DOCSLIB.ORG

Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü KARADENİZ TEKNİK ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ BİLGİSAYAR MÜHENDİSLİĞİ ANABİLİM DALI POLİNOMLAR İÇİN BİR SİMGESEL HESAPLAMA ÇATISININ TASARIMI VE GERÇEKLENMESİ YÜKSEK LİSANS TEZİ Seda EFENDİOĞLU HAZİRAN - 2017 TRABZON KARADENİZ TEKNİK ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsünce Unvanı Verilmesi İçin Kabul Edilen Tezdir. Tezin Enstitüye Verildiği Tarih : / / Tezin Savunma Tarihi : / / Tez Danışmanı : Trabzon KARADENİZ TEKNİK ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ başlıklı bu çalışma, Enstitü Yönetim Kurulunun / / gün ve sayılı kararıyla oluşturulan jüri tarafından yapılan sınavda YÜKSEK LİSANS TEZİ olarak kabul edilmiştir. Jüri Üyeleri Başkan : …...……………………....……… Üye : …...…………....………………… Üye : ……...……………....…………… Prof. Dr. Sadettin KORKMAZ Enstitü Müdürü ÖNSÖZ Fonksiyonların özel bir türü olan polinomlar, türevleri sürekli oldugu˘ için mühendis- lik problemlerinin birçogunun˘ temsilinde ve çözümünde kullanılır. Simgesel hesaplama, bir problemin tam çözümünün bilgisayarlar yardımıyla bulunabilmesi için gereklidir. Bu yüzden mühendislik alanında yer alan polinom problemlerini iyi analiz edebilecek ve bu problemleri çözebilecek nitelikli simgesel hesaplama uygulamalarına ihtiyaç duyulur. Yapılan tez çalı¸smasında,kullanıcıların polinom problemleriyle ilgili simgesel hesap- lama i¸slemlerinidesteklemek için kullanabilecekleri bir uygulama çatısının tasarım ve geli¸s- tirme a¸samalarısunulmu¸stur. Ayrıca bu çatı üzerinde geli¸stirilmi¸sMathBox isimli uygulama- nın, benzerlerini üretip adım adım çözebildigi˘ polinom problemleri ve bu problemlerle ili¸skili degerlendirmeler˘ gösterilmi¸stir. Simgesel hesaplamayla çözülebilen polinom problemlerini temsil etmek için biçimsel dil tanımlamalarından yararlanılmı¸stır. Polinomların simgesel he- saplanması alanında iyi bir uygulama çatısının geli¸stirilebilmesiiçin literatürdeki çalı¸smalar incelenmi¸stir. Geli¸stirilençatı, bu alandaki gereksinimleri kar¸sılayacakniteliklere sahiptir. Yüksek lisans tez çalı¸smamdadanı¸smanlıgımı˘ üstlenen hocam Yrd. Doç. Dr. Hüseyin PEHLIVAN’a˙ destek ve tecrübelerinden dolayı te¸sekkürlerimiborç bilirim. Her an yanımda olan, sevgi, ilgi ve bilgisini hiçbir zaman esirgemeyen e¸simHilmi Emre EFENDIO˙ GLU’na˘ çok te¸sekkürederim. Ba¸stababam olmak üzere, dünyadaki en iyi baba olma ihtimali oldukça yüksektir, annem, ablam Selin, kızkarde¸slerim ¸Seyma ve Gülsüm ile evimizin en küçügü˘ Miraç’ımıza sevgi dolu kalpleri, en stresli anlarımda bile bana kar¸sıolan sabır ve anlayı¸sları, kendimi en çaresiz hissettigim˘ zamanlarda bile bana verdikleri destek ve ne¸sedendolayı çok te¸sekkürederim. Seda EFENDIO˙ GLU˘ Trabzon 2017 III TEZ ETIK˙ BEYANNAMESI˙ Yüksek Lisans Tezi olarak sundugum˘ “POLINOMLAR˙ IÇ˙ IN˙ BIR˙ SIMGESEL˙ HE- SAPLAMA ÇATISININ TASARIMI VE GERÇEKLENMESI”˙ ba¸slıklıbu çalı¸smayıba¸stan sona kadar danı¸smanımYrd. Doç. Dr. Hüseyin PEHLIVAN‘ın˙ sorumlulugunda˘ tamamla- dıgımı,˘ verileri/örnekleri kendim topladıgımı,˘ deneyleri/analizleri ilgili laboratuarlarda yap- tıgımı/yaptırdı˘ gımı,˘ ba¸skakaynaklardan aldıgım˘ bilgileri metinde ve kaynakçada eksiksiz olarak gösterdigimi,˘ çalı¸smasürecinde bilimsel ara¸stırmave etik kurallara uygun olarak dav- randıgımı˘ ve aksinin ortaya çıkması durumunda her türlü yasal sonucu kabul ettigimi˘ beyan ederim. 