Building Conceptual Understandings of Equivalence

The equal sign is prevalent at all levels of mathematics however many students misunderstand the meaning of the equal sign and consider it an operational symbol for the completion of an algorithm (Baroody & Ginsburg, 1983; Rittle-Johnson & Alibali, 1999). Three constructs were studied through the lens of the Developing Mathematical Thinking (Brendefur, 2008), Relational Thinking, Spatial Reasoning and Modes of Representation. A review of literature was conducted to examine the effects of mathematics instruction on the development of students’ conceptual understanding of equivalence through the integration of spatial reasoning and relational thinking. The Developing Mathematical Thinking (DMT) curricular resources integrate Bruner’s enactive, iconic, and symbolic modes of representations (1966), using tasks designed to strengthen students’ spatial reasoning and relational thinking to develop mathematical equivalence. The research question “What is the effect of integrating iconic teaching methodology into mathematics instruction on first grade students’ relational thinking and spatial reasoning performance?” was analyzed to determine whether there was a significant difference in pre-and posttest scores for the two groups. Students were found to have a better opportunity to develop conceptual understanding of mathematics in their early years of school when taught with the progression of EIS, relational thinking and spatial reasoning

A Posture Sequence Learning System for an Anthropomorphic Robotic Hand

The paper presents a cognitive architecture for posture learning of an anthropomorphic robotic hand. Our approach is aimed to allow the robotic system to perform complex perceptual operations, to interact with a human user and to integrate the perceptions by a cognitive representation of the scene and the observed actions. The anthropomorphic robotic hand imitates the gestures acquired by the vision system in order to learn meaningful movements, to build its knowledge by different conceptual spaces and to perform complex interaction with the human operator

Perceptually-based language to simplify sketch recognition user interface development

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 473-495).Diagrammatic sketching is a natural modality of human-computer interaction that can be used for a variety of tasks, for example, conceptual design. Sketch recognition systems are currently being developed for many domains. However, they require signal-processing expertise if they are to handle the intricacies of each domain, and they are time-consuming to build. Our goal is to enable user interface designers and domain experts who may not have expertise in sketch recognition to be able to build these sketch systems. We created and implemented a new framework (FLUID - f acilitating user interface development) in which developers can specify a domain description indicating how domain shapes are to be recognized, displayed, and edited. This description is then automatically transformed into a sketch recognition user interface for that domain. LADDER, a language using a perceptual vocabulary based on Gestalt principles, was developed to describe how to recognize, display, and edit domain shapes. A translator and a customizable recognition system (GUILD - a generator of user interfaces using ladder descriptions) are combined with a domain description to automatically create a domain specific recognition system.(cont.) With this new technology, by writing a domain description, developers are able to create a new sketch interface for a domain, greatly reducing the time and expertise for the task Continuing in pursuit of our goal to facilitate UI development, we noted that 1) human generated descriptions contained syntactic and conceptual errors, and that 2) it is more natural for a user to specify a shape by drawing it than by editing text. However, computer generated descriptions from a single drawn example are also flawed, as one cannot express all allowable variations in a single example. In response, we created a modification of the traditional model of active learning in which the system selectively generates its own near-miss examples and uses the human teacher as a source of labels. System generated near-misses offer a number of advantages. Human generated examples are tedious to create and may not expose problems in the current concept. It seems most effective for the near-miss examples to be generated by whichever learning participant (teacher or student) knows better where the deficiencies lie; this will allow the concepts to be more quickly and effectively refined.(cont.) When working in a closed domain such as this one, the computer learner knows exactly which conceptual uncertainties remain, and which hypotheses need to be tested and confirmed. The system uses these labeled examples to automatically build a LADDER shape description, using a modification of the version spaces algorithm that handles interrelated constraints, and which also has the ability to learn negative and disjunctive constraints.by Tracy Anne Hammond.Ph.D

Qualitative Study Comparing the Instruction on Vectors Between a Physics Course and a Trigonometry Course

