that they teach in high school helped them improve their teaching practice.
Schillinger, Tammy. "Mathematical Instructional Practices and Self-Efficacy of Kindergarten Teachers". ScholarWorks, 2016. https://scholarworks.waldenu.edu/dissertations/2101.
Testo completoGraves, Barbara, e Christine Suurtamm. "Disrupting linear models of mathematics teaching|learning". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79920.
Testo completoTaylor, Carol H. "Promoting Mathematical Understanding through Open-Ended Tasks; Experiences of an Eighth-Grade Gifted Geometry Class". Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/msit_diss/36.
Testo completoCheng, Chun Chor Litwin. "Basic knowledge and Basic Ability: A Model in Mathematics Teaching in China". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79584.
Testo completoRao, Rashmi Jayathirtha. "Modeling learning behaviour and cognitive bias from web logs". The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492560600002105.
Testo completoNascimento, Anderson de Araújo. "Análise dos tipos de provas matemáticas e pensamento geométrico de alunos do 1º ano do Ensino Médio". Universidade Estadual da Paraíba, 2017. http://tede.bc.uepb.edu.br/jspui/handle/tede/2907.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The present research work investigated the level of geometric thinking and the types of mathematical proofs by 1st year high school students from the application of a Didactic Proposal. This research was constituted as a qualitative one, and as case study, having instruments of the application an essay with the theme Proofs and Mathematical Demonstrations, Didactic Proposal developed by a team of five members who worked collaboratively, inserted in the Project CAPES/OBEDUC/UFMS/UEPB/UFAL Edital 2012, participant observation and audio recording. We developed the didactic proposal with 18 activities, divided into four parts, which stimulated students to reflect, justify, prove and demonstrate. The application of this proposal occurred in June 2015 for 1st year high school students in a public school in the city of Areia, Paraíba. Our research took place in three moments. In the first moment, we apply the essay on the subject mathematical proofs and demonstrations. In the second moment we did a didactic intervention approaching definitions, theorems, proofs and mathematical demonstrations with the objective of taking to the students this knowledge. In the third moment, Part I and II of the Didactic Proposal were applied, involving activities to conjecture and demonstrate the Pythagorean Theorem, Internal Angle Sum Theorem and External Angle Theorem. This proposal helped in the investigation of the mathematical knowledge of the 1st year high school students, divided into 8 pairs and one trio, chosen freely. The two pairs of students who achieved the best performance in our Didactic Proposal were chosen for our case study and the one of better performance had its dialogue recorded and transcribed as a source of evidence of our case study. In our research we analyzed the answers given by the two pairs on Activities 1 and 3 (Part II) and Activity 2 (Part III), totaling in 3 questions. We used the data triangulation method for our case study. Firstly, we draw the profile of the two pairs of students in relation to Proofs and Mathematical Demonstrations. Next, we investigate the types of mathematical proofs used by them and their geometric thinking. To do so, we use discussions about the levels of geometric thinking proposed by Van Hiele and the types of evidence. From our results we can conclude that the pairs of students were able to develop informal justifications, that is, informal proofs. Thus, the pairs presented pragmatic evidence and the types of evidence Pragmatic Justification and Crucial Example. Regarding the geometric thinking proposed by Van Hiele, only one pair could be classified in one of the levels of development of geometric thinking, Level 3, informal deduction. Therefore, we come to the end of this research convinced that it is necessary to start working mathematical proofs and demonstrations in the basic education level, adapting its teaching to the degree of maturity and to the mathematical knowledge of the students, since our results point out that this subject is not approached properly in the classroom.
