Beslutsfattare i Sverige och internationellt har kommit fram till att undervisning i programmering är viktigt. I Sverige infördes således 2018 programmering i den svenska läroplanen där delar av programmeringsundervisningen ska bedrivas i matematikämnet. Många matematiklärare känner sig dock osäkra på hur denna undervisning ska utföras rent praktiskt. Syftet med detta arbete är att studera programmering i matematikämnet ur högstadieelevers perspektiv, och speciellt vad gäller matematiskt lärande och att lära sig hur man tänker vid programmering (datalogiskt tänkande). Detta görs som en fallstudie i en niondeklass som undervisades i programmering under 6 lektioner vid 5 tillfällen. Studien består av klassrumsobservationer, korta enkäter samt intervjuer med eleverna. Slutsatsen av fallstudien är att eleverna är övervägande positiva till programmering i matematik och ser det som något nytt och annorlunda. De ser programmeringen som kreativ jämfört med andra matematiklektioner och uppskattar den direkta responsen datorerna ger. Däremot har de svårt att se direkt lärande i matematik, förutom att de får använda variabler. Det räcker inte att programmeringsuppgifterna innehåller matematik för att eleverna ska uppleva att de lär sig matematik när de programmerar. Vilka tecken på datalogiskt tänkande som visar sig efter programmeringslektionerna beror på hur datalogiskt tänkande definieras. I detta arbete indelas datalogiskt tänkande i sex huvudkoncept: abstraktion, algoritmiskt tänkande, automatisering, nedbrytning i komponenter, felsökning och generalisering, varav eleverna i detta arbete visar tecken på algoritmiskt tänkande, uttrycker att de uppskattar automatisering och lär sig arbeta genom felsökning. Dessutom beskriver de att de samarbetar och kommunicerar mer på programmeringslektionerna än på andra matematiklektioner och uppskattar att få skapa egna programmeringsuppgifter och arbeta med öppna problem. / Decision makers in Sweden and internationally have come to the conclusion that teaching programming is important. In Sweden, programming was thus introduced in the Swedish curriculum in 2018, where parts of the programming education will be conducted in the subject of mathematics. Many mathematics teachers, however, feel uncertain about how this teaching should be carried out. The purpose of this work is to study programming in the subject of mathematics from the perspective of students in year 7-9, and especially in terms of mathematical learning and how to think when programming (computational thinking). This is done as a case study in a class in ninth grade that was taught programming during 6 lessons on 5 occasions. The study consists of classroom observations, short questionnaires and interviews with students. The conclusion of the case study is that the students are predominantly positive about programming in mathematics and see it as something new and different. They see programming as compared to other math lessons and appreciate the direct response the computers give. However, they have difficulty seeing direct learning in mathematics, except that the use of variables. It is not enough that the programming tasks contain mathematics for the students to experience that they learn mathematics when they program. What signs of computational thinking appear after the programming lessons depends on how computational thinking is defined. In this work, computational thinking is divided into six main concepts: abstraction, algorithmic thinking, automation, decomposition, troubleshooting and generalization, of which the students in this work show signs of algorithmic thinking, express that they appreciate automation and learn to work through troubleshooting. In addition, they describe that they collaborate and communicate more in the programming lessons than in other mathematics lessons and appreciate being able to create their own programming tasks and work with open problems.

[pt] Produzir tecnologia tem se mostrado uma habilidade cada vez mais indispensável na sociedade moderna. Os usuários estão deixando de ser simples consumidores e passando a ser produtores, usando a tecnologia para expressarem suas ideias. Nesse contexto, o aprendizado do chamado raciocínio computacional deve ser tão importante quanto o de disciplinas básicas, como a leitura, a escrita e a aritmética. Ao desenvolver tal habilidade o aluno vai conseguir se expressar através do software. Diversos projetos ao redor do mundo têm suas tecnologias e didáticas próprias a fim de auxiliar o aluno a desenvolver tal capacidade. Porém, sabemos que em um contexto que está em constante evolução como é o caso da informática, não podemos deixar que o aluno fique preso a uma única ferramenta ou meio de se expressar. Ferramentas podem ficar obsoletas e ele perderia seu poder de produtor de tecnologia. Pensando nisso, foi elaborado um modelo de transferência do aprendizado do raciocínio computacional a ser incorporado a sistemas de documentação ativa que apoiam o ensino-aprendizado desta habilidade. O modelo auxiliará o designer na criação de um artefato tecnológico que seja capaz de ajudar alunos e professores a aprenderem uma nova linguagem de programação. O modelo, que é baseado na Engenharia Semiótica, é a principal contribuição científica dessa dissertação de mestrado. / [en] Producing technology has been an increasingly essential ability in modern society. The users are no longer simple consumers but actually, also, technology producers, using technology to express their ideas. In this context, the learning of the so-called computational thinking should be as important as learning basic disciplines such as reading, writing and arithmetic. As long as the student can develop this ability, he will be able to express himself or herself through the software. Many projects around the world have their own technologies and pedagogy to help the student develop such capacity. However, we know that in a context that is constantly evolving as is the case of informatics, we cannot allow the student to be attached to a single tool or means. Tools may become obsolete and students would lose their technology producer status. With this in mind, we designed a learning transfer model of computational thinking, which will assist the designer in the creation of a technological artifact to help students and teachers learn a new programming language. The model, which is based on the Semiotic Engineering, is the main scientific contribution of this master s dissertation.