01/06/2017 Seda EFENDIO˙ GLU˘ IV IÇ˙ INDEK˙ ILER˙ Sayfa No ÖNSÖZ . III TEZ ETIK˙ BEYANNAMESI..............................˙ IV IÇ˙ INDEK˙ ILER.....................................˙ V ¸SEKILLER˙ DIZ˙ IN˙ I...................................˙ X TABLOLAR DIZ˙ IN˙ I..................................˙ XII KISALTMALAR DIZ˙ IN˙ I................................˙ XIV 1. GIR˙ I¸S......................................˙ 1 2. GENEL BILG˙ ILER˙ . .5 2.1. Polinomlar . 5 2.1.1. Çalı¸smaKapsamında Ilgilenilen˙ Polinom Problemleri . 5 2.1.2. Polinomların Bilgisayar Ortamında Temsil Edilmesi . 7 2.2. Agaçlarda˘ Dola¸smaYöntemleri . 8 2.2.1. Kök Önce Yöntemi . 8 2.2.2. Kök Ortada Yöntemi . 9 2.2.3. Kök Sonda Yöntemi . 10 2.3. Çeviriciler . 11 2.3.1. Yorumlayıcılar . 11 2.3.2. Derleyiciler . 11 2.4. Uygulama Çatıları . 16 2.5. Kullanılan Teknolojiler . 17 2.5.1. JavaScript . 17 2.5.2. JSON . 17 3. UYGULAMA ÇATISININ GENEL YAPISI . 19 3.1. MathBox . 20 4. POLINOM˙ PROBLEMLERIN˙ IN˙ ANALIZ˙ I..................˙ 23 4.1. Sözcüksel Analiz . 23 4.2. Sözdizimsel Analiz . 25 4.3. Soyut Sözdizim Agacının˘ JSON Verisine Dönü¸stürülmesi . 28 V 4.4. Matematik Nesneleri . 30 5. POLINOM˙ PROBLEMLERIN˙ IN˙ SADELE¸STIR˙ ILMES˙ I...........˙ 31 5.1. Temel Sınıf Yapıları Içerisinde˙ Yapılan Sadele¸stirmeler . 32 5.1.1. Toplama Sınıfı . 32 5.1.2. Çarpma Sınıfı . 35 5.1.3. Üs Sınıfı . 39 5.1.4. Çıkarma Sınıfı . 42 5.1.5. Bölme Sınıfı . 44 5.2. Özel Metodlar Yardımıyla Yapılan Sadele¸stirmeler. 45 5.2.1. Pascal Üçgeninin Hesaplanması . 45 5.2.2. Binom Açılımının Yapılması . 45 5.2.3. Benzer Ifadelerin˙ Eliminasyonu . 46 6. POLINOM˙ PROBLEMLERIN˙ IN˙ ÜRETILMES˙ I...............˙ 47 6.1. Soru Sınıfı . 47 6.2. Sayı Sınıfı . 48 6.3. Toplama Sınıfı . 49 6.4. Fonksiyon Sınıfı . 50 6.5. Degi¸sken˘ Sınıfı . 51 6.6. Benzer Problemlerin Üretim Analizleri . 52 6.6.1. Süre Analizi . 52 6.6.2. Bellek Analizi . 53 6.6.3. Performans Analizi . 54 6.6.4. Üretilen Problemlerin Farklılıgının˘ Analizi . 55 6.6.5. Dügüm˘ Sayısı ve Derinlik Analizi . 56 7. POLINOM˙ PROBLEMLERIN˙ IN˙ ADIM ADIM ÇÖZÜMÜ . 57 7.1. Geri Zincirleme . 57 7.2. Cam Kutu . 59 7.3. Çözüm Animasyonu . 59 7.4. Problemlerin Çözüm Analizleri . 60 7.4.1. Süre Analizi . 60 7.4.2. Bellek Analizi . 61 7.4.3. Performans Analizi . 62 VI 7.4.4. Dogruluk˘ Analizi . 63 7.4.5. Dügüm˘ Sayısı, Derinlik ve Sadele¸stirmeAnalizi . 64 8. ENTEGRASYON . 65 8.1. Uygulama Programlama Arayüzü (UPA) . 66 8.2. Entegrasyon Yakla¸sımları . 67 8.2.1. Çevrimiçi UPA Yardımıyla Entegrasyon . 67 8.2.2. Bile¸senOlarak Entegrasyon . 68 9. SONUÇLAR . 69 10. GELECEK ÇALI¸SMALAR . 71 11. KAYNAKLAR . 