Teaching of Ordinary Differential Equations Using the Assumptions of the PBL Method

Mathematics is of fundamental importance to any natural sciences program (because it provides analytical and approximate results that can be simulated and modeled) and perhaps to other areas of human knowledge. Ordinary differential equations (ODEs) are especially of fundamental importance to engineering programs because the modeling of all phenomena of interest for these programs involves ODE solutions; at the same time, students experience difficulties when learning ODEs and about their applications to real physical scenarios. In this study, the problem-based learning method was used to study a group of mechanical engineering students at theSENAICIMATECUniversityCenter. The study analyzes the effectiveness of ODE instruction given through this program using the specified methodology. To consolidate the study, Conceptual Field Theory is used together with an evaluation of the results to observe student behaviors and attitudes in relation to actions arising from the method. At the end of the study, a questionnaire was completed by the students, with which they evaluated the effectiveness of the teaching methodology employed

Enseñando los fundamentos de la Mecánica Cuántica en la Escuela Media: una Estructura Conceptual Propuesta

This paper is part of a doctoral thesis that investigates Basic Quantum Mechanics (QM) teaching in high school. A Conceptual Structure of Reference (CSR) based on the Path Integral Method of Feynman (1965) was rebuilt and a Proposed Conceptual Structure for Teaching (PCST) (Otero, 2006, 2007) the basics of Quantum Mechanics at secondary school was designed, analysed and carried out. This PCST does not follow the historical route and it is complementary to the canonical formalism. The concepts: probability distribution, quantum system, x(t) alternative, amplitude of probability, sum of probability amplitude, action, Planck's constant, and classicquantum transition were rebuilt with the students. Mathematical formalism was avoided by using simulation software assistance. The Proposed Conceptual Structure for Teaching (PCST) is described and some results from the test carried out by the class group are discussed. This information allows the analysis of the Conceptual Structure Effectively Reconstructed (CSER) to be initiated with the students.Este trabajo es parte de una tesis doctoral que investiga la enseñanza de los fundamentos de la Mecánica Cuántica en la Escuela media. Se reconstruyó una estructura Conceptual de Referencia (ECR) basada en el método de la Integral de Camino de Feynman (1965) y se diseñó, analizó e implementó una Estructura Conceptual Propuesta para Enseñar (ECPE) (Otero, 2006, 2007) fundamentos de Mecánica Cuántica en la escuela media. Esta ECPE no sigue el camino histórico y es complementaria al formalismo canónico. Los conceptos: distribución de probabilidad, sistema cuántico, trayectoria alternativa x(t), amplitud de probabilidad, suma de amplitud de probabilidad acción, constante de Planck y transición clásica-cuántica se reconstruyeron con los estudiantes. Se describe la Estructura Conceptual Propuesta para Enseñar (ECPE) y se discuten algunos resultados de la evaluación realizada por el grupo de clase. Esta información permite el análisis de la Estructura Conceptual Efectivamente Reconstruida (ECER) con los estudiantes.Instituto de Física La Plat

Video tutorial screencast and sketchup make (VTS-SUM) for low achievers in learning 3d geometry

Students’ weaknesses in learning 3-Dimensional (3D) geometry are mostly associated with their low level of geometric thinking. Although a 3D software has been proposed as a manipulative learning tool, they had difficulties using it. Therefore, a suitable learning strategy should be designed to overcome the problems. The purpose of the study was to assess a learning strategy, known as Video Tutorial Screencast SketchUp Make (VTS-SUM), which integrates screencast techniques with a 3D software. VTS-SUM is a know-how video that assists students to visualize steps in drawing the orthogonal projections for 3D objects. A total of 180 students from a secondary school were involved in the study, conducted using a quantitative approach, where, a van Hiele Geometric Thinking (vHGT) test was employed to find out the level of students’ geometric thinking. The findings obtained showed that the majority of the students were at the Lowest Level (Level L1). As for usability test, a total of thirty students were selected from among those below this level. They were given some time to watch the video and perform hands-on activities using the software. A seven-point Likert scale questionnaire, comprising four constructs, namely, usefulness, ease of use, ease of learning and satisfaction, was used to measure the students’ perceptions of the usability test. The results obtained indicated that the students had positive perceptions towards the usage of VTS-SUM in their learning, thus accentuating its good potentials to enhance learning in mathematics