Initiatives to implement computational thinking and science, technology, engineering & modelling into learning processes have been taken by many authorities worldwide, and in Sweden as well. The Swedish government made changes in the high school curriculum in order to develop student’s digital competence including programming which has been in force since June 2018 (Skolverket, 2018). The new curriculum, K9, sets challenges for both students and teachers that can be tackled with studies that point out the difficulties and the fields which require more time and work on learning materials used by schools. Digital simulations are fast becoming a key instrument in school education and several attempts to show and understand the outcome of the usage of simulations have been done recently. Previous studies report that the usage of Algodoo and other simulations programs in physics education has positive effects on students. A considerable amount of literature has been published on computational thinking and simulations. These studies provide insights into how students can benefit from simulations in Algodoo to improve their digital thinking and performance in physics. A study that examines this topic is "Algodoo for Interactive Learning: Effects on Students’ Achievement and Motivation Towards Science'' by Aslı Saylan Kirmizigül (2021). The study investigates how the Algodoo software affects students' attitudes, motivation and performance in physics using both qualitative and quantitative methods. The results show that the students had positive attitudes towards Algodoo and that the use of the software had a positive effect on the students' performance and their computational thinking. Another study on the subject by Elias Euler and Bor Gregorcic ”Never far from shore: productive patterns in physics students' use of the digital learning environment Algodoo” shows that simulations can improve students' understanding of physical concepts and help them develop a deeper understanding of the subject. (Euler & Gregorcic, 2020). This study examines high school students' computational thinking experience and perception, and their learning process and outcomes through the visual simulation program, Algodoo. The study was carried out in a physics class in Stockholm with one specific topic, optical density, and light propagation through different mediums. This is a case study with second- and third-year high school students and the data collected by researchers. Smart boards and personal computers were used to construct the demonstration. The participants' experiences and thoughts were documented in a questionnaire and observations, followed by an interview. The questionnaire consists of fifteen open-ended questions, and the verbal interviews were without any specific leading questions. The study used qualitative methods to collect and analyse primary data. / Initiativet för att implementera datalogiskt tänkande och vetenskap, teknik, ingenjörskonst & modellering i lärandeprocesser har tagits av många myndigheter över hela världen och även i Sverige. Den svenska regeringen gjorde ändringar i gymnasieskolans läroplan för att utveckla elevernas digitala kompetens inklusive programmering som trädde i kraft efter juni 2018 (Skolverket, 2018). Läroplanen för gymnasieskolan har som mål att eleven ska kunna ”använda såväl digitala som andra verktyg och medier för kunskapssökande, informationsbearbetning, problemlösning, skapande, kommunikation och lärande”, (Skolverket). Detta mål ställer både elever och lärare i utmaningar som kan hanteras med studier som pekar på svårigheterna och de områden som kräver mer tid och arbete med läromedel som används av skolor. Digitala simuleringar håller snabbt på att bli ett nyckelinstrument i skolundervisningen och flera försök att visa och förstå resultatet av användningen av simuleringar har gjorts i av många forskare.Tidigare studier rapporterar att användningen av Algodoo och andra simuleringsprogram i fysikundervisningen har positiva effekter på eleverna. Dessa studier ger insikter i hur elever kan dra nytta av simuleringar i Algodoo för att förbättra sitt datologisk tänkande och prestanda inom fysik. Enstudie som undersöker detta ämne är "Algodoo for Interactive Learning: Effects on Students Achievement and Motivation Towards Science'' av Aslı Saylan Kirmizigül (2021). Studien undersöker hur Algodoo-mjukvaran påverkar elevernas attityder, motivation och prestation i fysik med hjälp av både kvalitativa och kvantitativa metoder. Resultaten visar att eleverna hade positiva attityder till Algodoo och att användningen av mjukvaran hade en positiv effekt på elevernas prestationer och deras datalogiskt tänkande. En annan studie av Elias Euler och Bor Gregorcic ”Aldrig långt från land: produktiva mönster