72 ÖZGEÇMI¸S˙ VII Yüksek Lisans Tezi ÖZET POLINOMLAR˙ IÇ˙ IN˙ BIR˙ SIMGESEL˙ HESAPLAMA ÇATISININ TASARIMI VE GERÇEKLENMESI˙ Seda EFENDIO˙ GLU˘ Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü Bilgisayar Mühendisligi˘ Anabilim Dalı Danı¸sman:Yrd. Doç. Dr. Hüseyin PEHLIVAN˙ 2017, 75 Sayfa Simgesel hesaplama, bir problemin tam çözümünün bulunabilmesi için kullanılır. Sim- gesel hesaplamaları hatasız olarak hızlı bir ¸sekildeyapabilen çok sayıda uygulama geli¸sti- rilmi¸stir. Ancak bu uygulamalar sadece kendi kullanıcı arayüzleri ile kullanılacak ¸sekilde tasarlandıgı˘ için ba¸skahesaplama ortamlarına entegre edilemezler veya bu ortamların bir bile¸seniolarak çalı¸stırılamazlar. Bu çalı¸smada,kullanıcıların polinomlarla ilgili simgesel hesaplama i¸slemlerinides- teklemek için kullanabilecekleri bir uygulama çatısının tasarımı ve geli¸stirmea¸samalarısu- nulmu¸stur. Bir polinom problemini temsil etmek için biçimsel dil tanımlamalarından yarar- lanılmı¸stır. Öncelikle polinom problemlerinin biçimlerine yönelik olarak gramer kuralları tanımlanmı¸sve dil ayrı¸stırmai¸slemleriuygulanarak ilgili problemlerin soyut sözdizim agaç-˘ ları üretilmi¸stir. Bu agaçlar˘ tüm programlama dilleri tarafından kullanılabilmeleri için JSON (JavaScript Object Notation) veri degi¸simbiçimindeki˘ ifadelere dönü¸stürülüpkaydedilmi¸s- tir. Ardından sadele¸stirmei¸slemleriuygulanarak bu ifadelerin nesne temsilleri elde edilmi¸s- tir. Son olarak bu nesne temsilleri üzerinde çe¸sitlisayısal ve simgesel hesaplama i¸slemleri tanımlanarak polinom problemlerinin sadele¸stirilmesine,adım adım çözülmesine ve benzer- lerinin üretilmesine destek verilmi¸stir. Anahtar Kelimeler: Sembolik Hesaplama, Polinomlar, Otomatik Problem Üretimi, Adım-Adım Problem Çözümü, Sadele¸stirme, Gramerler, Ja- vaCC, AST, JSON, UPA. VIII Master Thesis SUMMARY DESIGN AND IMPLEMENTATION OF A SYMBOLIC COMPUTATION FRAMEWORK FOR POLYNOMIALS Seda EFENDIO˙ GLU˘ Karadeniz Technical University The Graduate School of Natural and Applied Sciences Computer Engineering Graduate Program Supervisor: Asst. Prof. Dr. Hüseyin PEHLIVAN˙ 2017, 75 Pages Symbolic computation is used to find exact solution of a problem. Numerous applica- tions have been developed that can quickly perform symbolic computations without errors. However, since these applications are designed to be used only with their own user interfa- ces, they can not be integrated into other computing environments or run as a component of those environments. In this study, the development stages of an application framework that can be used by users to support symbolic computation operations on polynomials are presented. Formal language definitions have been used to represent a polynomial problem. Firstly, grammar rules are defined for the forms of polynomial problems, and abstract syntax trees of related problems are generated by applying language parsing operations. These trees are converted to expressions in JSON (JavaScript Object Notation) data interchange format so that they can be used by all programming languages. Then simplification operations are applied to obtain object representations of these expressions. Finally, various numerical and symbolic com- putation operations are defined on these object representations to support the simplification of polynomial problems, the step by step solution of problems and the generation of similar problems. Key Words: Symbolic Computation, Polynomials, Automatic Problem Generation, Step-by-Step Problem Solution, Simplification, Grammars, JavaCC, AST, JSON, API. IX ¸SEKILLER˙ DIZ˙ IN˙ I˙ Sayfa No ¸Sekil2.1. ab/c ifadesini temsil eden agaçlar˘ . 7 ¸Sekil2.2.