Science and engineering instructors often observe that students have difficulty using or applying prerequisite mathematics knowledge in their courses. This qualitative project uses a case-study method to investigate the instruction in a trigonometry course and a physics course based on a different methodology and set of assumptions about student learning and the nature of mathematics than traditionally used when investigating students' difficulty using or applying prerequisite mathematics knowledge. Transfer theory examined within a positivist or post-positivist paradigm is often used to investigate students' issue applying their knowledge; in contrast, this qualitative case-study is positioned using constructionism as an epistemology to understand and describe mathematical practices concerning vectors in a trigonometry and a physics course. Instructor interviews, observations of course lectures, and textbooks served as the qualitative data for in-depth study and comparison, and Saussure's (1959) concept of signifier and signified provided a lens for examining the data during analysis. Multiple recursions of within-case comparisons and across-case comparison were analyzed for differences in what the instructors and textbooks explicitly stated and later performed as their practices. While the trigonometry and physics instruction differed slightly, the two main differences occurred in the nature and use of vectors in the physics course. First, the "what" that is signified in notation and diagrams differs between contextualized and context-free situations, and second, physics instruction taught vectors very similar to trigonometry instruction when teaching the mathematics for doing physics, but once instruction focused on physics, the manner in which vector notation and diagrams are used differed from what is explicitly stated during mathematics instruction.Educatio

Character Recognition

Character recognition is one of the pattern recognition technologies that are most widely used in practical applications. This book presents recent advances that are relevant to character recognition, from technical topics such as image processing, feature extraction or classification, to new applications including human-computer interfaces. The goal of this book is to provide a reference source for academic research and for professionals working in the character recognition field

A Semiotic Analysis of Textbooks’ Pictures in Iraqi Intermediate Schools

يركز البحث على تحليل المحتوى الثقافي الموجود في عدة صور من كتاب اللغة الإنجليزية المصمم للصف الأول المتوسط لمتعلمين اللغة الانجليزية. وفحص ثمانية صور لتحديد محتواها الثقافي ونوع الثقافة الممثلة. تستخدم الدراسة نهج التحليل النوعي ويستخدم نموذجًا انتقائيا يجمع بين إطار تحليل بيرس الإشاري وفئات الثقافة الخاصة بكورتازي وجين، وفئات المحتوى الثقافي في الإطار الأوروبي المشترك (CEF) لتحليل الصور. وكشف التحليل الإشاري عن تنوع المحتوى الثقافي للصور من العلاقات الشخصية إلى الطقوس والعادات. كان نوع الثقافة الممثلة في الصور إما الثقافة المصدرية أو الثقافة الدولية. تسلط الدراسة الضوء على فعالية استخدام التحليل السيميائي في فهم المحتوى الثقافي ونوع الثقافة الممثلة في صور الكتاب.The research focuses on analyzing the cultural content present in several pictures from an English language textbook designed for first intermediate learners in Iraq. Eight pictures were examined to determine their cultural content and type of culture represented. The study employs a qualitative analysis approach and uses an eclectic model that combines Peirce's semiotic analysis framework(1991), Cortazzi and Jin's (1999) types of culture, and the categories of cultural content by the Common European Framework (CEF)(2001) to analyze the pictures. The semiotic analysis revealed that the cultural content of the pictures varied from interpersonal relationships to rituals and customs. The type of culture represented in the pictures was either the source culture or an international culture. The study highlights the effectiveness of using semiotic analysis in understanding the cultural content and type of culture represented in a textbook's pictur

An image processing technique for the improvement of Sign2 using a dual camera approach

A non-intrusive translation system to transform American Sign Language to digital text forms the pivotal point of discussion in the following thesis. With so many techniques which are being introduced for the same purpose in the present technological arena, this study lays claim to that relatively less trodden path of developing an unobtrusive, user-friendly and straightforward solution. The phase 1 of the Sign2 Project dealt with a single camera approach to achieve the same end of creating a translation system and my present investigation endeavors to develop a solution to improve the accuracy of results employing the methodology pursued in the Phase1 of the project. The present study is restricted to spelling out the American Sign Language alphabet and hence the only area of concentration would be the hand of the subject. This is as opposed to considering the entire ASL vocabulary which involves a more complex range of physical movement and intricate gesticulation. This investigation involved 3 subjects signing the ASL alphabet repetitively which were later used as a reference to recognize the letters in the words signed by the same subjects. Though the subject matter of this study does not differ by much from the Phase 1, the employment of an additional camera as a means to achieve better accuracy in results has been employed. The reasoning behind this approach is to attempt a closer imitation of the human depth perception. The best and most convincing information about the three dimensional world is attained by binocular vision and this theory is exploited in the current approach. For the purpose of this study, a humble attempt to come closer to the concept of binocular vision is made and only one aspect, that of the binocular disparity, is attempted to be emulated. The inference drawn from this analysis has proven the improved precision with which the ‘fist’ letters were identified. Owing to the fewer number of subjects and technical snags, the comprehensive body of data has been deprived to an extent but this thesis promises to deliver a basic foundation on which to build the future study and lays the guidelines to achieve a more complete and successful translation system