i fysikstudenters användning av den digitala lärmiljön Algodoo” visar att simuleringar kan förbättra elevernas förståelse för fysiska begrepp och hjälpa dem att utveckla en djupare förståelse av ämnet (Euler & Gregorcic, 2020). Den här studien undersöker gymnasieelevers erfarenhet och uppfattning av datalogiskt tänkande och deras inlärningsprocess och dess resultat genom ett visuellt simuleringsprogram, Algodoo. Studien hade ägt rum i en fysikklass med ett specifikt ämne, optisk densitet och ljusspridning genom olika medier. Detta är en fallstudie med andra och tredje års gymnasieelever och data som samlats in av skribenten. Smartboard och persondatorer hade använts för att konstruera demonstrationen. Deltagarnas erfarenheter och tankar hade dokumenterats i ett frågeformulär, observationer och intervju efteråt. Enkäten består av femton öppna frågor och de verbala intervjuerna är utan några specifika ledande frågor. Studien använde kvalitativa metoder för att samla in och analysera primärdata.

Digitaliseringen har förändrat skolmiljön och skapat både nya utmaningar och möjligheter Det här examensarbetet, genomfört i samarbete med K-ULF projektet, syftar till att utveckla en pedagogisk lektionsplanering med tillhörande lärar- och elevhandledning som kombinerar teori och praktiska övningar. Målet är att stödja lärare i programmeringsundervisningen och främja elevernas lärande i en sociokulturell miljö. Bedömningen av elevernas förståelse genomfördes med hjälp av Blooms taxonomi, som utgår från det kognitivistiska perspektivet. Lärarhandledningen utformades baserat på tidigare forskningsresultat och input från en tekniklärare. Den omfattade tydliga syften och lärandemål enligt ämnesplanen för Teknik i gymnasiet, lektionsupplägg, lektionsinnehåll samt eventuella förberedelser för läraren. Därefter genomgick handledningen tre iterationer baserade på protokoll, deltagande observationer, diskussioner med läraren och insamlade elevsvar. Författarna testade handledningen genom att använda den i sin egen undervisning. Resultatet visade att handledningen fungerade som ett användbart verktyg för lärare som ville introducera programmering i sin undervisning. Den kunde anpassas efter klassens kunskapsnivå och lärarens egna erfarenheter. Undervisningen ägde rum i en sociokulturell klassrumsmiljö där eleverna arbetade både individuellt och i par. De insamlade elevsvaren visade att elevernas förståelse nådde upp till nivå sex enligt Blooms taxonomi när de arbetade i grupp, vilket innebar att de kunde skapa nya program och lösningar. Dock hamnade deras individuella förståelse upp till nivå fem, där de kunde bygga upp kunskap från minnesnivå till förståelse och tillämpning. Användningen av Blooms taxonomi för att bedöma elevernas förståelsenivå i en sociokulturell kontext visade sig vara en framgångsrik metod. De olika perspektiven på lärandet samverkade på ett effektivt sätt. / Digitalization has revolutionized the educational landscape, bringing forth new challenges and opportunities within schools. This master’s thesis, conducted in collaboration with the K-ULF project, aims to develop a pedagogical educational curriculum material that combines theory and practical exercises for teachers and students. The material focuses on programming instruction and fostering student learning within a sociocultural environment. To assess students’ understanding, Bloom’s taxonomy, rooted in the cognitivist perspective, was employed. The teacher guide was designed based on prior research findings and insights from a technology teacher. It encompasses clear objectives, learning goals aligned with the secondary school technology curriculum, lesson plans, lesson content, and necessary teacher preparations. The guide underwent three iterations, incorporating protocols, participant observations, discussions with the teacher and collected student solutions. To evaluate the effectiveness of the teacher guide, the authors utilized it in their own teaching. The results demonstrated that the guide served as a valuable resource for teachers seeking to incorporate programming into their instruction. It could be tailored to accommodate the student’s knowledge level and the teacher’s experience. The teaching took place in a sociocultural environment, where students engaged in both individual and collaborative work. Analysis of student solutions indicated that group work led to a higher level of understanding, reaching level six of Bloom’s taxonomy, enabling students to create new programs and devise solutions. However, individual understanding reached level five, characterized by the ability to evaluate. The use of Bloom’s taxonomy as an assessment tool within a sociocultural context proved successful, effectively integrating diverse perspectives on learning.

