[ES] La presente tesis doctoral se enmarca en un conjunto de investigaciones centradas en el empleo de metodologías activas en el ámbito de las matemáticas, con el propósito de incrementar tanto los logros de aprendizaje como la motivación de los estudiantes en los niveles de educación secundaria y universitaria. En un contexto en el que se observa una disminución en el interés de los alumnos hacia las matemáticas, disciplina que perciben como desafiante y abstracta, se reconoce la necesidad apremiante de que los docentes proporcionen herramientas innovadoras y adopten enfoques pedagógicos que revitalicen el interés de los estudiantes en esta materia. La profunda comprensión de los conceptos matemáticos se revela como un componente crucial para un aprendizaje significativo y requiere de una diversidad de enfoques y estrategias educativas que puedan aplicarse para fortalecer la formación de los alumnos, promoviendo el desarrollo integrado de competencias matemáticas y tecnológicas. A través de metodologías activas, como flipped classroom, aprendizaje cooperativo, aprendizaje basado en juegos o gamificación, que poseen un gran potencial didáctico, los alumnos tienen la oportunidad de alcanzar un aprendizaje efectivo, lo que implica que pueden comprender de manera efectiva y eficiente los conceptos matemáticos, al mismo tiempo que se mejora el potencial del grupo clase Las experiencias recopiladas en esta investigación, que incluyen la implementación de la metodología flip, el uso de vídeos didácticos enriquecidos, la gamificación, materiales manipulativos, herramientas tecnológicas y la promoción del pensamiento computacional, entre otras, abarcan tanto la educación preuniversitaria, que engloba secundaria y bachillerato, como la universitaria. La metodología de investigación se fundamenta en un enfoque exploratorio, pre-experimental y cuasi-experimental de naturaleza transversal. En todos los casos, se incorporan fundamentos teóricos que respaldan las experiencias realizadas, así como análisis cuantitativos y cualitativos de los datos recopilados. Los resultados obtenidos en estos estudios reflejan un notorio aumento en los logros de aprendizaje y la motivación de los estudiantes como consecuencia de la implementación de estas metodologías. En resumen, esta tesis doctoral se erige como un compendio de investigaciones que subrayan la importancia de las metodologías activas en la enseñanza de las matemáticas en los niveles de educación secundaria y universitaria. Los hallazgos respaldan la efectividad de estas metodologías para reavivar el interés de los estudiantes en las matemáticas y promover un aprendizaje más profundo y motivador en estas áreas. Con ello, se sientan las bases para una mejora continua en la enseñanza de las matemáticas en todos los niveles educativos. / [CA] La present tesi doctoral s'emmarca en un conjunt d'investigacions centrades en l'ús de metodologies actives en l'àmbit de les matemàtiques, amb el propòsit d'incrementar tant els assoliments d'aprenentatge com la motivació dels estudiants en els nivells d'educació secundària i universitària. En un context en el qual s'observa una disminució en l'interés dels alumnes cap a les matemàtiques, disciplina que perceben com a desafiadora i abstracta, es reconeix la necessitat urgent que els docents proporcionen eines innovadores i adopten enfocaments pedagògics que revitalitzen l'interés dels estudiants en esta matèria. La profunda comprensió dels conceptes matemàtics es revela com un component crucial per a un aprenentatge significatiu i requereix d'una diversitat d'enfocaments i estratègies educatives que puguen aplicar-se per a enfortir la formació dels alumnes, promovent el desenvolupament integrat de competències matemàtiques i tecnològiques. A través de metodologies actives, com flipped classroom, aprenentatge cooperatiu, aprenentatge basat en jocs o ludificació, que posseeixen un gran potencial didàctic, els alumnes tenen l'oportunitat d'aconseguir un aprenentatge efectiu, la qual cosa implica que poden comprendre de manera efectiva i eficient els conceptes matemàtics, al mateix temps que es millora el potencial del grup classe Les experiències recopilades en esta investigació, que