ZATLAB : recognizing gestures for artistic performance interaction

Most artistic performances rely on human gestures, ultimately resulting in an elaborate interaction between the performer and the audience. Humans, even without any kind of formal analysis background in music, dance or gesture are typically able to extract, almost unconsciously, a great amount of relevant information from a gesture. In fact, a gesture contains so much information, why not use it to further enhance a performance? Gestures and expressive communication are intrinsically connected, and being intimately attached to our own daily existence, both have a central position in our (nowadays) technological society. However, the use of technology to understand gestures is still somehow vaguely explored, it has moved beyond its first steps but the way towards systems fully capable of analyzing gestures is still long and difficult (Volpe, 2005). Probably because, if on one hand, the recognition of gestures is somehow a trivial task for humans, on the other hand, the endeavor of translating gestures to the virtual world, with a digital encoding is a difficult and illdefined task. It is necessary to somehow bridge this gap, stimulating a constructive interaction between gestures and technology, culture and science, performance and communication. Opening thus, new and unexplored frontiers in the design of a novel generation of multimodal interactive systems. This work proposes an interactive, real time, gesture recognition framework called the Zatlab System (ZtS). This framework is flexible and extensible. Thus, it is in permanent evolution, keeping up with the different technologies and algorithms that emerge at a fast pace nowadays. The basis of the proposed approach is to partition a temporal stream of captured movement into perceptually motivated descriptive features and transmit them for further processing in Machine Learning algorithms. The framework described will take the view that perception primarily depends on the previous knowledge or learning. Just like humans do, the framework will have to learn gestures and their main features so that later it can identify them. It is however planned to be flexible enough to allow learning gestures on the fly. This dissertation also presents a qualitative and quantitative experimental validation of the framework. The qualitative analysis provides the results concerning the users acceptability of the framework. The quantitative validation provides the results about the gesture recognizing algorithms. The use of Machine Learning algorithms in these tasks allows the achievement of final results that compare or outperform typical and state-of-the-art systems. In addition, there are also presented two artistic implementations of the framework, thus assessing its usability amongst the artistic performance domain. Although a specific implementation of the proposed framework is presented in this dissertation and made available as open source software, the proposed approach is flexible enough to be used in other case scenarios, paving the way to applications that can benefit not only the performative arts domain, but also, probably in the near future, helping other types of communication, such as the gestural sign language for the hearing impaired.Grande parte das apresentações artísticas são baseadas em gestos humanos, ultimamente resultando numa intricada interação entre o performer e o público. Os seres humanos, mesmo sem qualquer tipo de formação em música, dança ou gesto são capazes de extrair, quase inconscientemente, uma grande quantidade de informações relevantes a partir de um gesto. Na verdade, um gesto contém imensa informação, porque não usá-la para enriquecer ainda mais uma performance? Os gestos e a comunicação expressiva estão intrinsecamente ligados e estando ambos intimamente ligados à nossa própria existência quotidiana, têm uma posicão central nesta sociedade tecnológica actual. No entanto, o uso da tecnologia para entender o gesto está ainda, de alguma forma, vagamente explorado. Existem já alguns desenvolvimentos, mas o objetivo de sistemas totalmente capazes de analisar os gestos ainda está longe (Volpe, 2005). Provavelmente porque, se por um lado, o reconhecimento de gestos é de certo modo uma tarefa trivial para os seres humanos, por outro lado, o esforço de traduzir os gestos para o mundo virtual, com uma codificação digital é uma tarefa difícil e ainda mal definida. É necessário preencher esta lacuna de alguma forma, estimulando uma interação construtiva entre gestos e tecnologia, cultura e ciência, desempenho e comunicação. Abrindo assim, novas e inexploradas fronteiras na concepção de uma nova geração de sistemas interativos multimodais . Este trabalho propõe uma framework interativa de reconhecimento de gestos, em tempo real, chamada Sistema Zatlab (ZtS). Esta framework é flexível e extensível. Assim, está em permanente evolução, mantendo-se a par das diferentes tecnologias e algoritmos que surgem num ritmo acelerado hoje em dia. A abordagem proposta baseia-se em dividir a sequência temporal do movimento humano nas suas características descritivas e transmiti-las para posterior processamento, em algoritmos de Machine Learning. A framework descrita baseia-se no facto de que a percepção depende, principalmente, do conhecimento ou aprendizagem prévia. Assim, tal como os humanos, a framework terá que aprender os gestos e as suas principais características para que depois possa identificá-los. No entanto, esta está prevista para ser flexível o suficiente de forma a permitir a aprendizagem de gestos de forma dinâmica. Esta dissertação apresenta também uma validação experimental qualitativa e quantitativa da framework. A análise qualitativa fornece os resultados referentes à aceitabilidade da framework. A validação quantitativa fornece os resultados sobre os algoritmos de reconhecimento de gestos. O uso de algoritmos de Machine Learning no reconhecimento de gestos, permite a obtençãoc¸ ˜ao de resultados finais que s˜ao comparaveis ou superam outras implementac¸ ˜oes do mesmo g´enero. Al ´em disso, s˜ao tamb´em apresentadas duas implementac¸ ˜oes art´ısticas da framework, avaliando assim a sua usabilidade no dom´ınio da performance art´ıstica. Apesar duma implementac¸ ˜ao espec´ıfica da framework ser apresentada nesta dissertac¸ ˜ao e disponibilizada como software open-source, a abordagem proposta ´e suficientemente flex´ıvel para que esta seja usada noutros cen´ arios. Abrindo assim, o caminho para aplicac¸ ˜oes que poder˜ao beneficiar n˜ao s´o o dom´ınio das artes performativas, mas tamb´em, provavelmente num futuro pr ´oximo, outros tipos de comunicac¸ ˜ao, como por exemplo, a linguagem gestual usada em casos de deficiˆencia auditiva

