This research aims to describe investigate possibilities of learning situations in mathematics concepts related to polynomial functions of the 1st degree ( In order Function ) with students from 1st grade of Technical Education Middle Level Integrated IFS - Campus São Cristóvão making use of a teaching sequence mediated by the use of a dynamic geometry software, Geogebra. To this purpose, a study, based on the ideas of Machado (2008 ), Pais (2011 ) and Oliveira (2013 ), based on the Engineering Curriculum discussed by Artigue (1996 ) with two classes from 1st Series Technical Course Intermediate Level Integrated was conducted Federal Institute of Education, Science and Technology of Sergipe - Campus São Cristóvão / SE, which formed study groups that we call group with the experiment and group without the experiment. At the end of the experiment it was found that the group with the experiment had better results than the group without the experiment. The data indicated that using a dynamic geometry software in a dynamic geometry environment provides a great interaction between the participants constituting a positive factor to learning, since they facilitate the construction of new concepts, provide a comparison between different forms of representation of a function, thereby enabling conditions for the participant to recognize the graphical representation of an polynomial function of the first degree as a straight, expressing the relation between the coefficients of the straight equation with its graphical and algebraic representations. / A presente pesquisa tem como objetivo geral investigar possibilidades de situações de aprendizado da Matemática de conceitos relativos às funções polinomiais do 1º grau (Função Afim) com alunos da 1ª série do Ensino Técnico de Nível Médio Integrado do IFS Campus São Cristóvão fazendo uso de uma Sequência Didática mediada pelo uso de um software de geometria dinâmica, o GeoGebra. Para tanto, foi realizado um estudo, pautado nas ideias de Machado (2008), Pais (2011) e Oliveira (2013), embasados na Engenharia Didática discutida por Artigue (1996) com duas turmas da 1ª Série do curso Técnico de Nível Médio Integrado do Instituto Federal de Educação, Ciência e Tecnologia de Sergipe Campus São Cristóvão/SE, que formaram os grupos de estudo que denominamos de Grupo com o experimento (GCE) e Grupo sem o experimento (GSE). Ao término da experiência ficou constatado que o GCE apresentou melhores resultados do que o GSE. Os dados indicaram que utilizar um software de geometria dinâmica em um ambiente de geometria dinâmica proporciona uma grande interação entre os participantes constituindo um fator positivo ao aprendizado, uma vez que facilitam a construção de novos conceitos, proporcionam a comparação entre as diferentes formas de representação de uma função, possibilitando, assim, condições para o participante de reconhecer a representação gráfica de uma função polinomial do primeiro grau como uma reta, expressar a relação entre os coeficientes da equação da reta com sua representação gráfica e algébrica.

TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra

Les outils technologiques sont omniprésents dans la société et leur utilisation est de plus en plus grande dans les salles de classe. Du côté de l'enseignement et de l'apprentissage des mathématiques, ces outils se sont vu attribuer des rôles qui ont évolué avec les années. Les rôles de soutien, de visualisation et d'enrichissement des contenus en sont des exemples. Une utilisation des outils technologiques dans l'enseignement s'accompagne d'apports pragmatiques et épistémiques potentiels, mais comporte également des limites et des risques. Il s’avère important d’examiner le rôle accordé à l’outil technologique dans les activités qui le mobilisent. Puisque le raisonnement mathématique fait partie d'une des compétences visées à l’école (MELS, 2006) et que les futurs enseignants semblent accorder moins d'importance à la validation et la preuve comme composantes de ce raisonnement (Mary, 1999), nous émettons l'hypothèse qu'une séquence d'activités montrant la complémentarité de la preuve et des explorations tirant parti de la technologie pourrait aider les futurs enseignants à mieux saisir ces enjeux. La présente recherche s’appuie sur l'ingénierie didactique pour développer et valider une séquence d'activités intégrant le logiciel GeoGebra. Cette séquence d'activités a été conçue dans les buts suivants : initier les futurs enseignants en mathématiques au secondaire à un logiciel de géométrie dynamique et leur donner l'occasion de voir des activités mathématiques utilisant la technologie et visant le développement du raisonnement, par l’articulation de l’exploration et de la preuve. Le cadre théorique sur lequel repose cette recherche intègre des éléments de l'approche anthropologique (Chevallard, 1992, 1998, 2003) et de l'approche instrumentale (Vérillon et Rabardel, 1995; Trouche, 2000, 2003, 2007; Guin et Trouche, 2002). Certaines idées