inclouen la implementació de la metodologia flip, l'ús de vídeos didàctics enriquits, la ludificació, materials manipulatius, eines tecnològiques i la promoció del pensament computacional, entre altres, abasten tant l'educació preuniversitària, que engloba secundària i batxillerat, com la universitària. La metodologia d'investigació es fonamenta en un enfocament exploratori, pre-experimental i quasiexperimental de naturalesa transversal. En tots els casos, s'incorporen fonaments teòrics que recolzen les experiències realitzades, així com anàlisis quantitatives i qualitatives de les dades recopilades. Els resultats obtinguts en estos estudis reflecteixen un notori augment en els assoliments d'aprenentatge i la motivació dels estudiants a conseqüència de la implementació d'estes metodologies. En resum, esta tesi doctoral s'erigeix com un compendi d'investigacions que subratllen la importància de les metodologies actives en l'ensenyament de les matemàtiques en els nivells d'educació secundària i universitària. Les troballes recolzen l'efectivitat d'estes metodologies per a reavivar l'interés dels estudiants en les matemàtiques i promoure un aprenentatge més profund i motivador en estes àrees. Amb això, s'estableixen les bases per a una millora contínua en l'ensenyament de les matemàtiques en tots els nivells educatius. / [EN] This doctoral thesis is part of a set of research projects focused on the use of active methodologies in the field of mathematics, with the aim of increasing both learning achievements and student motivation in secondary and university levels. In a context where there is a decline in students' interest in mathematics, a discipline perceived as challenging and abstract, it is recognized the pressing need for teachers to provide innovative tools and adopt pedagogical approaches that revitalise students' interest in this subject. A deep understanding of mathematical concepts emerges as a crucial component for meaningful learning and requires a diversity of approaches and educational strategies that can be applied to strengthen students' education, promoting the integrated development of mathematical and technological competencies. Through active methodologies such as flipped classroom, cooperative learning, game-based learning, or gamification, which have great didactic potential, students can achieve effective learning, implying that they can understand mathematical concepts effectively and efficiently while enhancing the potential of the class group. The experiences gathered in this research, including the implementation of the flip methodology, the use of enriched educational videos, gamification, manipulative materials, technological tools, and the promotion of computational thinking, among others, span both pre-university education, including secondary and high school, and university education. The research methodology is based on an exploratory, pre-experimental, and quasi-experimental cross-sectional approach. In all cases, theoretical foundations supporting the experiences are incorporated, along with quantitative and qualitative analysis of the collected data. The results obtained in these studies reflect a noticeable increase in learning achievements and student motivation because of the implementation of these methodologies. In summary, this doctoral thesis stands as a compendium of research highlighting the importance of active methodologies in the teaching of mathematics at the secondary and university levels. The findings support the effectiveness of these methodologies in reigniting students' interest in mathematics and promoting deeper and more motivating learning in these areas. With this, it lays the groundwork for continuous improvement in the teaching of mathematics at all educational levels. / Jiménez Hernández, C. (2024). Diseño, implementación y análisis de diferentes metodologías activas en el proceso de enseñanza-aprendizaje de matemáticas [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/203650