The fundamentals of computer science are increasingly important to consider as critical educational and occupational competencies, as evidenced by the rapid growth of computing capabilities and the proliferation of the Internet in the 21st century, combined with reimagined national education standards. Despite this technological and social transformation, the general education environment has yet to embrace widespread incorporation of computational concepts within traditional curricular content and instruction. Researchers have posited that exercises in computational thinking can result in gains in other academic areas (Baytak & Land, 2011; Olive, 1991), but their studies aimed at identifying any measurable educational benefits of teaching computational concepts to school age children have often lacked both sufficient experimental control and inclusion of psychometrically sound measures of cognitive abilities and academic achievement (Calao, Moreno-León, Correa, & Robles, 2015). The current study attempted to shed new light on the question of whether using a graphically-based computer coding environment and semi-structured curriculum –the Creative Computing Course in the Scratch programming language –can lead to demonstrable and significant changes in problem solving, creative thinking, and knowledge of computer programming concepts. The study introduced 24 youth in a summer educational program in Philadelphia, PA to the Scratch programming environment through structured lessons and open-ended projects for approximately 25 hours over the course of two weeks. A delayed treatment, control trial design was utilized to measure problem solving ability with a modified version of the Woodcock-Johnson Tests of Cognitive Abilities, Fourth Edition (WJ-IV), Concept Formation subtest, and the Kaufman Tests of Educational Achievement, Third Edition (KTEA-3) Math Concepts and Applications subtest. Creative problem solving was measured using a consensual assessment technique (Amabile, 1982). A pre-test and post-test of programming conceptual knowledge was used to understand how participants’ computational thinking skills influenced their learning. In addition, two questionnaires measuring computer use and the Type-T (Thrill) personality characteristic were given to participants to examine the relationship between risk-taking or differences in children’s usage of computing devices and their problem solving ability and creative thinking skills. There were no differences found among experimental and control groups on problem solving or creative thinking, although a substantial number of factors limited and qualified interpretation of the results. There was also no relationship between performance on a pre-test of computational thinking, and a post-test measuring specific computational thinking skills and curricular content. There were, however, significant, moderate to strong correlations among academic achievement as measured by state standardized test scores, the KTEA-3 Math Concepts and Applications subtest, and both the pre and post Creative Problem Solving test developed for the study. Also, higher levels of the Type T, or thrill-seeking, personality characteristic were associated with lower behavioral reinforcement token computer “chips," but there were no significant relationships among computer use and performance on assessments. The results of the current study supported retention of the null hypothesis, but were limited by small sample size, environmental and motivational issues, and problems with the implementation of the curriculum and selected measures. The results should, therefore, not be taken as conclusive evidence to support the notion that computer programming activities have no impact in other areas of cognitive functioning, mathematic conceptual knowledge, or creative thinking. Instead, the results may help future researchers to further refine their techniques to both deliver effective instruction in the Scratch programming environment, and also target assessments to more accurately measure learning. / Educational Psychology

[pt] No nosso quotidiano ouvimos com frequência falar da importância das Tecnologias de Informação e Comunicação (TIC) pelos diversos atores sociais. A influência das TIC atravessa as diversas áreas da sociedade como: agricultura, serviços, comércio, indústria, investigação, entre outros. Se fizermos um raciocínio inverso será difícil nomearmos campos sociais que não sejam influenciados direta ou indiretamente pelas TIC. Além disso a demanda de trabalhadores em Computer Science e áreas relacionadas a STEM (Science, Technology, Engineering and Mathematics) está em aumento. É por isso mesmo que é importante que as crianças desde tenra idade se interessem pela tecnologia (Programação de computadores) e participem dela de uma forma divertida e lúdica. O presente trabalho propõe a criação de uma ferramenta de Realidade Virtual que permite que os estudantes aprendem conceitos básicos da programação e pensamento computacional tendo como finalidade que eles desfrutem da tecnologia e se sintam motivados em aprender mais. A ferramenta é uma Linguagem Visual de Programação. Os algoritmos são formados mediante a montagem de blocos-, resolvendo com isso um dos principais problemas dos estudantes que são os erros de sintaxe. Além disso a ferramenta traz consigo um conjunto de desafios ordenados por níveis, que têm como finalidade ensinar aos estudantes princípios básicos da programação e a lógica (programação sequencial, estrutura de dados repetitiva e condicional), onde em cada nível o aluno aprenderá as diferentes conceitos e comportamentos do