sur les constructions robustes et molles (Soury-Lavergne, 2011), la distinction figure/dessin (Laborde et Capponi, 1994) et le réseau déductif (Tanguay, 2006) ont servi de repères dans la construction de la séquence d'activités. Cette recherche s'est déroulée au cours de l'hiver 2016 dans une université québécoise, dans le cadre d’un cours de didactique de la géométrie auprès de futurs enseignants au secondaire en mathématiques. Un questionnaire pré-expérimentation a été rempli par les participants afin de voir leurs connaissances préalables sur les programmes, les outils technologiques ainsi que leurs conceptions au sujet de l'enseignement et de l'apprentissage des mathématiques. Par la suite, les étudiants ont expérimenté la séquence d'activités et ont eu à se prononcer sur les connaissances mises en jeu dans chacune des activités, l’opportunité de son utilisation avec des élèves du secondaire, et les adaptations perçues nécessaires pour sa réalisation (s'il y a lieu). Des traces écrites de leur travail ont été conservées ainsi qu'un journal de bord au fur et à mesure du déroulement de la séquence. En triangulant les diverses données recueillies, il a été constaté que la séquence, tout en contribuant à l’instrumentation des participants au regard du logiciel utilisé, a eu chez certains d’entre eux un impact sur leur vision du développement du raisonnement mathématique dans l’enseignement des mathématiques au secondaire. L’analyse des données a mis en lumière la place accordée au raisonnement par les futurs enseignants, les raisonnements mobilisés par les étudiants dans les diverses activités ainsi que des indices sur les genèses instrumentales accompagnant ces raisonnements ou les induisant. Suite à l’analyse de ces données et aux constats qui en découlent, des modifications sont proposées pour améliorer la séquence d’activités. / Technological tools are ubiquitous in society and their use is growing in the classroom. In mathematics education, these tools have been assigned roles that have evolved over the years: support, visualization, content enrichment. The use of technological tools in education comes with potential pragmatic and epistemic contributions, but also has limitations and risks. We must therefore examine at the activity level the role technology should play. Mathematical reasoning is one of the competencies aimed by school (MELS, 2006) and future teachers seem to place less emphasis on validation and proving processes as components of this reasoning (Mary, 1999). We hypothesize that a sequence of activities showing the complementarity of the proving processes with explorations leveraging technology could help future teachers better understand these issues. This research is based on didactical engineering to develop and validate a sequence of activities with GeoGebra software. The sequence of activities has been designed to: introduce pre-service secondary mathematics teachers to dynamic geometry software and give them the opportunity to see mathematical activities using technology that aim at developing mathematical reasoning and proof. The theoretical framework on which this research is based integrates elements of the anthropological theory of the didactic (Chevallard, 1992, 1998, 2003) and of the instrumental approach (Vérillon and Rabardel, 1995; Trouche, 2000, 2003, 2007; Guin and Trouche, 2002). Some ideas on robust and soft constructions (Soury-Lavergne, 2011), the distinction between figure and drawing (Laborde and Capponi, 1994) and the deductive network (Tanguay, 2006) served as benchmarks in the construction of the sequence of activities. This research took place at a Quebec university during the winter of 2016, in a geometry didactics course for pre-service secondary mathematics teachers. A preliminary questionnaire was given to the participants to capture their prior knowledge of programs, technological tools and conceptions about mathematics teaching and learning. Subsequently, the students experienced the sequence of activities and had to decide on the knowledge involved in each activity, the relevance of its use with high school students, and the perceived adaptations necessary for its realization (if considered). Written traces of their work have been kept as well as a diary as the sequence unfolds. By triangulating the various data collected, it was found that the sequence, while contributing to the instrumentation of the participants with regard to the software used, had, for some of them, an impact on their vision of the development of mathematical reasoning in mathematics education at secondary level. The analysis of the data highlighted the place given to the reasoning by the future teachers, the reasonings mobilized by the students in the various activities and also signs of the instrumental geneses inducing these reasonings and accompanying them. Following the analysis of these data and the findings that follow, modifications are proposed to improve the sequence of activities.