End-to-End Multiview Gesture Recognition for Autonomous Car Parking System

The use of hand gestures can be the most intuitive human-machine interaction medium. The early approaches for hand gesture recognition used device-based methods. These methods use mechanical or optical sensors attached to a glove or markers, which hinders the natural human-machine communication. On the other hand, vision-based methods are not restrictive and allow for a more spontaneous communication without the need of an intermediary between human and machine. Therefore, vision gesture recognition has been a popular area of research for the past thirty years. Hand gesture recognition finds its application in many areas, particularly the automotive industry where advanced automotive human-machine interface (HMI) designers are using gesture recognition to improve driver and vehicle safety. However, technology advances go beyond active/passive safety and into convenience and comfort. In this context, one of America’s big three automakers has partnered with the Centre of Pattern Analysis and Machine Intelligence (CPAMI) at the University of Waterloo to investigate expanding their product segment through machine learning to provide an increased driver convenience and comfort with the particular application of hand gesture recognition for autonomous car parking. In this thesis, we leverage the state-of-the-art deep learning and optimization techniques to develop a vision-based multiview dynamic hand gesture recognizer for self-parking system. We propose a 3DCNN gesture model architecture that we train on a publicly available hand gesture database. We apply transfer learning methods to fine-tune the pre-trained gesture model on a custom-made data, which significantly improved the proposed system performance in real world environment. We adapt the architecture of the end-to-end solution to expand the state of the art video classifier from a single image as input (fed by monocular camera) to a multiview 360 feed, offered by a six cameras module. Finally, we optimize the proposed solution to work on a limited resources embedded platform (Nvidia Jetson TX2) that is used by automakers for vehicle-based features, without sacrificing the accuracy robustness and real time functionality of the system