pensamento computacional. Para as avaliações com os usuários se contou com a participação de 18 alunos com idades entre 12 e 15 anos provenientes de duas instituições públicas do Rio de Janeiro. Nestas avaliações considerou-se também medir a sensação de imersão mediante a Telepresença, Presença Social e Usabilidade. / [en] Nowadays, we often hear about the importance of Information and Communication Technologies (ICT) by various social actors. The influence of ICT crosses the various areas of society as agriculture, services, trade, industry, research, among others. If we do an inverse reasoning, it will be difficult to name social fields that are not directly or indirectly influenced by ICTs. In addition, the demand for workers in Computer Science and areas related to the STEM (Science, Technology, Engineering, and Mathematics) is on the rise. That is why it is important to make the young person interested in technology (Computer programming) and participate in it in a fun and playful way. The present work proposes the creation of a Virtual Reality tool that allows students to learn basic concepts of programming and computational thinking with the purpose that they enjoy the technology and feel motivated to learn more. The tool is a Visual Programming Language; the algorithms are formed by block-assembly, thereby solving one of the students main problems, which are syntax errors. In addition, the tool brings with it a set of level-ordered challenges aimed at teaching students basic principles of programming and logic (sequential programming, repetitive and conditional data structure), where at each level the student will learn the different concepts and behaviors of computational thinking. For the evaluations with the users we counted on the participation of 18 students between 12 and 15 years old coming from two public institutions of Rio de Janeiro. In these evaluations it was also considered to measure the sensation of immersion through Telepresence, Social Presence and Usability.

A presente tese apresenta uma investigação acerca do desenvolvimento do raciocínio condicional, considerado um componente chave do pensamento lógico-dedutivo, em crianças e adolescentes que participaram de uma experiência de programação com o software Squeak Etoys. O desenvolvimento do raciocínio condicional é classificado em etapas relacionadas à composição e reversão de transformações que operam sobre a implicação, culminando com a plena reversibilidade que corresponde, na teoria piagetiana, à construção e mobilização do grupo de transformações INRC (Identidade, Negação, Recíproca, Correlativa). Tais etapas são identificadas a partir de entrevistas realizadas segundo o método clínico piagetiano, através da aplicação de três desafios de programação com complexidade crescente, cuja solução envolvia o uso da operação lógica da implicação. As entrevistas foram realizadas com oito crianças, com idades entre 10 e 16 anos, que cursavam as séries finais do Ensino Fundamental de duas escolas públicas. Com base nos dados, a análise revela a importância do pensamento combinatório, que permite aos adolescentes testarem, sistematicamente, todas as possibilidades de ordenamento e inclusão dos comandos sugeridos, e a obterem as conclusões lógicas adequadas, enquanto que as crianças mais novas não obtém o mesmo êxito. Além disso, na tese é realizada uma discussão sobre a inclusão da escola numa cultura digital sob uma perspectiva construtivista de construção do conhecimento. Nesse contexto, a metodologia de projetos de aprendizagem foi apresentada como sendo adequada e o software Squeak Etoys despontou como uma possibilidade interessante de se desenvolver projetos e de promover a aprendizagem de matemática. Por último, neste trabalho também é realizado um debate sobre a importância de se aprender a programar na escola. / The present thesis presents an investigation into the development of conditional reasoning, considered a key component of logical-deductive thinking, in children and adolescents who participated in a programming experience with the software Squeak Etoys. The development of conditional reasoning is classified into stages related to the composition and reversal of transformations that operate on the implication, culminating in the full reversibility that corresponds, in Piaget’s theory, to the construction and mobilization of the Transformations INRC (Identity, Negation, Reciprocity and Correlation). These steps are identified from interviews conducted according to Piaget’s clinical method, through the application of three programming challenges with increasing complexity, whose solution involved the use of the logical operation of the implication. The interviews were conducted with eight children aged 10-16, who attended the final series of the Elementary School of two public schools. Based on the data, the analysis revealed the importance of combining thinking, which allows teenagers to systematically test all the possibilities for ordering and inclusion of the suggested commands, and to obtain the appropriate logical conclusions, while younger children do not achieve the same results. Moreover, in the thesis a discussion is conducted on the inclusion of the school in a digital culture under a constructivist perspective of building knowledge. In this context, the methodology of learning through projects has been presented as being appropriate and the Squeak Etoys software has appeared as an interesting possibility of developing projects and promoting the learning of mathematics. Finally, in this study a debate is also conducted on the importance of learning to plan in the school.