Eliciting preschoolers’ number abilities using open, multi-touch environments

Research has highlighted the potential of digital technology to support the development of children’s number sense abilities. However, the main focus of such research has been on apps affording directed interactions, where only one solution strategy is available, and it has targeted mostly cardinality. Little is known, in these terms, about task design and implementation in more open environments where several different solution strategies are available. To explore this direction, we chose to study TouchCounts, an open environment that combines multi-touch affordances with aural, visual and symbolic ones as well. Using tasks that were designed to address different number sense abilities, we experimented with 4-year-old preschoolers. In this paper we present two tasks, their expected potential with respect to strengthening number sense abilities, and analyses of data collected during the preschoolers’ interactions with TouchCounts. The analyses reveal that the children used different strategies in response to the two tasks, and that a broad range of abilities related to number sense were elicited, including both cardinality and ordinality. An important contribution of this study is also a theoretical framework capable of identifying children’s learning in a multi-touch environment

An Education 4.0 Pedagogical Approach for Introducing Smart Manufacturing to 5th grade students

Esta investigação é desenvolvida no âmbito do projeto Europeu "ShapiNG" (Shaping the next Generation of Manufacturing Professionals), cujo objetivo principal é atrair estudantes para atividades no campo da indústria. Proporcionar aos estudantes experiências de aprendizagem que os ajudem a compreender as competências necessárias para ser bem sucedido no local de trabalho é uma proposta desafiante no mundo de hoje em rápida mudança e dominado pela tecnologia. O objetivo deste estudo é identificar as tecnologias e abordagens-chave que, combinadas, podem constituir uma arquitetura pedagógica adequada para criar consciência e motivação entre os jovens estudantes, a fim de os inspirar a escolher uma carreira em Engenharia. Com base na teoria de aprendizagem de David Ausubel, foi realizado um estudo de caso para avaliar a eficácia da arquitetura concebida. A população da metodologia de pesquisa consistiu em 60 alunos do 5º ano de escolaridade que frequentavam a aula de "STEM" na "Escola Global". Os tópicos abordados foram modelação e impressão 3D. Após uma revisão minuciosa da literatura e um profundo trabalho de campo envolvendo observação direta e participante, questionários e entrevistas foram feitas com o objetivo de recolher dados relativos a (a) conhecimentos obtidos sobre os tópicos abordados, (b) benefícios de trabalhar colaborativamente e individualmente, (c) eficácia do material instrucional, e (d) motivação para seguir uma carreira em Engenharia. Por fim, através do trabalho realizado conseguimos obter os seguintes resultados principais: não há diferenças significativas no conhecimento adquirido entre o trabalho individual e colaborativo para as atividades propostas; os benefícios do trabalho colaborativo estão associados à possibilidade de negociar conceitos e aprimorar as competências de liderança e organização, enquanto os benefícios do trabalho individual estão relacionados com a possibilidade de auto-superação e de ser criativo; a motivação influenciou a qualidade percebida do material instrucional, sendo que os estudantes motivados classificaram melhor o material instrucional do que os não motivados; os estudantes do sexo masculino estão mais motivados a seguir uma carreira na Engenharia do que os do sexo feminino. Em última análise, os principais resultados deste estudo proporcionam um ponto de partida conceptual e prático para o desenvolvimento de abordagens eficazes em futuros trabalhos de investigação e para atividades que pretendam motivar jovens estudantes para seguir uma carreira na Engenharia.This research is developed within the scope of the European project "ShapiNG" (Shaping the next Generation of Manufacturing Professionals), whose main goal is to attract young students for activities in the field of manufacturing. Providing students with learning experiences that help them to understand the skills they need to succeed in the workplace is a difficult proposition in today's quickly changing world pervaded by technology. The purpose of this study is to identify key technologies and approaches that combined may constitute a suitable pedagogical architecture to create awareness and motivation among young students as to inspire them to pursue a career in Engineering. Drawing on David Ausubel's theory of learning, a case study was conducted to evaluate the effectiveness of the conceived architecture. The research methodology population consisted of 60 students from the 5th grade attending the "STEM" class at "Escola Global". The covered topics were 3D modeling and 3D printing. After a thorough literature review and an in-depth fieldwork involving both direct and participant observation, questionnaires and interviews were done in order to collect data regarding the (a) knowledge obtained on the covered topics, (b) benefits of working collaboratively and individually, (c) effectiveness of the instructional material, and (d) motivation to pursue a career in Engineering. Ultimately, through our research we were able to obtain the following main results: there are no significant differences on the acquired knowledge between individual and collaborative work for the proposed activities; benefits of collaborative work are related to the possibility of negotiating concepts and enhancing leadership and organizational skills, whilst benefits of individual work are related to the possibility of self-overcoming and being creative; motivation influenced the perceived quality of instructional material with motivated students rating better the instructional material than the unmotivated ones; male students are more motivated to pursue a career in Engineering than female. Ultimately, the main results of this study provide a conceptual and practical gateway to bring in effective approaches to future research and activities focused on motivating young students to pursue a career in Engineering