Orientador: Rita de Cássia Pavan Lamas / Banca: Flavia Souza Machado da Silva / Banca: Durval José Tonon / Resumo: Uma das aplicações das funções trigonométricas é a modelagem de alguns fenômenos periódicos, são exemplos de tais fenômenos, o movimento da luz solar, as fases da Lua, a circulação do sangue e o movimento dos planetas. Abordamos aqui aspectos teóricos das funções seno e cosseno, essas são as principais funções trigonométricas trabalhadas no ensino médio. Utilizando um dos materiais oficiais das escolas públicas, o Caderno do Aluno, propusemos atividades sobre as funções trigonométricas a uma turma da 2ª série do Ensino Médio da Rede do Estado de São Paulo, posteriormente analisamos os resultados da nossa aplicação, em sala de aula, de tais atividades. Apresentaremos ainda uma proposta de aula com a utilização do software GeoGebra para a aplicação na sala de informática no intuito de tornar a aprendizagem das funções trigonométricas um pouco mais dinâmica. Analisamos também os resultados dessa aplicação / Abstract: One of the applications of the trigonometric functions is the modeling some periodic phenomenas, examples of such phenomenas are the movement of sunlight, the phases of the Moon, the circulation of blood and the movement of the planets. We address here theoretical aspects of the sine and cosine functions, these are the main trigonometric functions worked out in high school. Using one of the official public school materials, Student Notebook, we proposed activities on the trigonometric functions of high school class from the State of São Paulo. Later, we analyzed the results of our application in the classroom, of such activities. We will present a lesson proposal with the use of GeoGebra software for the application in the computer laboratory in order to make the learning of the trigonometric functions a little more dynamic. We also analyze the results of this application / Mestre

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One major challenge facing mathematics education in South Africa in general and Limpopo in particular, is learners’ underachievement and lack of motivation to learn the subject. Some studies have shown that one of the topics that learners dread is linear functions. Many teachers also find it difficult to teach the topic effectively. Studies in other parts of the world have advocated the integration of graphing software with the teaching and learning of functions to enhance learners’ learning of mathematics. This study therefore investigated the effect of integrating GeoGebra graphing software into the teaching of linear functions on the achievement of Grade 9 learners. The study was guided by APOS theory which, in accordance with constructivist theories, posits that an individual needs to construct the necessary cognitive structures in order to make sense of mathematical concepts. A total of 127 Grade 9 learners from four schools in a circuit in Mopani district of Limpopo Province participated in the study which followed a pretestpost- test quasi-experimental study design. Two schools, namely B (35 learners) and D (33 learners) formed the experimental groups while school A (31 learners) and school C (28 learners) were the control groups. Data were collected using an achievement test and analyzed using descriptive and inferential statistics. The pretest results showed that the groups were of comparable cognitive abilities. The post-test results showed that there was a significant difference between the mean scores of the experimental groups and control groups. There were also statistically significant differences between group treatment means (p < .05). Bonferroni post-hoc test results showed that there were no statistically significant differences between treatments A and C. The results showed that the learners in the two control groups were of comparable cognitive abilities. The implications of the findings are discussed and recommendations made. / Mathematics Education / M. Sc. (Mathematics Education)