A presente tese apresenta uma investigação acerca do desenvolvimento do raciocínio condicional, considerado um componente chave do pensamento lógico-dedutivo, em crianças e adolescentes que participaram de uma experiência de programação com o software Squeak Etoys. O desenvolvimento do raciocínio condicional é classificado em etapas relacionadas à composição e reversão de transformações que operam sobre a implicação, culminando com a plena reversibilidade que corresponde, na teoria piagetiana, à construção e mobilização do grupo de transformações INRC (Identidade, Negação, Recíproca, Correlativa). Tais etapas são identificadas a partir de entrevistas realizadas segundo o método clínico piagetiano, através da aplicação de três desafios de programação com complexidade crescente, cuja solução envolvia o uso da operação lógica da implicação. As entrevistas foram realizadas com oito crianças, com idades entre 10 e 16 anos, que cursavam as séries finais do Ensino Fundamental de duas escolas públicas. Com base nos dados, a análise revela a importância do pensamento combinatório, que permite aos adolescentes testarem, sistematicamente, todas as possibilidades de ordenamento e inclusão dos comandos sugeridos, e a obterem as conclusões lógicas adequadas, enquanto que as crianças mais novas não obtém o mesmo êxito. Além disso, na tese é realizada uma discussão sobre a inclusão da escola numa cultura digital sob uma perspectiva construtivista de construção do conhecimento. Nesse contexto, a metodologia de projetos de aprendizagem foi apresentada como sendo adequada e o software Squeak Etoys despontou como uma possibilidade interessante de se desenvolver projetos e de promover a aprendizagem de matemática. Por último, neste trabalho também é realizado um debate sobre a importância de se aprender a programar na escola. / The present thesis presents an investigation into the development of conditional reasoning, considered a key component of logical-deductive thinking, in children and adolescents who participated in a programming experience with the software Squeak Etoys. The development of conditional reasoning is classified into stages related to the composition and reversal of transformations that operate on the implication, culminating in the full reversibility that corresponds, in Piaget’s theory, to the construction and mobilization of the Transformations INRC (Identity, Negation, Reciprocity and Correlation). These steps are identified from interviews conducted according to Piaget’s clinical method, through the application of three programming challenges with increasing complexity, whose solution involved the use of the logical operation of the implication. The interviews were conducted with eight children aged 10-16, who attended the final series of the Elementary School of two public schools. Based on the data, the analysis revealed the importance of combining thinking, which allows teenagers to systematically test all the possibilities for ordering and inclusion of the suggested commands, and to obtain the appropriate logical conclusions, while younger children do not achieve the same results. Moreover, in the thesis a discussion is conducted on the inclusion of the school in a digital culture under a constructivist perspective of building knowledge. In this context, the methodology of learning through projects has been presented as being appropriate and the Squeak Etoys software has appeared as an interesting possibility of developing projects and promoting the learning of mathematics. Finally, in this study a debate is also conducted on the importance of learning to plan in the school.

A presente tese apresenta uma investigação acerca do desenvolvimento do raciocínio condicional, considerado um componente chave do pensamento lógico-dedutivo, em crianças e adolescentes que participaram de uma experiência de programação com o software Squeak Etoys. O desenvolvimento do raciocínio condicional é classificado em etapas relacionadas à composição e reversão de transformações que operam sobre a implicação, culminando com a plena reversibilidade que corresponde, na teoria piagetiana, à construção e mobilização do grupo de transformações INRC (Identidade, Negação, Recíproca, Correlativa). Tais etapas são identificadas a partir de entrevistas realizadas segundo o método clínico piagetiano, através da aplicação de três desafios de programação com complexidade crescente, cuja solução envolvia o uso da operação lógica da implicação. As entrevistas foram realizadas com oito crianças, com idades entre 10 e 16 anos, que cursavam as séries finais do Ensino Fundamental de duas escolas públicas. Com base nos dados, a análise revela a importância do pensamento combinatório, que permite aos adolescentes testarem, sistematicamente, todas as possibilidades de ordenamento e inclusão dos comandos sugeridos, e a obterem as conclusões lógicas adequadas, enquanto que as crianças mais novas não obtém o mesmo êxito. Além disso, na tese é realizada uma discussão sobre a inclusão da escola numa cultura digital sob uma perspectiva construtivista de construção do conhecimento. Nesse contexto, a metodologia de projetos de aprendizagem foi apresentada como sendo adequada