Load more

Recommended publications
  • Estimado Profesor
    México, D.F., a 15 de abril de 2016 CURRICULUM VITAE Nombre: RICARDO LÓPEZ BAUTISTA Departamento de Adscripción: CIENCIAS BASICAS, Profesor titular "A", tiempo Completo, definitivo en UAM-Azcapotzalco Correo electrónico: [email protected] Formación Profesional: DOCTOR EN CIENCIAS en la especialidad de Matemáticas por el Centro de Investigación y de Estudios Avanzados del I.P.N. (CINVESTAV) con Mención Honorífica. ESTANCIA POSTDOCTORAL Departamento de Matemáticas de la Ohio StateUniversity (USA). 2000 Líneas de investigación: 1) EVALUACIÓN EN LINEA y GENERACIÓN AUTOMATIZADA DE MILLONES DE REACTIVOS CON RETROALIMENTACION AUTOMATICA, PARA BANCOS DE EXÁMENES EN MATEMÁTICAS. a. Experto en plataforma MOODLE- LCMS (Learning Content Management System) b. Programador en diversos CAS (Computer Algebraic System) Axiom, Mathematica, Maple, Mathlab, Geogebra, Magma, SageMath, Maxima, SymPy, Xcas, Yacas, Pari-GP, Octave, GAP, CoCoA, Algebrator, MathCad 2) TEORIA ALGEBRAICA DE NUMEROS, FACTORIZACION DE ENTEROS, SEGURIDAD ELECTRONICA 3) SISTEMAS ALGEBRAICOS COMPUTACIONALES (CAS). a. INVESTIGACIÓN Y APLICACIONES DE CAS EN TEORÍA DE NÚMEROS. b. INVESTIGACIÓN Y APLICACIONES DE CAS EN MODELOS MIXTOS PARA LA EDUCACIÓN Y EVALUACIÓN EN MATEMÁTICAS 4) TECNOMATEMÁTICA EDUCATIVA EN MODELOS PRESENCIALES, NO PRESENCIALES Y MIXTOS. SISTEMAS ALGEBRAICOS COMPUTACIONALES EN LA EDUCACION Y EVALUACION EN MATEMÁTICAS. a. Portales activos para la comunidad en UAM-A: http://galois.azc.uam.mx http://evaluacionenlinea.azc.uam.mx http://matematicas.azc.uam.mx Proyecto CONACyT: Evaluación del aprendizaje en Matemáticas y propuesta de evaluaciones automáticas en línea. Aprobado en 2012, por concluir. 1 Formación de recursos humanos: Tesis de alumna de maestría: Jurado en examen doctoral. Uam Proyectos Terminales en Maestría en Ciencias de la Iztapalapa.
    [Show full text]
  • Constructing a Computer Algebra System Capable of Generating Pedagogical Step-By-Step Solutions
    DEGREE PROJECT IN COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2016 Constructing a Computer Algebra System Capable of Generating Pedagogical Step-by-Step Solutions DMITRIJ LIOUBARTSEV KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF COMPUTER SCIENCE AND COMMUNICATION Constructing a Computer Algebra System Capable of Generating Pedagogical Step-by-Step Solutions DMITRIJ LIOUBARTSEV Examenrapport vid NADA Handledare: Mårten Björkman Examinator: Olof Bälter Abstract For the problem of producing pedagogical step-by-step so- lutions to mathematical problems in education, standard methods and algorithms used in construction of computer algebra systems are often not suitable. A method of us- ing rules to manipulate mathematical expressions in small steps is suggested and implemented. The problem of creat- ing a step-by-step solution by choosing which rule to apply and when to do it is redefined as a graph search problem and variations of the A* algorithm are used to solve it. It is all put together into one prototype solver that was evalu- ated in a study. The study was a questionnaire distributed among high school students. The results showed that while the solutions were not as good as human-made ones, they were competent. Further improvements of the method are suggested that would probably lead to better solutions. Referat Konstruktion av ett datoralgebrasystem kapabelt att generera pedagogiska steg-för-steg-lösningar För problemet att producera pedagogiska steg-för-steg lös- ningar till matematiska problem inom utbildning, är vanli- ga metoder och algoritmer som används i konstruktion av datoralgebrasystem ofta inte lämpliga. En metod som an- vänder regler för att manipulera matematiska uttryck i små steg föreslås och implementeras.
    [Show full text]
  • A Meta-Analysis of the Past Decade of Mathematics Learning Based on the Computer Algebra System (CAS)
    Journal of Physics: Conference Series PAPER • OPEN ACCESS A Meta-Analysis of the Past Decade of Mathematics Learning Based on the Computer Algebra System (CAS) To cite this article: M Tamur et al 2021 J. Phys.: Conf. Ser. 1882 012060 View the article online for updates and enhancements. This content was downloaded from IP address 170.106.33.14 on 23/09/2021 at 10:32 SEA-STEM 2020 IOP Publishing Journal of Physics: Conference Series 1882 (2021) 012060 doi:10.1088/1742-6596/1882/1/012060 A Meta-Analysis of the Past Decade of Mathematics Learning Based on the Computer Algebra System (CAS) M Tamur1,4, Y S Ksumah2, D Juandi2, V S Kurnila1, E Jehadus1 and A O Samura3 1Universitas Katolik Indonesia Santu Paulus Ruteng, Ruteng, Indonesia 2Universitas Pendidikan Indonesia, Bandung, Indonesia 3Institut Agama Islam Negeri Ternate, Ternate, Indonesia E-mail: [email protected] Abstract. Hundreds of studies have been found in the literature on mathematics learning supported by the use of the computer algebra system (CAS). However, there are numerous reports with mixed and even contradictory findings. This has the potential to lead to errors in concluding. This meta-analysis study was conducted to test the overall effect size (ES) of CAS-based mathematics learning. This study also aims to analyze the level of variation in individual studies and consider its implications. The ERIC, SAGE, SpringerLink, and Google Scholar databases were examined to achieve relevant research. The search results found 136 related journal articles published between 2010 and 2020. As per the study protocol, 31 articles were eligible, and 36 ES were analyzed.