The creation of an instructional genius hour framework for classroom implementation is an objective of this study. Currently, genius hour educators use a wide variety of frameworks. Some genius hour educators do not follow a set framework, yet others continually modify their genius hour frameworks. This study draws attention to the need to create an instructional framework for classroom implementation. This study was conducted through semi-structured interviews with five of the most respected genius hour educators. For the purposes of this study, each individual educator was treated as a separate case study. During the semi-structured interviews, genius hour educators shared their personal experience with implementing genius hour, their personal philosophies and ideas related to genius hour, their recommendations regarding genius hour implementation, and their recommendations regarding genius hour frameworks for classroom implementation. Moreover, this study also conducted two observations of genius hour classrooms in action. These classroom observations offered data related to genius hour educational philosophy and the need for a genius hour framework. This study recommends that educators use an instructional framework when implementing genius hour. A framework will have a positive effect on the performance of genius hour because of the added structure and clarity it provides for students and educators. It is recommended that educators choose a framework, and modify it in order to best serve the academic needs of their particular genius hour programme. This study moves beyond the genius hour framework by identifying major themes that genius hour educators should consider when implementing genius hour in the classrooms. Alongside the importance of the framework model, the common themes of front-loading, learning from failure, developing passion, and mentoring emerged from the interviews and observations. In essence, this study developed a framework model, game time, based around the importance of incorporating the aforementioned themes. The findings within this study offer an understanding of the importance of using a genius hour framework for classroom implementation. This study envisions that educators can use the research gathered in order to create an optimal genius hour framework for classroom implementation. This offers a framework for classroom implementation, which should be individualized in order to best suit the classroom specific needs. / Hierdie studie het die skepping van ʼn genie-uur-onderrigraamwerk vir klaskamer-implementering ten doel. Tans gebruik genie-uuropvoeders ’n wye verskeidenheid raamwerke. Sommige genie-uuropvoeders volg nie ’n vasgestelde raamwerk nie, terwyl andere voortdurend hul genie-uurraamwerke verander. Hierdie studie vestig aandag op die behoefte om ʼn onderrigraamwerk vir klaskamerimplementering te skep. Hierdie studie is uitgevoer deur middel van halfgestruktureerde onderhoude met vyf van die mees gerespekteerde genie-uuropvoeders. Vir die doeleindes van hierdie studie is elke individuele opvoeder as ’n afsonderlike gevallestudie behandel. Gedurende die halfgestruktureerde onderhoude het genie-uuropvoeders hul persoonlike ervarings van die inwerkingstelling van genie-uur, hul persoonlike filosofieë en idees oor genie-uur, hul aanbevelings vir genie-uurimplementering, en hul aanbevelings vir genie-uurraamwerke vir klaskamerimplementering gedeel. Verder het hierdie stude ook twee waarnemings van genie-uurklaskamers-in-aksie uitgevoer. Hierdie klaskamerwaarnemings het data in verband met genie-uuronderwysfilosofie en die behoefte aan ’n genie-uurraamwerk opgelewer. Hierdie studie beveel aan dat opvoeders ʼn onderrigraamwerk gebruik wanneer hulle genie-uur in werking stel. ’n Raamwerk sal ’n positiewe uitwerking op die uitvoering van genie-uur hê as gevolg van die bykomende struktuur en duidelikheid wat dit aan studente en opvoeders bied. Daar word aanbeveel dat opvoeders ’n raamwerk kies en dit aanpas ten einde die beste in die akademiese behoeftes van hul betrokke genie-uurprogram te voorsien. Hierdie studie beweeg verder as die genie-uurraamwerk deur belangrike temas te identifiseer wat genie-uuropvoeders kan oorweeg wanneer hulle genie-uur in die klaskamers in werking stel. Afgesien van die belangrikheid van die raamwerkmodel het die algemene temas van voorkantlading, leer uit mislukking, ontwikkeling van passie