A presente pesquisa investigou o nível do pensamento geométrico e os tipos de provas matemáticas de alunos do 1º ano do Ensino Médio a partir da aplicação de uma Proposta Didática. Esta pesquisa se constituiu como qualitativa, e estudo de caso, tendo como instrumentos a aplicação de uma redação com o tema Provas e Demonstrações Matemáticas, Proposta Didática desenvolvida por uma equipe de cinco membros que trabalhou de forma colaborativa, inserida no Projeto CAPES/OBEDUC/UFMS/UEPB/ UFAL Edital 2012, observação participante e gravação em audio do diálgo de umas das duplas participantes da pesquisa. Elaboramos uma proposta didática com 18 atividades, dividida em quatro partes, que estimulavam aos alunos refletirem, justificarem, provarem e demonstrarem. A aplicação dessa proposta se deu em junho de 2015 para alunos do 1º ano do Ensino Médio de uma escola pública da cidade de Areia, Paraíba. Nossa pesquisa se deu em três momentos. No primeiro momento, aplicamos a redação sobre o tema provas e demonstrações matemáticas. No segundo momento realizamos uma intervenção didática abordando definições, teoremas, provas e demonstrações matemáticas com o objetivo de levar aos alunos esses conhecimentos. No terceiro momento foi aplicado a Parte I e II da Proposta Didática, envolvendo atividades de conjecturar e demonstrar o Teorema de Pitágoras, Teorema da Soma dos Ângulos Internos e Teorema dos Ângulo Externo. Essa proposta auxiliou na investigação do conhecimento matemático dos alunos do 1º ano do Ensino Médio, divididos em 8 duplas e um trio, escolhidos livremente. As duas duplas de alunos que obteveram melhores desempenhos em nossa Proposta Didática foram escolhidas para o nosso estudo de caso e a de melhor desenpenho teve seu diálogo gravado e transcrito como fonte de evidência de nosso estudo de caso. Em nossa pesquisa analisamos as respostas dadas pelas duas duplas sobre Atividades 1 e 3 (Parte II) e Atividade 2 (Parte III), totalizando em 3 questões. Utilizamos o método de triângulação de dados para nosso estudo de caso. Primeiramente, traçamos o perfil das duas duplas de alunas com relação às Provas e Demonstrações Matemáticas. Em seguida, investigamos os tipos de provas matemáticas utilizadas por elas e o seu pensamento geométrico. Para tanto, utilizamos as discussões sobre os níveis do pensamento geométrico proposto por Van Hiele e os tipos de provas. A partir de nossos resultados pudemos concluir que as duplas de alunas conseguiram desenvolver justificativas informais, ou seja, provas informais. Assim, as duplas apresentaram provas pragmáticas e os tipos de provas Justificativa Pragmática e Exemplo Crucial. Com relação ao pensamento geométrico proposto por Van Hiele, apenas uma dupla pôde ser classificada em um dos níveis de desenvolvimento do pensamento geométrico, o Nível 3, dedução informal. Portanto, chegamos ao final desta pesquisa convictos de que é preciso iniciar o trabalho das provas e demonstrações matemáticas na Educação Básica, adequando seu ensino ao grau de maturidade e aos conhecimentos matemáticos dos alunos, visto que nossos resultados apontam que esse tema não é abordado adequadamente em sala de aula.
Atz, Dafne. "A análise combinatória no 6º Ano do Ensino Fundamental pormeio da resolução de problemas". reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2017. http://hdl.handle.net/10183/164618.
Testo completoThis dissertation shows the development of research related to teaching Combinatorics, through Problem Solving, at a 6th grade level. A lesson plan was prepared and aimed to confront students of middle school with problems involving Combinatorics, allowing them to work with such concepts before high school. Based on this lesson plan, our intent was to verify how Problem Solving, according to Onuchic e Allevato, helped the students to understand initial concepts of Combinatorics. Also, using David Tall’s studies about Mathematical Thinking as reference. We could verify that the Problem Solving Theory helped the students to expand and modify their Concept Images related to Combinatorics.
Bango, Siduduzile. "An investigation into Grade 7 learners’ knowledge of ratios". Diss., University of Pretoria, 2002. http://hdl.handle.net/2263/78505.
