Role of an artefact of Dynamic algebra in the conceptualisation of the algebraic equality

In this contribution, we explore the impact of Alnuset, an artefact of dynamic algebra, on the conceptualisation of algebraic equality. Many research works report about obstacles to conceptualise this notion due to interference of the previous arithmetic knowledge. New meanings need to be assigned to the equal sign and to letters used in algebraic expressions. Based on the hypothesis that Alnuset can be effectively used to mediate the conceptual development necessary to master the algebraic equality notion, two experiments have been designed and implemented in Italy and in France. They are reported in the second part of this pape

3D modeling of the human upper limb including the biomechanics of joints, muscles and soft tissues

The challenge in virtual human modeling is to achieve the representation of the main human characteristics with as much realism as possible. Such achievements would allow the simulation and/or analysis of many virtual situations involving humans. Simulation is especially useful to derive information from the models so as to predict and/or reproduce the behaviors that would be observed in real situations. Computer methods in visualization and simulation have thus great potential for advances in medicine. The processes of strength generation and motion coordination are some of these phenomena for which there is still much remaining to be understood. The human shoulder is also probably the articulation of the human body which deserves more than any other to be named "terra incognita". Investigations towards the biomechanical modeling and simulation of the human upper limb are therefore presented in this study. It includes thorough investigation into the musculoskeletal anatomy and biomechanics of the human upper limb, into the biomechanical constitutive modeling of muscles and soft tissues, and into the nonlinear continuum mechanics and numerical methods, especially the incremental finite element methods, necessary for their simulation. On this basis, a 3-D biomechanical musculoskeletal human upper limb model has been designed using the Visible Human Data provided by the U.S. National Library of Medicine, and applied to the dynamic musculoskeletal simulation of the human upper limb. This research has been achieved in the context of the EU ESPRIT Project CHARM, whose objective has been to develop a comprehensive human animation resource database and a set of software tools allowing the modeling of the human complex musculoskeletal system and the simulation of its dynamics, including the finite element simulation of soft tissue deformation and muscular contraction. An investigation towards the application of this knowledge for the realistic modeling and animation of the upper limb in computer animation is then presented. The anatomical and biomechanical modeling of the scapulo-thoracic constraint and the shoulder joint sinus cones are proposed and applied to the realistic animation, using inverse kinematics, of a virtual skeleton and an anatomic musculoskeletal body model

Multimedia Development of English Vocabulary Learning in Primary School

In this paper, we describe a prototype of web-based intelligent handwriting education system for autonomous learning of Bengali characters. Bengali language is used by more than 211 million people of India and Bangladesh. Due to the socio-economical limitation, all of the population does not have the chance to go to school. This research project was aimed to develop an intelligent Bengali handwriting education system. As an intelligent tutor, the system can automatically check the handwriting errors, such as stroke production errors, stroke sequence errors, stroke relationship errors and immediately provide a feedback to the students to correct themselves. Our proposed system can be accessed from smartphone or iPhone that allows students to do practice their Bengali handwriting at anytime and anywhere. Bengali is a multi-stroke input characters with extremely long cursive shaped where it has stroke order variability and stroke direction variability. Due to this structural limitation, recognition speed is a crucial issue to apply traditional online handwriting recognition algorithm for Bengali language learning. In this work, we have adopted hierarchical recognition approach to improve the recognition speed that makes our system adaptable for web-based language learning. We applied writing speed free recognition methodology together with hierarchical recognition algorithm. It ensured the learning of all aged population, especially for children and older national. The experimental results showed that our proposed hierarchical recognition algorithm can provide higher accuracy than traditional multi-stroke recognition algorithm with more writing variability

Enacting Inquiry Learning in Mathematics through History

International audienceWe explain how history of mathematics can function as a means for enacting inquiry learning activities in mathematics as a scientific subject. It will be discussed how students develop informed conception about i) the epistemology of mathematics, ii) of how mathematicians produce mathematical knowledge, and iii) what kind of questions that drive mathematical research. We give examples from the mathematics education at Roskilde University and we show how (teacher) students from this program are themselves capable of using history to establish inquiry learning environments in mathematics in high school. The realization is argued for in the context of an explicit-reflective framework in the sense of Abd-El-Khalick (2013) and his work in science education

Logic and intuition in architectural modelling: philosophy of mathematics for computational design

This dissertation investigates the relationship between the shift in the focus of architectural modelling from object to system and philosophical shifts in the history of mathematics that are relevant to that change. Particularly in the wake of the adoption of digital computation, design model spaces are more complex, multidimensional, arguably more logical, less intuitive spaces to navigate, less accessible to perception and visual comprehension. Such spatial issues were encountered much earlier in mathematics than in architectural modelling, with the growth of analytical geometry, a transition from Classical axiomatic proofs in geometry as the basis of mathematics, to analysis as the underpinning of geometry. Can the computational design modeller learn from the changing modern history, philosophy and psychology of mathematics about the construction and navigation of computational geometrical architectural system model space? The research is conducted through a review of recent architectural project examples and reference to three more detailed architectural modelling case studies. The spatial questions these examples and case studies raise are examined in the context of selected historical writing in the history, philosophy and psychology of mathematics and space. This leads to conclusions about changes in the relationship of architecture and mathematics, and reflections on the opportunities and limitations for architectural system models using computation geometry in the light of this historical survey. This line of questioning was motivated as a response to the experience of constructing digital associative geometry models and encountering the apparent limits of their flexibility as the graph of dependencies grew and the messiness of the digital modelling space increased. The questions were inspired particularly by working on the Narthex model for the Sagrada Família church, which extends to many tens of thousands of relationships and constraints, and which was modelled and repeatedly partially remodelled over a very long period. This experience led to the realisation that the limitations of the model were not necessarily the consequence of poor logical schema definition, but could be inevitable limitations of the geometry as defined, regardless of the means of defining it, the ‘shape’ of the multidimensional space being created. This led to more fundamental questions about the nature of Space, its relationship to geometry and the extent to which the latter can be considered simply as an operational and notational system. This dissertation offers a purely inductive journey, offering evidence through very selective examples in architecture, architectural modelling and in the philosophy of mathematics. The journey starts with some questions about the tendency of the model space to break out and exhibit unpredictable and not always desirable behaviour and the opportunities for geometrical construction to solve these questions is not conclusively answered. Many very productive questions about computational architectural modelling are raised in the process of looking for answers

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field

History of Mathematics in Mathematics Education: Recent devlopments

International audience<p>This is a concise survey on the recent developments (since 2000) concerning research on the relations between History and Pedagogy of Mathematics (the <i>HPM domain</i>). Section 1 explains the rationale of the study and formulates the key issues. Section 2 gives a brief historical account of the development of the <i>HPM domain</i> with focus on the main activities in its context and their outcomes. Section 3 provides a sufficiently comprehensive bibliographical survey of the work done in this area since 2000. Finally, section 4 summarizes the main points of this study.</p