Investigating the factors which influence the child's conception of angle.

The aim of the present study is to investigate the factors which influence the child's understanding of angle. Fifty-four students aged from 6 to 14, were set 92 activities to solve in three separate sections. The activities were elaborated according to six interwoven variables: (a) activities in static and dynamic perspectives carried out under (b) three different representational systems: oral (everyday life model), written (paper and pencil model), and bodysyntonic (Logo model). These were inserted in three situations (c), rotation, navigation and comparison, using (d) different materials. The children were asked (e) to perform an action or to recognise differences and similarities between angles, followed by an explanation, or description of what they had done. All activities involved (f) different sizes of angle. The findings were submitted to both quantitative and posteriori qualitative analysis. Cross-sectionally by age, the data indicate a strong trend of improved performance with age. This points to a developmental effect, but the school's influence has to be taken into account. The results suggest that the child's acquisition of the conception of angle has a dynamic perspective as its starting-point. In particular, the children performed better within activities which involved rotation. This does not imply that every child used the dynamic perspective of angle consistently across all tasks. In fact the choice of perspective frequently changedaccording to the meaning of the situation, which could sometimes be depended on cultural influences. This was particularly apparent in the watch arena, the situation which the children were most successful. In a comparison of representational systems, the best performances were achieved in activities on Logo, while activities conducted with paper & pencil proved to be the most difficult. Performance was also enhanced in tasks which required action by the children. These findings indicate that there exist various factors influencing a child's understanding of angle, and these factors are close interrelated

Baghera Assessment Project, designing an hybrid and emergent educational society

Edited by Sophie Soury-Lavergne ; Available at: http://www-leibniz.imag.fr/LesCahiers/2003/Cahier81/BAP_CahiersLaboLeibniz.PDFResearch reportThe Baghera Assessment Project (BAP) has the objective to ex plore a new avenue for the design of e-Learning environments. The key features of BAP's approach are: (i) the concept of emergence in multi-agents systems as modelling framework, (ii) the shaping of a new theoretic al framework for modelling student knowledge, namely the cK¢ model. This new model has been constructed, based on the current research in cognitive science and education, to bridge research on education and research on the design of learning environments

Mathematical warrants, objects and actions in higher school mathematics

'Higher school mathematics' connotes typical upper secondary school and early college mathematics. The mathematics at this level is characterised by moves to (1) rigour in justification,(2) abstraction in content and (3) fluency in symbolic manipulation. This thesis investigates these three transitions - towards rigour, abstraction, and tluencyusing philosophical method: for each of the three transitions a proposition is presented and arguments are given in favour of that proposition. These arguments employ concepts and results from contemporary English language-medium philosophy and also rely crucially on classroom issues or accounts of mathematical experience both to elucidate meaning and for the domain of application. These three propositions, with their arguments, are the three sub-theses at the centre of the thesis as a whole. The first of these sub-theses (1) argues that logical deduction, quasi-empiricism and visualisation are mathematical warrants, while authoritatively based justification is essentially non-mathematical. The second sub-thesis (2) argues that the reality of mathematical entities of the sort encountered in the higher school mathematics curriculum is actual not metaphoric. The third sub-thesis (3) claims that certain 'mathematical action' can be construed as non-propositional mathematical knowledge. The application of these general propositions to mathematics in education yields the following: 'coming to know mathematics' involves:(1) using mathematical warrants for justification and self conviction; (2) ontological commitment to mathematical objects; and (3)developing a capability to execute some mathematical procedures automatically

A design approach to research in technology enhanced mathematics education

EThOS - Electronic Theses Online ServiceGBUnited Kingdo