e o software Squeak Etoys despontou como uma possibilidade interessante de se desenvolver projetos e de promover a aprendizagem de matemática. Por último, neste trabalho também é realizado um debate sobre a importância de se aprender a programar na escola. / The present thesis presents an investigation into the development of conditional reasoning, considered a key component of logical-deductive thinking, in children and adolescents who participated in a programming experience with the software Squeak Etoys. The development of conditional reasoning is classified into stages related to the composition and reversal of transformations that operate on the implication, culminating in the full reversibility that corresponds, in Piaget’s theory, to the construction and mobilization of the Transformations INRC (Identity, Negation, Reciprocity and Correlation). These steps are identified from interviews conducted according to Piaget’s clinical method, through the application of three programming challenges with increasing complexity, whose solution involved the use of the logical operation of the implication. The interviews were conducted with eight children aged 10-16, who attended the final series of the Elementary School of two public schools. Based on the data, the analysis revealed the importance of combining thinking, which allows teenagers to systematically test all the possibilities for ordering and inclusion of the suggested commands, and to obtain the appropriate logical conclusions, while younger children do not achieve the same results. Moreover, in the thesis a discussion is conducted on the inclusion of the school in a digital culture under a constructivist perspective of building knowledge. In this context, the methodology of learning through projects has been presented as being appropriate and the Squeak Etoys software has appeared as an interesting possibility of developing projects and promoting the learning of mathematics. Finally, in this study a debate is also conducted on the importance of learning to plan in the school.

Submitted by Wagner Junior (wagner.junior@unioeste.br) on 2018-07-26T20:37:44Z No. of bitstreams: 2 Felipe_Jose_Rezende_de_Carvalho_2018.pdf: 2958592 bytes, checksum: e4b0edf98a631b77128766f37cc19717 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-07-26T20:37:44Z (GMT). No. of bitstreams: 2 Felipe_Jose_Rezende_de_Carvalho_2018.pdf: 2958592 bytes, checksum: e4b0edf98a631b77128766f37cc19717 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-07-15 / Mathematical Modeling is a trend of Mathematics Education that values, among other things, the exploratory work by the students on themes linked to daily life.It creates the possibility of a an interdisciplinary work together with other tendencies, allowing the construction of knowledge in a dynamic way. Our interest is in the area of inquiry that concerns the association of Mathematical Modeling and Digital Technologies of Information and Communication, specifically regarding the possibilities and challenges of allying computer programming to a Mathematical Modeling task. Moved by this interest, we establish the question: What is revealed of a task of Mathematical Modeling, in the environment of computer programming, developed by students of Basic Education? We seek to understand what is shown when we develop a Mathematical Modeling task allied to computer programming and what the possibilities and the challenges are which emerge from this association. This question guided all research, conducted by a qualitative approach according to a phenomenological view. In order to account for our questioning, we constructed a task of Mathematical Modeling that was developed by students of Basic Education of a public school in the interior of the state of Minas Gerais, through programming in blocks, using Scratch software. The development of this task was recorded by filming videos that were watched several times in such a way that, in the light of our research question, we could highlight relevant passages that converged to our question, and, from them, build our units of meaning. After the construction of these units, from repeated readings, we established convergences, which culminated in four categories, namely: C1: On the debates, discussions and talks between students and between students and teachers in the development of the task; C2: On the actions of the students in the context of the Modeling task; C3: On relationships with school mathematics that emerged in the development of the Modeling task; C4: On the ways students viewed the project. These categories, interpreted hermeneutically, allowed us to observe, among other things, that the task of Modeling guided the development of computational thinking through a computer programming activity, strengthening the discussions and reflections on the context involved by the task, opening space to learn-with-another, in a dialogic and dynamic environment built by the synergy of Modeling with computer programming. / El Modelado Matemático es una tendencia de la Educación Matemática que valora, entre otras cosas, el trabajo exploratorio por parte de los alumnos sobre temáticas relacionadas al