en leidinggewing uit die onderhoude en waarnemings na vore gekom. Hierdie studie het wesenlik ’n raamwerkmodel ontwikkel, genaamd speeltyd, wat gebaseer is op die belangrikheid daarvan om die voorgenoemde temas te inkorporeer. Die bevindings van hierdie studie bied ʼn begrip van die belangrikheid daarvan om ’n genie-uurraamwerk vir klaskamerimplementering te gebruik. Hierdie studie stel in die vooruitsig dat opvoeders die navorsing sal gebruik wat ingesamel is om ʼn optimale genie-uurraamwerk vir klaskamerimplementering te skep. Dit bied ’n raamwerk vir klaskamerimplementering, wat geïndividualiseer behoort te word om die beste in die spesifieke behoeftes van elke klaskamer te voorsien. / Ukwakhiwa kohlaka lokufundisa ngendlela ye-genius hour oluzosetshenziswa ekilasini yiyona njongo yalolu cwaningo. Njengamanje, othisha abalandela indlela yegenius hour basebenzisa izinhlobonhlobo zezinhlaka. Abanye othisha abalandela indlela yegenius hour abasebenzisi izinhlaka ezibekiwe, kodwa abanye bayaqhubeka nokulungisa izinhlaka zabo zegenius hour. Lolu cwaningo luveza isidingo sokwakhiwa kohlaka lokufundisa oluzosetshenziswa ekilasini. Lolu cwaningo lwaluqhutshwa ngokuxoxisana okuhleliwe nothisha abahlanu abahlonishwa kakhulu begenius hour. Ngokwenjongo yalolu cwaningo, uthisha ngamunye wayethathwa njengowahlukile kwabanye abasetshenziswe ocwaningweni. Ngenkathi kuqhubeka izingxoxo ezihleliwe, othisha begenius hour baxoxa ngabahlangabezana nakho uma beqalisa ukusebenzisa igenius hour, imigomo abayilandelayo kanye namasu ahambisana negenius hour, izincomo zabo mayelana negenius hour kanye nezincomo zabo ngezinhlaka zegenius hour ezizosetshenziswa ekilasini. Phezu kwalokho, lolu cwaningo luphinde lwabuka kusetshenziswa igenius hour kabili emakilasini ngenkathi eqhubeka. Lokhu kubhekwa kwamakilasi kwaveza imininingwane eqondene nemigomo yezemfundo yegenius hour kanye nesidingo sohlaka lwegenius hour. Lolu cwaningo luncoma ukuba othisha basebenzise uhlaka lokufundisa uma beqala ukusebenzisa igenius hour. Uhlaka luzoba nomphumela omuhle ekusebenzeni kwegenius hour, ngenxa yokwakheka okwengeziwe kanye nokucacisa, ihlinzekela abafundi nothisha. Kunconywa ukuba othisha bakhethe uhlaka, balulungise kahle ukuze luhambisane nezidingo zezemfundo zohlelo lwabo oluthile lwegenius hour. Lolu cwaningo luhamba ludlulele ngale kohlaka lwegenius hour ngokuhlonza izingqikithi okufanele othisha begenius hour bacabange ngazo uma beqala ukusebenzisa igenius hour emakilasini. Ngaphandle kokubaluleka kwesimo sohlaka, izingqikithi ezejwayelekile zokufundisa ngokuhlahla indlela, ukufunda ngokwehluleka kuqala, ukukhula kothando kanye nokwalusa kwavela ezingxoxweni nasekubukeni. Empeleni. lolu cwaningo selwakhe isimo sohlaka, isikhathi semidlalo, okuncike ekubalulekeni kokuhlanganisa lezi zingqikithi ezibaliwe. Okutholakele kulolu cwaningo kunikeza ukuqonda kokubaluleka kokusebenzisa uhlaka lwegenius hour ekilasini. Lolu cwaningo lubona ukuthi othisha bangasebenzisa imininingwane etholakale ocwaningweni ukwakha uhlaka lwegenius hour olusebenza kahle oluzosetshenziswa ekilasini. Lokhu kuhlinzeka uhlaka oluzosetshenziswa ekilasini, okumele lwenziwe lusebenzele umuntu ngamunye ukuze luhambisane kahle nezidingo zekilasi ngalinye. / Curriculum and Instructional Studies / D. Ed. (Curriculum and Instructional Studies)

<p>Co and Ni are two major elements in high temperature structural alloys that include superalloys for turbine engines and hard metals for cutting tools. The recent development of complex concentrated alloys (CCAs), loosely defined as alloys without a single principal element (e.g. CoNiFeMn), offers additional opportunities in designing new alloys through extensive composition and structure modifications. Within CCAs and Co- and Ni-based superalloys, solid-solution strengthening and stacking fault energy engineering are two of the most important strengthening mechanisms. While studied for decades, the potency and quantitative materials properties of these mechanisms remain elusive. </p> <p><br></p> <p>Solid-solution strengthening originates from stress field interactions between dislocations and solute of various species in the alloy. These stress fields can be engineered by