    [Show full text]
  • An Approach to Teach Calculus/Mathematical Analysis (For
    Sandra Isabel Cardoso Gaspar Martins Mestre em Matemática Aplicada An approach to teach Calculus/Mathematical Analysis (for engineering students) using computers and active learning – its conception, development of materials and evaluation Dissertação para obtenção do Grau de Doutor em Ciências da Educação Orientador: Vitor Duarte Teodoro, Professor Auxiliar, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa Co-orientador: Tiago Charters de Azevedo, Professor Adjunto, Instituto Superior de Engenharia de Lisboa do Instituto Politécnico de Lisboa Júri: Presidente: Prof. Doutor Fernando José Pires Santana Arguentes: Prof. Doutor Jorge António de Carvalho Sousa Valadares Prof. Doutor Jaime Maria Monteiro de Carvalho e Silva Vogais: Prof. Doutor Carlos Francisco Mafra Ceia Prof. Doutor Francisco José Brito Peixoto Prof. Doutor António Manuel Dias Domingos Prof. Doutor Vítor Manuel Neves Duarte Teodoro Prof. Doutor Tiago Gorjão Clara Charters de Azevedo Janeiro 2013 ii Título: An approach to teach Calculus/Mathematical Analysis (for engineering students) using computers and active learning – its conception, development of materials and evaluation 2012, Sandra Gaspar Martins (Autora), Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa e Universidade Nova de Lisboa A Faculdade de Ciências e Tecnologia e a Universidade Nova de Lisboa tem o direito, perpétuo e sem limites geográficos, de arquivar e publicar esta dissertação através de exemplares impressos reproduzidos em papel ou de forma digital, ou por qualquer outro meio conhecido ou que venha a ser inventado, e de a divulgar através de repositórios científicos e de admitir a sua cópia e distribuição com objectivos educacionais ou de investigação, não comerciais, desde que seja dado crédito ao autor e editor.
    [Show full text]
  • Masarykova Univerzita Informační Technologie Pro
    MASARYKOVA UNIVERZITA 5 c FAKULTA INFORMATIKY m INFORMAČNÍ TECHNOLOGIE PRO MODELOVÁNÍ A SIMULACE DIPLOMOVÁ PRÁCA Brno, 2013 Bc. KAMIL DUREC 5 c m PREHLÁSENIE Prehlasujem, že táto práca je mojím pôvodným autorským dielom, ktoré som vypracoval samostatne. Všetky zdroje, pramene a literatúru, ktoré som pri vypracovaní použil alebo z nich čerpal, v práci riadne citujem s uvedením úplného odkazu na príslušný zdroj. Bc. Kamil Durec Vedúci práce: prof. RNDr. Jiří Hřebíček, CSc. ZHRNUTIE Cieľom mojej diplomovej práce je prieskum v oblasti súčasného stavu informačných a komunikačných technológií určených na modelovanie a simulácie procesov v praxi. Z prieskumu bude vybraná vhodná ICT, ktorá bude podrobne preskúmaná a popísané jej vlastnosti. Určením vhodného problému, bude predvedený postup jeho riešenia za pomoci vybratej ICT a pomocou počítačovej simulácie analýza vlastností získaného riešenia. KĽÚČOVÉ SLOVÁ simulácia, modelovanie, systém počítačovej algebry, computer algebra system, CAS, Maple, MapleSim, robotická ruka Obsah 1 Úvod ...................................................................................................................................... 5 2 Teória simulácie a modelovania ............................................................................................ 6 2.1. Experiment ......................................................................................................................... 7 2.2. Model ................................................................................................................................