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / Este trabalho discute relaÃÃes entre a Metodologia de Ensino SequÃncia Fedathi (SF) e a Teoria do Pensamento MatemÃtico AvanÃado (PMA), buscando a compreensÃo de como a aÃÃo docente favorece o desenvolvimento do pensamento matemÃtico discente, à medida que possibilita aÃÃo-reflexÃo em sala de aula. Com efeito, o objetivo principal foi compreender como a mediaÃÃo docente, apoiada na SF, influencia no desenvolvimento do PMA de alunos de licenciatura em aulas de Ãlgebra Linear. Caracterizou-se como um estudo de natureza qualitativa, cujas questÃes de pesquisa remeteram ao estudo de caso. A investigaÃÃo de campo dividiu-se em trÃs etapas: (a) observaÃÃo de uma disciplina de Ãlgebra Linear; (b) realizaÃÃo de um curso de extensÃo; e (c) grupo de estudos, com participantes da etapa anterior. As duas primeiras etapas trataram do ensino na Ãlgebra Linear utilizando a SF e a terceira cuidou de seu estudo como metodologia de ensino. Nos resultados, identificou-se, na mediaÃÃo docente, o incentivo à mobilizaÃÃo de variados processos mentais, desencadeados mediante o uso de perguntas, que propiciaram a mediaÃÃo dialogada, bem como do uso do software Geogebra e da maneira como as representaÃÃes matemÃticas foram exploradas. AlÃm disso, foram explorados o tratamento e a conversÃo dos registros de representaÃÃo. Os processos de generalizaÃÃo e abstraÃÃo foram notados com maior Ãnfase na aÃÃo/mediaÃÃo docente, em especial, quando se incentivava os alunos a observar a estrutura matemÃtica subjacente ao conteÃdo. AlÃm disso, foram identificadas evidÃncias de que a SF pode contribuir nÃo apenas para o desenvolvimento cognitivo dos estudantes, mas, tambÃm, para o desenvolvimento social, afetivo e metacognitivo, que contribuem significativamente para a predisposiÃÃo do aluno em adquirir conhecimentos e pÃr em prÃtica o raciocÃnio investigativo. Concluiu-se que a SF pode propiciar um ambiente favorÃvel ao desenvolvimento de processos de PMA de alunos de licenciatura em MatemÃtica nas aulas de Ãlgebra Linear, uma vez que favorece a aÃÃo discente e orienta o professor quanto à maneira de interagir e realizar a mediaÃÃo do conteÃdo em sala de aula, de modo a respeitar o tempo de maturaÃÃo do aluno, seu desenvolvimento cognitivo, levando-o a entender os conceitos de modo significativo, sem se limitar à memorizaÃÃo de regras e manipulaÃÃo algorÃtmica. / Este trabalho discute relaÃÃes entre a Metodologia de Ensino SequÃncia Fedathi (SF) e a Teoria do Pensamento MatemÃtico AvanÃado (PMA), buscando a compreensÃo de como a aÃÃo docente favorece o desenvolvimento do pensamento matemÃtico discente, à medida que possibilita aÃÃo-reflexÃo em sala de aula. Com efeito, o objetivo principal foi compreender como a mediaÃÃo docente, apoiada na SF, influencia no desenvolvimento do PMA de alunos de licenciatura em aulas de Ãlgebra Linear. Caracterizou-se como um estudo de natureza qualitativa, cujas questÃes de pesquisa remeteram ao estudo de caso. A investigaÃÃo de campo dividiu-se em trÃs etapas: (a) observaÃÃo de uma disciplina de Ãlgebra Linear; (b) realizaÃÃo de um curso de extensÃo; e (c) grupo de estudos, com participantes da etapa anterior. As duas primeiras etapas trataram do ensino na Ãlgebra Linear utilizando a SF e a terceira cuidou de seu estudo como metodologia de ensino. Nos resultados, identificou-se, na mediaÃÃo docente, o incentivo à mobilizaÃÃo de variados processos mentais, desencadeados mediante o uso de perguntas, que propiciaram a mediaÃÃo dialogada, bem como do uso do software Geogebra e da maneira como as representaÃÃes matemÃticas foram exploradas. AlÃm disso, foram explorados o tratamento e a conversÃo dos registros de representaÃÃo. Os processos de generalizaÃÃo e abstraÃÃo foram notados com maior Ãnfase na aÃÃo/mediaÃÃo docente, em especial, quando se incentivava os alunos a observar a estrutura matemÃtica subjacente ao conteÃdo. AlÃm disso, foram identificadas evidÃncias de que a SF pode contribuir nÃo apenas para o desenvolvimento cognitivo dos estudantes, mas, tambÃm, para o desenvolvimento social, afetivo e metacognitivo, que contribuem significativamente para a predisposiÃÃo do aluno em adquirir conhecimentos e pÃr em prÃtica o raciocÃnio investigativo. Concluiu-se que a SF pode propiciar um ambiente favorÃvel ao desenvolvimento de processos de PMA de alunos de licenciatura em MatemÃtica nas aulas de Ãlgebra Linear, uma vez que favorece a aÃÃo discente e orienta o professor quanto à maneira de interagir e realizar a mediaÃÃo do conteÃdo em sala de aula, de modo a respeitar o tempo de maturaÃÃo do aluno, seu desenvolvimento cognitivo, levando-o a entender os conceitos de modo significativo, sem se limitar à memorizaÃÃo de regras e manipulaÃÃo algorÃtmica.