Testo completoDissertation (MEd)--University of Pretoria, 2020.
Science, Mathematics and Technology Education
MEd
Unrestricted
Szyjka, Sebastian. "Cognitive And Attitudinal Predictors Related To Graphing Achievement Among Pre-Service Elementary Teachers". OpenSIUC, 2009. https://opensiuc.lib.siu.edu/dissertations/43.
Testo completoCarvalho, Liliane Maria Teixeira Lima de. "O papel dos artefatos na construÃÃo de significados matemÃticos por estudantes do ensino fundamental II". Universidade Federal do CearÃ, 2008. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=2617.
Testo completoA pesquisa investiga se diferentes formas de conceber o papel dos artefatos e apresentaÃÃo da informaÃÃo influenciam a construÃÃo de significados matemÃticos por estudantes de 11 a 14 anos. A cogniÃÃo humana à concebida como processo mediado pela tradiÃÃo cultural e histÃrica das representaÃÃes enquanto artefatos, inserindo-se essa anÃlise no Ãmbito do raciocÃnio matemÃtico. Utilizou-se o mÃtodo experimental aliado a uma pesquisa-aÃÃo envolvendo o design intencional de tarefas. Explorou-se o papel mediacional das tarefas, desde a sua confecÃÃo e introduÃÃo na sala de aula de matemÃtica, atà o seu uso pelos estudantes. Essa abordagem se concretizou por meio de seis experimentos, dos quais participaram 922 estudantes: 598 oriundos do key Stage Three (corresponde em idade ao 7Â, 8 e 9 anos do Ensino Fundamental II no Brasil) de quatro escolas inglesas, e 324 oriundos do 7Â, 8 e 9 anos de duas escolas brasileiras. O Experimento 1 investiga se grÃficos, tabelas ou casos isolados influenciam o raciocÃnio dos estudantes sobre variÃveis discretas. O Experimento 2 verifica se diferentes informaÃÃes sobre variÃveis contÃnuas influenciam a interpretaÃÃo grÃfica dos estudantes. O Experimento 3 analisa se interaÃÃes de aspectos visuais e conceituais da informaÃÃo sobre variÃveis contÃnuas influenciam a interpretaÃÃo grÃfica dos estudantes. O Experimento 4 investiga se grÃficos, tabelas ou a combinaÃÃo de ambas as representaÃÃes influencia interaÃÃes de aspectos visuais e conceituais da informaÃÃo. Esses quatro experimentos foram realizados nas escolas inglesas. As tarefas usadas no primeiro e quarto experimentos foram aplicadas nas escolas brasileiras, sendo designados Experimentos 5 e 6, respectivamente. As tarefas foram potencialmente facilitadoras ao uso de conteÃdos matemÃticos. Os Experimentos 1 e 5 oferecem evidÃncias de que estudantes jà familiarizados com representaÃÃes em tabelas e grÃficos para representar variÃveis discretas nÃo se beneficiam em atividades em que eles precisam organizar os dados por eles mesmos. Estudantes ingleses tiram proveito igualmente de tabelas e grÃficos. Estudantes brasileiros nÃo se beneficiam do uso de tabelas. Os Experimentos 2 e 3 confirmam resultados de estudos prÃvios de que informaÃÃes grÃficas sobre variÃveis contÃnuas possuem diferentes nÃveis de complexidade. Ler pontos à significativamente mais fÃcil do que interpretar problemas globais. Os Experimentos 2 e 3 tambÃm confirmam a hipÃtese de que os problemas de inferÃncia inversa explicam as dificuldades com informaÃÃes globais. Essa dificuldade à acentuada em grÃficos com inclinaÃÃo negativa. O Experimento 4 mostra que a forma de apresentaÃÃo da informaÃÃo nÃo afeta o desempenho dos estudantes na resoluÃÃo de problemas sobre variÃveis contÃnuas. O raciocÃnio dos estudantes sobre variÃveis contÃnuas, no entanto, à influenciado pela forma de apresentaÃÃo da informaÃÃo. A pesquisa sugere a necessidade de uma discriminaÃÃo da informaÃÃo nÃo apenas quanto ao tipo de variÃvel, discreta ou contÃnua, ou tipo de relaÃÃo proporcional, direta ou inversa, mas tambÃm quanto ao tipo de inferÃncias requeridas dos estudantes
Mulder, Isabella Dorothea. "Graad 12-punte as voorspeller van sukses in wiskunde by 'n universiteit van tegnologie / I.D. Mulder". Thesis, North-West University, 2011. http://hdl.handle.net/10394/10338.