    [Show full text]
  • Ïé Ôðå Óôçí Åêðáßäåõóç
    ΠΕΡΙΕΧΟΜΕΝΑ 1. ΕΙΣΑΓΩΓΗ……………………………………………………………… 2 ΟΙ ΤΠΕ ΣΤΗΝ ΕΚΠΑΙ∆ΕΥΣΗ 2. ΘΕΩΡΗΣΕΙΣ ΓΙΑ ΤΑ ΜΑΘΗΜΑΤΙΚΑ ………………………………... 10 3. ΟΙ ΤΠΕ ΚΑΙ ΤΑ ΜΑΘΗΜΑΤΙΚΑ……………………………………… 19 4. ΛΟΓΙΣΜΙΚΟ ΓΙΑ ΤΗΝ ∆Ι∆ΑΣΚΑΛΙΑ ΤΩΝ ΜΑΘΗΜΑΤΙΚΩΝ……. 23 5. ΕΚΠΑΙ∆ΕΥΤΙΚΕΣ ∆ΡΑΣΤΗΡΙΟΤΗΤΕΣ………………………………. 41 5.1. ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ - ΣΧΕ∆ΙΑΣΜΟΣ ΕΚΠΑΙ∆ΕΥΤΙΚΩΝ ∆ΡΑΣΤΗΡΙΟΤΗΤΩΝ………………………………………………… 44 5.2. ΚΡΙΤΗΡΙΑ ΕΠΙΛΟΓΗΣ ∆Ι∆ΑΚΤΙΚΩΝ ΑΝΤΙΚΕΙΜΕΝΩΝ………….45 5.3. ΚΑΤΑΓΡΑΦΗ Α∆ΥΝΑΜΙΩΝ ΤΩΝ ΜΑΘΗΤΩΝ ΣΤΑ ΜΑΘΗΜΑΤΙΚΑ ΚΑΙ ΕΙ∆ΙΚΟΤΕΡΑ ΣΤΗΝ ΚΑΤΑΝΟΗΣΗ ΤΗΣ ΕΝΝΟΙΑΣ ΤΗΣ ΟΜΟΙΟΤΗΤΑΣ ΤΡΙΓΩΝΩΝ…………………………………………..47 6. ΚΡΙΤΗΡΙΑ ΕΠΙΛΟΓΗΣ ΤΩΝ ΛΟΓΙΣΜΙΚΩΝ Sketchpad ΚΑΙ Microworlds Pro ΓΙΑ ΤΗ ∆Ι∆ΑΣΚΑΛΙΑ ΤΗΣ ΕΝΝΟΙΑΣ ΤΗΣ ΟΜΟΙΟΤΗΤΑΣ ΤΡΙΓΩΝΩΝ……………………………………………… 51 7. ΕΦΑΡΜΟΓΗ ΣΤΟ ΣΧΟΛΕΙΟ……………………………………………53 8. ΠΑΡΟΥΣΙΑΣΗ ∆Ι∆ΑΚΤΙΚΩΝ ∆ΡΑΣΤΗΡΙΟΤΗΤΩΝ ΓΙΑ ΤΗΝ ΟΜΟΙΟΤΗΤΑ ΤΡΙΓΩΝΩΝ ………………………………………………56 9. ΣΥΜΠΕΡΑΣΜΑΤΑ……………………………………………………..112 10. ΒΙΒΛΙΟΓΡΑΦΙΑ……………………………………………………….116 1 1. ΕΙΣΑΓΩΓΗ Οι ΤΠΕ στην εκπαίδευση Σύµφωνα µε τη διεθνή ερευνητική εµπειρία (Hoyles and Noss 1992), αλλά και µε τις σύγχρονες φιλοσοφικές και παιδαγωγικές θέσεις (Olson 1987, Noss 1988) οι Τεχνολογίες της Πληροφορίας και της Επικοινωνίας µπορούν να δώσουν δυνατότητες που ήταν ανύπαρκτες µέχρι τώρα. Οι καταλυτικές αλλαγές στην τεχνολογία και η εµφάνιση των Η/Υ επαναστατικοποίησαν όλες τις περιοχές της γνώσης και της επιστήµης και συνέβαλαν αποφασιστικά στην ποιοτική µεταβολή της κοινωνίας µε τη µετάβασή της από τη βιοµηχανική, στην τεχνολογική κοινωνία της γνώσης και της πληροφορίας. Η προσφορά της πληροφορικής στην εκπαίδευση σήµερα καθορίζεται από τις λύσεις που παρέχει σε διάφορα διδακτικά προβλήµατα αλλά κυρίως µέσα από τις δυνατότητες µεταφοράς διδακτικών τεχνικών και την ανάπτυξη νέων εκπαιδευτικών µεθόδων. Ο υπολογιστής ως πνευµατικό εργαλείο είναι µία άλλη προσφορά της πληροφορικής που συνεισφέρει στους παραπάνω τοµείς και ανοίγει νέους δρόµους στη µαθησιακή διαδικασία. (Παναγιωτακόπουλος 2002, Μικρόπουλος και Κόµης 2002).
    [Show full text]
  • Analysis of a Selection of Educational ICT Systems
    Analysis of a selection of educational ICT systems for mathematics Jean-François Nicaud, Jehad Alshwaikh, Papadopoulo Argyro, Michele Cerulli, Brigitte Grugeon, Mirko Maracci, Jana Trgalova To cite this version: Jean-François Nicaud, Jehad Alshwaikh, Papadopoulo Argyro, Michele Cerulli, Brigitte Grugeon, et al.. Analysis of a selection of educational ICT systems for mathematics. 2006. hal-00591619 HAL Id: hal-00591619 https://hal.archives-ouvertes.fr/hal-00591619 Submitted on 10 May 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. D20.5.1 (Final) Analysis of a selection of educational ICT systems for mathematics Main author : Jean-François Nicaud (UJF) Nature of the deliverable : Report Dissemination level : Public Planned delivery date : October 2006 No part of this document may be distributed outside the consortium / EC without written permission from the project co-ordinator Prepared for the European Commission, DG INFSO, under contract N°. IST 507838 as a deliverable from WP20 Submitted on 18-11-2006 Summary The deliverable describes a grid that has been designed to study ILEs (Iteractive Learning Environments) in arithmetic and algebra, a process for choosing 6 ILEs to be studied and the result of the studies.