Abstracts in English, Afrikaans and Zulu / The purpose of this study was to explore the learners’ understanding of trigonometric functions using GeoGebra software. A qualitative case study approach was used with six Grade 11 learners at a school in Tshwane South District. The data were collected during a seven-day period using multiple methods: a diagnostic test, worksheets, a smart recorder, a trigonometric functions test, one-on-one interviews and focus-group discussions. The findings showed clearly that the use of GeoGebra enhanced Grade 11 learners’ understanding of trigonometric functions. The findings also showed that the use of GeoGebra helped the learners to understand the basic trigonometric functions graphs. This enabled them to sketch freely without using the point-by-point method. Based on this study, it is recommended that GeoGebra should be made available to all Grade 11 learners. This will encourage them use the software out of regular school hours. / Die doel van hierdie studiegids was om die leerder se kennis van die gebruik van GeoGebra sagteware, ten opsigte van trigonometriese funksies te ondersoek. ‘n Kwalitatiewe benadering is gevolg met ses Graad 11 leerders by ‘n skool in die Tshwane Suid Distrik. Die data is ingewin oor ‘n periode van sewe dae, deur gebruik te maak van verskeie metodes: ‘n diagnostiese toets, werkkaarte, ‘n “smart” opname, ‘n trigonometriese funksies toets, een-tot-een onderhoude en fokusgroepe waar besprekings plaasgevind het. Die data-analise wys duidelik dat die gebruik van GeoGebra, die Graad 11 leerders gehelp het om trigonometriese funksies beter te verstaan. Die uitkomste wys ook duidelik dat GeoGebra die leerders gehelp het met ‘n beter begrip van die basiese trigonometriese funksies. Dit het hulle gehelp om vryhand sketse te doen en nie noodwendig die punt-tot-punt metode nie. Gebaseer op hierdie studie beveel ons aan dat GeoGebra beskikbaar gemaak moet word aan aale Graad 11 leerders. Dit sal leerders motiveer om ook die sagteware op hulle eie buite skoolure te gebruik. / Injongo yocwaningo lolu bekuyikuhlola ukuzwisisa kwabantwana amagrafu e-trigonometry ma bewafunda nge softhiwe ye GeoGebra. Abantwana abayisithupha abakubanga letshumi lanye abaphuma kusigodi se Tshwane South babambiqhaza kulolucwaningo lwendlela ye ‘qualitative case study’. Imininingo iqoqwe kumalanga ayisikhombisa kusetshenziswa indlela ezilandelayo: ukuhlolwa kwe-diagnostic, amaphepha okusebenzela, isingxoxo zamunye ngamunye lezingxoxo leqembu. Iziphumo ezinkulu zikhombe ngokucacile ukuthi ukusetshenziswa kwesofthiwe yeGeoGebra kukhulise ukuzwisisa kwamagrafu e-trigonometry ngabafundi bebanga letshumi lanye.Iziphumo njalo zibonise ukuthi abafundi bazwisisa izinto eziyisiseko ngala magrafu ma bewafunda ngesofthiwe ye GeoGebra. Lokhu kunike abafundi amandla okudwebadweba lamagrafu ngokushesha ngokukhululeka. Kusekelwa ngalezi ziphumo, kunconyiwe ukuthi abafundi bafumane isofthiwe yeGeoGebra ngaso sonke isikhathi. Lokhu kuzabakhuthaza ukuthi basebenzise lesofthiwe noma bengaphandle kwesikolo. / Mathematics Education / M. Ed. (Mathematics Education)

Der vorliegende Beitrag behandelt die kinematische und statische Analyse eines Biglide-Getriebes mit fünf Gliedern und zwei Schubantrieben zur Führung eines Punktes in der x-y-Ebene. Als mathematische Hilfsmittel werden die beiden Programme PTC Mathcad Prime 3.1 und GeoGebra 5.0 eingesetzt, die sich einander in hervorragender Weise ergänzen. Dabei ist Mathcad hier vorwiegend für Matrizenrechnungen und GeoGebra besonders anschaulich für geometrische Grundaufgaben mit Animationen zuständig. Die Effizienz der vorgestellten Algorithmen und Hilfsmittel wird anhand zweier Anwendungsbeispiele aufgezeigt.