composition modification in CCAs, and therefore a wide range of alloys with promising mechanical strength may be designed. This thesis initially reports on experimental and computational validation of newly developed theories for solid-solution strengthening in 3d transition metal (MnFeCoNi) alloys. The strengthening effects of Al, Ti, V, Cr, Cu and Mo as alloying elements are quantified by coupling the Labusch-type strengthening model and experimental measurements. With large atomic misfits with the base alloy, Al, Ti, Mo, and Cr present strong strengthening effects comparable to other Cantor alloys. </p> <p> </p> <p>Stacking fault energy engineering can enable novel deformation mechanisms and exceptional strength in face-centered cubic (FCC) materials such as austenitic TRIP/TWIP steels and CoNi-based superalloys exhibiting local phase transformation strengthening via Suzuki segregation. We employed first-principles calculations to investigate the Suzuki segregation and stacking fault energy of the FCC Co-Ni binary alloys at finite temperatures and concentrations. We quantitatively predicted the Co segregation in the innermost plane of the intrinsic stacking fault (ISF). We further quantified the decrease of stacking fault energy due to segregation.  </p> <p><br></p> <p>We further investigated the driving force of segregation and the origin of the segregation behaviors of 3d, 4d and 5d elements in the Co- and Ni-alloys. Using first-principles calculations, we calculated the ground-state solute-ISF interaction energies and revealed the trends across the periodic table. We discussed the relationships between the interaction energies and the local lattice distortions, charge density redistribution, density of states and local magnetization of the solutes. </p> <p><br></p> <p>Finally, this thesis reports on new methodologies to accelerate first-principles calculations utilizing active learning techniques, such as Bayesian optimization, to efficiently search for the ground-state energy line of the system with limited computational resources. Based on the expected improvement method, new acquisition strategies were developed and will be compared and presented. </p>

Indiana University-Purdue University Indianapolis (IUPUI) / Anatomy A215: Basic Human Anatomy (Anat A215) is an undergraduate human anatomy course at Indiana University Bloomington (IUB) that serves as a requirement for many degree programs at IUB. The difficulty of the course, coupled with pressure to achieve grades for admittance into specific programs, has resulted in high remediation rates. In an attempt to help students to improve their study habits and metacognitive skills Medical Sciences M100: Improving Learning Skills in Anatomy (MSCI M100) was developed. MSCI M100 is an undergraduate course at IUB which is taught concurrently with Anat A215, with the hopes of promoting academic success in Anat A215. This multifaceted study was designed to analyze the factors associated with students who remediate Anat A215, to predict at-risk students in future semesters, and assess the effectiveness of MSCI M100. The first facet involved analysis of Anat A215 students’ demographic information and class performance data from the spring semester of 2004 through the spring semester of 2010. Results of data analysis can be used by IUB instructors and academic advisors to identify students at risk for remediating, as well as provide other undergraduate anatomy instructors across the U.S. with potential risk factors associated with remediation. The second facet of this research involved analyzing MSCI M100 course assignments to determine if there are improvements in student study habits and metacognitive skills. This investigation involved quantitative analysis of study logs and a learning attitudes survey, as well as a thorough inductive analysis of students’ weekly journal entries. Lastly, Anat A215 exam scores and final course grades for students who completed MSCI M100 and students who did not complete MSCI M100 were compared. Results from these analyses show promising improvements in students’ metacognition and study habits, but further research will better demonstrate the efficacy of MSCI M100.