    [Show full text]
  • Analysis of a Selection of Educational ICT Systems for Mathematics
    See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/281884782 Analysis of a selection of educational ICT systems for mathematics Article · January 2006 CITATIONS READS 0 18 7 authors, including: Jean-François Nicaud Jehad Alshwaikh University Joseph Fourier - Grenoble 1 Birzeit University 68 PUBLICATIONS 282 CITATIONS 29 PUBLICATIONS 40 CITATIONS SEE PROFILE SEE PROFILE Mirko Maracci Jana Trgalova University of Pavia Claude Bernard University Lyon 1 28 PUBLICATIONS 119 CITATIONS 66 PUBLICATIONS 86 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Wits Maths Connect Secondary Project View project M C Squared View project All content following this page was uploaded by Jean-François Nicaud on 01 October 2015. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Analysis of a selection of educational ICT systems for mathematics Jean-Fran¸coisNicaud, Jehad Alshwaikh, Papadopoulo Argyro, Michele Cerulli, Brigitte Grugeon, Mirko Maracci, Jana Trgalova To cite this version: Jean-Fran¸coisNicaud, Jehad Alshwaikh, Papadopoulo Argyro, Michele Cerulli, Brigitte Gru- geon, et al.. Analysis of a selection of educational ICT systems for mathematics. deliverable D20.5.1 from ERT Telma in the NoE Kaleidscope. 2006. <hal-00591619> HAL Id: hal-00591619 https://hal.archives-ouvertes.fr/hal-00591619 Submitted on 10 May 2011 HAL is a multi-disciplinary open access L'archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destin´eeau d´ep^otet `ala diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publi´esou non, lished or not.
    [Show full text]
  • Programa De Pós-Graduação Em Educação Em Ciências E Matemática
    PROGRAMA DE PÓS-GRADUAÇÃO EM EDUCAÇÃO EM CIÊNCIAS E MATEMÁTICA Ana Cristina Andrejew Ferreira O USO DO COMPUTADOR COMO RECURSO MEDIADOR NA DISCIPLINA DE MATEMÁTICA NO ENSINO MÉDIO Dissertação de mestrado Porto Alegre, 2004. 2 Ana Cristina Andrejew Ferreira O USO DO COMPUTADOR COMO RECURSO MEDIADOR NA DISCIPLINA DE MATEMÁTICA NO ENSINO MÉDIO Dissertação apresentada como Requisito Parcial à obtenção do grau de mestre, pelo programa de Pós-Graduação em Educação em Ciências e Matemática da Pontifícia Universidade Católica do Rio Grande do Sul Orientador: Dr. Lorí Viali Porto Alegre, 2004. Dados Internacionais de Catalogação na Publicação (CIP) F383u Ferreira, Ana Cristina Andrejew O uso do computador como recurso mediador na disciplina de matemática no ensino médio / Ana Cristina Andrejew Ferreira. - Porto Alegre, 2004. 126f. : il. Dissertação (Mestrado) - Fac. de Química, PUCRS, 2004. 1. Informática na Educação. 2. Matemática - Ensino. 3. Ensino através do Computador. 4. Métodos e Técnicas de Ensino. 5. Tecnologia Educacional. I. Título. CDD 371.39445 Bibliotecária Responsável: Deisi Hauenstein CRB-10/1479 4 Agradecimentos Aos meus familiares, que trouxeram inspiração, tranqüilidade, desejo de superação e vontade de vencer. Aos professores com os quais aprendi, especialmente meu orientador Dr. Lorí Viali, e aos amigos que auxiliaram e contribuíram para o desenvolvimento deste trabalho. 5 “Estamos saindo da civilização reta do estilo para entrar na dos teclados, planária, volumosa e descentrada. Isso nos mudará, corpos e almas, e isso transformará o tempo”. (Serres, p. 25) 6 Resumo O propósito deste trabalho é abordar o uso do computador como ferramenta auxiliar da aprendizagem Matemática no Ensino Médio. Para isto foi levantado o uso de softwares, tutoriais, sites , applets , portais e planilha no ensino de Matemática.