cotidiano, posibilitando un trabajo interdisciplinar y conjunto con otras tendencias, dando oportunidad a la construcción de conocimientos de manera dinámica. Nuestro interés está en la región de investigaciones en lo que toca a la asociación del Modelado Matemático y las Tecnologías Digitales de la Información y Comunicación, más específicamente en lo relacionado a las posibilidades y retos de unir la programación de ordenadores a una tarea de Modelado Matemático. Movidos por ese interés, establecemos la pregunta: ¿Qué se revela de una tarea de Modelado Matemático, en el ambiente de programación de ordenadores, desarrollada por estudiantes de la Educación Básica? Buscamos comprender qué se enseña cuando desarrollamos una tarea de Modelado Matemático junto a la programación de ordenadores, cuáles son las posibilidades y los retos que emergen de esa asociación. Esa cuestión ha guiado toda la investigación, conducida por un abordaje cualitativo según una visión fenomenológica. Buscando dar cuenta de nuestra pregunta, construimos una tarea de Modelado Matemático que fue desarrollada por estudiantes de la Educación Básica de una escuela pública del interior del estado de Minas Gerais, por medio de programación en bloques, utilizando para ello el software Scratch. El desarrollo de esa tarea ha sido registrado por grabación de videos que han sido asistidos diversas veces de tal modo que pudiéramos, a la luz de nuestra cuestión de investigación, destacar trechos relevantes que convergían para nuestra pregunta, y, a partir de ellos, construir nuestras unidades de significado. Tras la construcción de esas unidades, a partir de repetidas lecturas, hemos establecido convergencias, que han culminado en cuatro categorías, a saber: C1: Sobre los debates, discusiones y tertulias entre alumnos y entre alumnos y profesores en el desarrollo de la tarea; C2: Sobre las acciones de los alumnos en el contexto de la tarea de Modelado; C3: Sobre las relaciones con la matemática escolar que emergieron en el desarrollo de la tarea de Modelado; C4: Sobre los modos que los alumnos han visto el proyecto. Esas categorías, interpretadas hermenéuticamente, permitieron observar, entre otras cosas, que la tarea de Modelado orientado el desarrollo del pensamiento computacional a través de una actividad de programación de ordenadores, potenciando las discusiones y reflexiones sobre el contexto implicado en la tarea, abriendo espacio para aprender-con-otro, en un ambiente dialógico y dinámico construido por la sinergia del Modelado con la programación de ordenadores. / A Modelagem Matemática é uma tendência da Educação Matemática que valoriza, entre outras coisas, o trabalho exploratório por parte dos alunos sobre temáticas ligadas ao cotidiano, possibilitando um trabalho interdisciplinar e conjunto com outras tendências, oportunizando a construção de conhecimentos de maneira dinâmica. Nosso interesse está na região de inquérito que diz respeito à associação da Modelagem Matemática e as Tecnologias Digitais da Informação e Comunicação, mais especificamente no que tange às possibilidades e desafios de aliar a programação de computadores a uma tarefa de Modelagem Matemática. Movidos por esse interesse, estabelecemos a interrogação: O que se revela de uma tarefa de Modelagem Matemática, no ambiente de programação de computadores, desenvolvida por estudantes da Educação Básica? Buscamos compreender o que se mostra quando desenvolvemos uma tarefa de Modelagem Matemática aliada à programação de computadores, quais são as possibilidades e os desafios que emergem dessa associação. Essa interrogação guiou toda a pesquisa, conduzida por uma abordagem qualitativa segundo uma visão fenomenológica. Buscando dar conta de nossa interrogação, construímos uma tarefa de Modelagem Matemática que foi desenvolvida por estudantes da Educação Básica de uma escola pública do interior do estado de Minas Gerais, por meio de programação em blocos, utilizando para isso o software Scratch. O desenvolvimento dessa tarefa foi registrado por gravação de vídeos que foram assistidos diversas vezes de tal modo que pudéssemos, à luz da nossa interrogação de pesquisa, destacar trechos relevantes que convergiam para nossa interrogação, e, a partir deles, construir nossas unidades de significado. Após a construção dessas unidades, a partir de repetidas leituras, estabelecemos convergências, que culminaram em quatro categorias, a saber: C1: Sobre os debates, discussões e falas entre alunos e entre alunos e professores no desenvolvimento da tarefa; C2: Sobre as ações dos alunos no contexto da tarefa de Modelagem; C3: Sobre as relações com a matemática escolar que emergiram no desenvolvimento da tarefa de Modelagem; C4: Sobre os modos que os alunos viram o projeto. Essas categorias, interpretadas hermeneuticamente, permitiram observar, dentre outras coisas, que a tarefa de Modelagem norteou o desenvolvimento do pensamento computacional por meio de uma atividade de programação de computadores, potencializando as discussões e reflexões sobre o contexto envolvido pela tarefa, abrindo espaço para aprender-com-outro, em um ambiente dialógico e dinâmico construído pela sinergia da Modelagem com a programação de computadores.