Testo completoMEd, Learning and Teaching, North-West University, Vaal Triangle Campus, 2011
Bilous, Olena Anatoliivna, Елена Анатольевна Белоус e Олена Анатоліївна Білоус. "Міжпредметні зв`язки при вивченні математичних дисциплін". Thesis, Видавництво СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/4270.
Testo completoZulatto, Rúbia Barcelos Amaral. "A natureza da aprendizagem matemática em um ambiente online de formação continuada de professores /". Rio Claro : [s.n.], 2007. http://hdl.handle.net/11449/102133.
Testo completoBanca: João Pedro Mendes da Ponte
Banca: Marcelo de Carvalho Borba
Banca: Maria Elizabeth Bianconcini Trindade Morato Pinto de Almeida
Banca: Vani Moreira Kenski
Resumo: A presente pesquisa analisa a natureza da aprendizagem matemática em um curso online de formação continuada de professores, denominado Geometria com Geometricks. Nele, alunos-professores de uma mesma rede de escolas, situadas em diferentes localidades do país, desenvolveram atividades de Geometria utilizando-se do software Geometricks, e se encontravam para discuti-las. Esses encontros aconteceram a distância, em tempo real, por chat ou videoconferência. Nessa proposta pedagógica, a telepresença condicionou a comunicação e oportunizou o estar-junto-virtual-com-mídias. De modo singular, os recursos da videoconferência permitiram que construções geométricas fossem compartilhadas visualmente e realizadas por todos os envolvidos, fomentando a interação e a participação ativa, constituindo, por meio do diálogo, uma comunidade virtual de aprendizagem. Os resultados levam a inferir que, nesse contexto, a aprendizagem matemática teve natureza colaborativa, na virtualidade das discussões, tecidas a partir das contribuições de todos os participantes; coletiva, na medida em que a produção matemática era condicionada pelo coletivo pensante de seres-humanos-com-mídias; e argumentativa, uma vez que conjecturas e justificativas matemáticas se desenvolveram intensamente do decorrer do processo, contando para isso com as tecnologias presentes na interação ocorrida de forma constante e colaborativa.
Abstract: This study was conducted to analyze the nature of mathematical learning in an online continuing education course for teachers entitled Geometry with Geometricks. Teachers employed in a nation-wide network of privately-supported schools developed geometry activities using the software Geometricks and discussed them in virtual meetings, in real time, via chat or video-conference. In this pedagogical proposal, tele-presence conditioned the communication and provided the opportunity for virtual-togetherness-with-media. In a unique way, the resources of the videoconference made it possible for everyone to participate in and visually share geometrical constructions, encouraging interaction and active participation and constituting a virtual learning community through dialogue. The results indicate that, in this context, mathematical learning nature was characterized by: collaboration, in the virtual discussions that were woven from the contributions of all the participants; collectivity, to the degree to which mathematical production was conditioned by the humans-with-media thinking collective; and argumentation, as the development of mathematical conjectures and justifications was intense throughout the process, aided by the technologies that were present in the constant, collaborative interaction.
Doutor
Wielewski, Sergio Antonio. "Pensamento instrumental e pensamento relacional na educação matemática". Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11325.