Intermediate calculus bridges secondary school and advanced university mathematics courses. Most mathematics education research literatures indicated that the conceptual knowledge in intermediate calculus has challenged first year undergraduate mathematics and science learners to a great extent through the lecture method. The content knowledge attained by them has been tremendously decreasing. Negative attitude exhibited by students toward calculus was highly influenced by the lecture method used. Generally, students have not looked at the learning of all mathematics courses offered in universities as normal as other courses. Due to this lack of background conceptual knowledge in learners, they have been highly frustrated by the learning of advanced mathematics courses. Taking the understanding of teaching and learning challenge of conceptual knowledge of calculus into consideration, Ethiopian public universities have been encouraging instructors to devise and implement active learning methods through any professional development training opportunity. The training was aimed to enhance learners’ content knowledge and attitude towards calculus. This is one of the main reasons for the motivation of this study that experimental group learners were allowed to be nurtured by the lecture method in their mainstream class, and then also the active learning intervention method integrated with GeoGebra in the mathematics laboratory class. Only conventional lecture method was used to teach the comparison group in both the mainstream and mathematics laboratory class. The purpose of the study was to explore the Gambari and Yusuf (2016) stimulus of the jigsaw co-operative learning method combined with GeoGebra (JCLGS) on statistics and chemistry learners’ content knowledge improvement and change of their attitude towards calculus. The post-positivism mixed methods tactic was used in a non-equivalent pre- and post-test comparison group quasi-experimental design. The population of the study was the whole freshman mathematics and science degree program learners of two public universities in Ethiopia in 2017. Samples of the size 150 in both the experimental and comparison groups were drawn utilizing two-stage random sampling technique. A questionnaire using a Likert-scale on attitudes and an achievement test were sources used for data collection. Data analysis employed descriptive statistics conducting an independent samples t-test and a Two Way ANOVA for repeated measures using SPSS23. Each of the findings on content knowledge, conceptual knowledge, and procedural knowledge development produced through the TWO-Way ANOVA, respectively as F(1,148)=80.917; 𝜂2=.353; p<.01, F(1,148)=106.913; 𝜂2=.419; p<.01, and F(1,148)=7.328; 𝜂2=.047; p<.01, revealed a statistically significant difference between the treatment and comparison groups from pre-test to post-test. These findings show that the experimental group participants were highly beneficial in developing their content knowledge and conceptual knowledge through the active learning approach and technology-based learning strategy using Vygotsky’s socio-cultural learning theory. The JCLGS learning environment representing Vygotsky’s socio-cultural learning theory modestly influenced the procedural knowledge learning of the experimental group learners’. Although the lecture method affected the comparison group students’ knowledge development in calculus during the academic semester, the impact was not comparable to that of the active learning approach and technology-based learning strategy. The major reason for this was the attention and care given to the active learning intervention integrated with GeoGebra by the researcher, data collectors, and research participants. Overall findings showed that the active learning intervention allowed the experimental group students to considerably enhance their conceptual knowledge and content knowledge in calculus. Learners also positively changed their opinion towards calculus and GeoGebra. The intervention was a group interactive environment that allowed students’ to be reflective, share prior experience and knowledge, and independent learners. As a matter of fact, educators are advised to model such a combination of active learning approach and technology-based learning strategy in their classroom instructional setting and practices. Consequently, their learners will adequately benefit to understand the subject matter and positively change their opinion towards university mathematics. / Mathematics Education / Ph. D. (Mathematics, Science and Technology Education)