    [Show full text]
  • CAS Computer Algebra System
    Wspomaganie obliczeń matematycznych dr inż. Michał Michna Wspomaganie obliczeń matematycznych Potrzeby Projektowanie Modelowanie Symulacja Analiza wyników Narzędzia Obliczenia algebraiczne, optymalizacja Rozwiązywanie układów równań algebraicznych i różniczkowych Prezentacja wyników, interpolacja, aproksymacja Import / eksport danych 2 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych Numeryczne obliczenia Matlab Scilab Octave obliczenia w dużej skali algorytmy numeryczne wizualizacja wyników Toolbox’y – Matlab Simulink 3 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych CAS – computer algebra system Obliczenia symboliczne Maple Mathematica MathCad Maxima Algorytmy numeryczne, Wizualizacja wyników możliwości składu tekstów matematycznych 4 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych Metoda rachunku numeryczny symboliczny Możliwość rozwiązywania trudnych zazwyczaj tak zazwyczaj nie zadań praktycznych Wielość metod o różnej tak tak skuteczności Wymaga wiedzy wykraczającej poza najczęściej tak najczęściej nie rozwiązywane zadanie skończony zestaw liczb wzór lub informacja o Wynik lub rysunek charakterze rozwiązania 5 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych Metoda rachunku numeryczny symboliczny Potrafi działać na nie tak abstrakcyjnych obiektach Dobrze radzi sobie z zazwyczaj nie zazwyczaj tak nieskończonościami Dobrze radzi sobie z tak nie mnogością parametrów teoretycznie Precyzja wyniku ograniczona nieskończona Ostateczna jakość niepewna
    [Show full text]
  • Propuesta: Diplomado En Enseñanza De Las Matemáticas Asistidas Por Software
    INSTITUTO TECNOLÓGICO SUPERIOR DE CALKINÍ EN EL ESTADO DE CAMPECHE PROPUESTA: DIPLOMADO EN ENSEÑANZA DE LAS MATEMÁTICAS ASISTIDAS POR SOFTWARE EN EL NIVEL SUPERIOR 2011-2012 M. E. Julio César Pech Salazar Dr. Juan Manuel Camacho Pérez Diplomado en Enseñanza de las Matemáticas en el Nivel Superior Asistidas 1 por Software INSTITUTO TECNOLÓGICO SUPERIOR DE CALKINÍ EN EL ESTADO DE CAMPECHE Contenido I Datos generales Nombre de la propuesta Constancia que se otorgará Proponen Responsables de la propuesta II Fundamentación de la propuesta III Plan de estudios Objetivo general Objetivos específicos Dirigido a Perfil del egresado Requisitos escolares previos Estructura del plan de estudios Esquema curricular Calendarización de los módulos Descripción sintética del programa de cada módulo IV Requisitos académicos-administrativos Requisitos de ingreso Requisitos de permanencia Requisitos de egreso V Recursos humanos, físicos y cupo Recursos humanos Cupo VI Mecanismos de seguimiento y evaluación del plan de estudios Instrumentos de evaluación Diplomado en Enseñanza de las Matemáticas en el Nivel Superior Asistidas 2 por Software INSTITUTO TECNOLÓGICO SUPERIOR DE CALKINÍ EN EL ESTADO DE CAMPECHE I. Datos generales Nombre de la propuesta: Diplomado en Enseñanza de las Matemáticas Asistidas por Software. en el Nivel Superior Constancia que se otorgará: Documento que certifica los estudios realizados. Propone: Academia de Matemáticas del ITESCAM Responsables de la propuesta: M. E. Julio César Pech Salazar Dr. Juan Manuel Camacho Pérez II. Fundamentación de la propuesta. Actualmente la computadora, a través del software desempeña un papel importante en la educación, investigación y desarrollo tecnológico, percibiendo su impacto futuro y sus ventajas como herramienta en los procesos de enseñanza-aprendizaje.
    [Show full text]
  • The Effectiveness of the Application of Mathematical Software in Indonesia; a Meta-Analysis Study
    International Journal of Instruction October 2020 ● Vol.13, No.4 e-ISSN: 1308-1470 ● www.e-iji.net p-ISSN: 1694-609X pp. 867-884 Received: 06/10/2019 Revision: 19/05/2020 Accepted: 09/06/2020 OnlineFirst:29/08/2020 The Effectiveness of the Application of Mathematical Software in Indonesia; A Meta-Analysis Study Maximus Tamur M.Ed., Indonesia University of Education, Indonesia, [email protected], [email protected] Dadang Juandi Dr., Indonesia University of Education, Indonesia, [email protected] Yaya Sukjaya Kusumah Prof., Indonesia University of Education, Indonesia, [email protected] This study aims to investigate the effectiveness of the application of mathematical software to the mathematical abilities of students in Indonesia. For this purpose, 64 effect sizes from 51 studies published in national and international journals from 2011 to 2019 were analyzed using the meta-analysis method. Comprehensive Meta-Analysis (CMA) software is used to assist the analysis. Hedges's g coefficient was used when the effect sizes were calculated and the confidence level was accepted as 95%. As a result of the study, the overall effect size was 1.162, with a standard error of 0.091 according to the random-effects model. These results indicate that the average student who is ranked 13th in the experimental group is equivalent to those who are ranked 4th in the control group. The study was conducted by considering four characteristics, producing a significant difference in terms of the year when the study was conducted and the type of software used. Thus the use of mathematical software produces a larger effect on mathematical ability than conventional approaches.
    [Show full text]