Testo completoCoordenação de Aperfeiçoamento de Pessoal de Nível Superior
This doctoral thesis contains theoretical discussions as well as results of an empirical study. The general starting point has been the thesis that our mathematical thinking is largely ruled by certain dualities or complementarities of which that between the representational and instrumental aspects of concepts is best known. Ernst Cassirer, presents in his famous book Substanzbegriff und Funktionsbegriff (Substance and Function) of 1910 the general thesis that the historical development of science could be described as a transition from merely referential Aristotelian concepts to operative concepts or functions. The very same duality has been discussed widely in mathematics education starting from the work of Richard Skemp. Our first goal has consequently been to find connections between Cassirer and Skemp. The discussion of these connections and differences leads then in a second part of the thesis to a presentation of the results of an empirical case study with fourteen participants. These had been confronted with a number of problem situations and their problem solving activities have afterwards been analyzed in terms of the aforementioned complementarity between relational and operative thinking
Nesta tese estão apresentados resultados de investigação teórica e empíricos. O alvo da pesquisa é identificação de características e análise das reflexões relativas a dualidades inerentes ao pensamento matemático. Tomou-se como pressuposto que o conhecimento de dualidades do pensamento matemático, e o como se utilizar desse conhecimento, se num sentido de complementaridade, seja relevante para o processo de ensino e aprendizagem da Matemática. A referência inicial do estudo foi a obra de Ernst Cassirer, Substance and Function (1910). Nessa obra é apresentado o desenvolvimento histórico da teoria do conceito de Aristóteles ao século XIX, isto é, desenvolvimento esse que vai das propriedades de substância à noção de função. Cassirer,como neo-kantiano, dá forte ênfase aos aspectos operativos e instrumentais do conceito. Na continuidade do estudo é destacado a fundamental importância de um conceito teórico ser compreendido nos termos de uma dualidade, em seus aspectos operativos e referencial. O trabalho didático de Richard Skemp é outro que explora dualidade semelhante. Trata -se da dualidade de aprender e de compreender, que Skemp chama de compreensão instrumental e relacional. Nossa investigação centra-se então na busca de conexão entre as concepções de Cassirer e Skemp. Para tal levamos em conta aspectos educacionais, reflexões filosóficas e pedagógicas, postura profissional do educador, exemplos de situações a-didáticas e didáticas. Esses aspectos, reflexões e exemplos nortearam a exploração empírica desta tese. Esta exploração teve o caráter de uma pesquisa qualitativa, tendo sido desenvolvidas atividades didáticas. O objetivo dessas atividades era avaliar a utilização pelos sujeitos do pensamente relacional e do pensamento instrumental
Wilson, Therese Maree. "Statistical reasoning at the secondary tertiary interface". Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16358/3/Therese%20Wilson%20Thesis.pdf.
Testo completoWilson, Therese Maree. "Statistical reasoning at the secondary tertiary interface". Queensland University of Technology, 2006. http://eprints.qut.edu.au/16358/.
Testo completoAbramovitz, Buma, Miryam Berezina, Abraham Berman e Ludmila Shvartsman. "Proofs and "Puzzles"". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79279.
Testo completoCarmo, Paulo Ferreira do. "Pensamento matemático avançado: como essa noção repercute em dissertações e teses brasileiras?" Pontifícia Universidade Católica de São Paulo, 2018. https://tede2.pucsp.br/handle/handle/21736.