Many have used the principles of statistics and Bayesian decision theory to model specific learning problems. It is less common to see models of the processes of learning in general. One exception is the model of the supervised learning process known as the "Extended Bayesian Formalism" or EBF. This model is descriptive, in that it can describe and compare learning algorithms. Thus the EBF is capable of modeling both effective and ineffective learning algorithms. We extend the EBF to model un-supervised learning, semi-supervised learning, supervised learning, and empirical function optimization. We also generalize the utility model of the EBF to deal with non-deterministic outcomes, and with utility functions other than 0-1 loss. Finally, we modify the EBF to create a "prescriptive" learning model, meaning that, instead of describing existing algorithms, our model defines how learning should optimally take place. We call the resulting model the Unified Bayesian Decision Theoretical Model, or the UBDTM. WE show that this model can serve as a cohesive theory and framework in which a broad range of questions can be analyzed and studied. Such a broadly applicable unified theoretical framework is one of the major missing ingredients of machine learning theory. Using the UBDTM, we concentrate on supervised learning and empirical function optimization. We then use the UBDTM to reanalyze many important theoretical issues in Machine Learning, including No-Free-Lunch, utility implications, and active learning. We also point forward to future directions for using the UBDTM to model learnability, sample complexity, and ensembles. We also provide practical applications of the UBDTM by using the model to train a Bayesian variation to the CMAC supervised learner in closed form, to perform a practical empirical function optimization task, and as part of the guiding principles behind an ongoing project to create an electronic and print corpus of tagged ancient Syriac texts using active learning.

Researchers conceptually recommend inquiry-based learning as a necessary means to alleviate the problems of learning but this study has embarked on practical implementation of inquiry-based facilitation and learning in Euclidean Geometry. Inquiry-based learning is student-centred. Therefore, the teaching or monitoring of inquiry-based learning in this study is referred to as inquiry-based facilitation. The null hypothesis discarded in this study explains that there is no difference between inquiry-based facilitation and traditional axiomatic approach in teaching Euclidean Geometry, that is, H0: μinquiry-based facilitation = μtraditional axiomatic approach. This study emphasises a pragmatist view that constructivism is fundamental to realism, that is, inductive inquiry supplements deductive inquiry in teaching and learning. Participants in this study comprise schools in Tshwane North district that served as experimental group and Tshwane West district schools classified as comparison group. The two districts are in the Gauteng Province of South Africa. The total number of students who participated is 166, that is, 97 students in the experimental group and 69 students in the comparison group. Convenient sampling applied and three experimental and three comparison group schools were sampled. Embedded mixed-method methodology was employed. Quantitative and qualitative methodologies are integrated in collecting data; analysis and interpretation of data. Inquiry-based-facilitation occurred in experimental group when the facilitator probed asking students to research, weigh evidence, explore, share discoveries, allow students to display authentic knowledge and skills and guiding students to apply knowledge and skills to solve problems for the classroom and for the world out of the classroom. In response to inquiry-based facilitation, students engaged in cooperative learning, exploration, self-centred and self-regulated learning in order to acquire knowledge and skills. In the comparison group, teaching progressed as usual. Quantitative data revealed that on average, participant that received intervention through inquiry-based facilitation acquired inquiry-based learning skills and improved (M= -7.773, SE= 0.7146) than those who did not receive intervention (M= -0.221, SE = 0.4429). This difference (-7.547), 95% CI (-8.08, 5.69), was significant at t (10.88), p = 0.0001, p<0.05 and represented a large effect size of 0.55. The large effect size emphasises that inquiry-based facilitation contributed significantly towards improvement in inquiry-based learning and that the framework contributed by this study can be considered as a framework of inquiry-based facilitation in Euclidean Geometry. This study has shown that the traditional axiomatic approach promotes rote learning; passive, deductive and algorithmic learning that obstructs application of knowledge in problem-solving. Therefore, this study asserts that the application of Inquiry-based facilitation to implement inquiry-based learning promotes deeper, authentic, non-algorithmic, self-regulated learning that enhances problem-solving skills in Euclidean Geometry. / Mathematics Education / Ph. D. (Mathematics, Science and Technology Education)