Testo completoMade available in DSpace on 2018-12-12T09:30:07Z (GMT). No. of bitstreams: 1 Paulo Ferreira do Carmo.pdf: 863389 bytes, checksum: 85bcbdd002e1538d36adf2efa4d1c569 (MD5) Previous issue date: 2018-09-25
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Theories focused on the conceptualization of mathematical thinking have developed in the scope of mathematical education. These theories are cognitivist and aim to know the processes of formation of mathematical thinking, and in this way they make a valuable contribution to teaching and especially to learning in this area of knowledge. This thesis presents an investigation on this theme of the formation of advanced mathematical thinking, more specifically on the notions of Brazilian mathematical educators expressed in dissertations and theses produced in the period from 2010 to 2016. In this context, we have as an objective of this thesis, to understand and analyze in which, as and to what purpose the notion of advanced mathematical thinking appears in Brazilian production, and to evaluate what results were measured in these works and whether they express in any way different conceptions of this notion. The methodological procedures performed to reach this goal were to read and analyze scientific publications that somehow brought the theme of advanced mathematical thinking theory, which began to appear from the late 1970s, being David Tall and Tommy Dreyfus the leading researchers in the development of this theory. In the composition of the corpus of analysis there are 26 dissertations and theses selected because they fulfill the requirements announced in the proposed objective. Based on the precepts of the methodology of content analysis, we created two categories that reflect the objectives, the research questions and the results of the academic papers analyzed. The analysis of these categories indicated that Brazilian dissertations and theses presented in the period studied associate the notion of advanced mathematical thinking with mathematical thinking developed in the learning of mathematical contents of higher education and the formalization of mathematical concepts. The analysis of the corpus also revealed that it is admitted that the process of formation of mathematical thinking, necessary for the development of certain activities, is guided by cognitive obstacles and as a consequence, these obstacles generate learning difficulties. We can point out as a result of this research that the theory of advanced mathematical thinking is being used to understand the functioning of the process of the formation of this thinking, and from this to find elements that illuminate teaching strategies that promote learning in a more qualified way of mathematical concepts
As teorias voltadas à conceituação do pensamento matemático têm se desenvolvido no âmbito da educação matemática. Essas teorias são de cunho cognitivista e visam conhecer os processos de formação do pensamento matemático, e dessa forma elas trazem uma contribuição valiosa ao ensino e principalmente à aprendizagem dessa área do conhecimento. Esta tese apresenta uma investigação sobre esse tema da formação do pensamento matemático avançado, mais especificamente sobre concepções de educadores matemáticos brasileiros expressas em dissertações e teses defendidas no período de 2010 a 2016. Nesse contexto elencamos como objetivos desta tese, compreender e analisar em quais, como e com que finalidade aparece a noção de pensamento matemático avançado em dissertações e teses brasileiras, e avaliar que resultados foram nelas aferidos e se os mesmos expressam de algum modo diferentes concepções dessa noção. Os procedimentos metodológicos realizados para atingirmos esses objetivos foram de leitura e análise de publicações cientificas que, de alguma forma traziam, o tema da teoria do pensamento matemático avançado, literatura essa que começa a aparecer a partir do final da década de 1970, sendo David Tall e Tommy Dreyfus os principais pesquisadores no desenvolvimento dessa teoria. Na composição do corpus de análise constam 26 dissertações e teses selecionadas por preencherem os quesitos anunciados nos objetivos propostos. Tomando por base os preceitos da metodologia da análise de conteúdo, criamos duas categorias à quais refletem os objetivos e os resultados dos trabalhos acadêmicos analisados. A análise dessas categorias, nos indicaram que as dissertações e teses brasileiras apresentadas no período estudado associam a noção de pensamento matemático avançado ao pensamento matemático desenvolvido na aprendizagem de conteúdos matemáticos de ensino superior e à formalização dos conceitos matemáticos. A análise do corpus também revelou que é admitido que o processo de formação do pensamento matemático, necessário para o desenvolvimento de certas atividades, é pautado por obstáculos cognitivos e em consequência, esses obstáculos são geradores de dificuldades de aprendizagem. Podemos apontar como resultado desta pesquisa que a teoria do pensamento matemático avançado está sendo utilizada para se compreender o funcionamento do processo da formação desse pensamento, e, a partir disso, para se buscar elementos que iluminem estratégias de ensino que promovam de forma mais qualificada a aprendizagem dos conceitos matemáticos