Abstract The purpose of this study was to develop mathematical games to assist children in learning addition and subtraction computation. The investigator designed games and experimented through four extra lessons, then studied children¡¦s mathematical learning after the lessons. Participants of this study were second grade children from two elementary schools in Kaohsiung. The experimentation was divided into three phases: pilot phase, first edition phase, and, second edition phase. Data collection and administration included pre-test and post-test; questionnaire of children¡¦s attitude towards mathematics; questionnaire of children¡¦s attitude towards games; record sheets for loan of games; children¡¦s worksheets; learning diaries; researcher¡¦s observation notes; and, researcher¡¦s reflections on design of games. The researcher referred to the above data source, later, evaluated according to the results of experimentation, and completed final revisions. Data analyses and results were three: Design, implementation, and revision. Design. When designing a game, the materials followed that of children¡¦s real life experiences. The characteristics of the four games were: Cooperation, challenge, education, and, chance and luck. Implementation. Children changed from ¡§individual responsibility¡¨ to ¡§co-ordination and cooperation in group¡¨, from ¡§assurance¡¨ to ¡§lack of confidence¡¨, from ¡§marginal participation¡¨ to ¡§eager to play with laughter¡¨, and ¡§no control of shouting¡¨. From the data analyses, children performed well in cognition, attitude, and skills. Revision. The principles of modification were to evaluate games¡¦ strengths and weaknesses, and adjusting games design. The respective revisions were tutoring play, children as key persons, formulating regulations, and, enriching contents. The findings of this study suggested that children benefit from mathematical games and constitute mathematical learning in two-digit number computation. If instructors try hard to design games, be keen in administration, and adjusted games, children will learn through games and result more effective mathematics learning. Finally, it is concluded that the goal of enhancing mathematics learning through games-based instruction as feasible. Key word¡Gmathematics games, addition and subtraction computation

Syftet med studien är att undersöka hur nio elever i årskurs 5 erfar subtraktionstecknet. Studien kommer också presentera och synliggöra elevernas olika uppfattningar och svårigheter kring subtraktionstecknet. Studien har genomförts med hjälp av  kvalitativa intervjuer där nio elever beskriver hur de erfar subtraktionstecknet utifrån olika sammanhang. Den teoretiska utgångspunkten för studien är livsvärldsfenomenologin. Vid analys av studiens datamaterial har teman formats som sedan behandlas i studiens resultatkapitel. Resultatet är att eleverna betraktar subtraktionstecknet som att något ska tas bort eller minskar ett annat tal. Studiens resultat visar också att eleverna anser att subtraktion är svårt, och att fel ofta begås för att det är flera steg vid genomförandet av beräkningarna. Resultatet synliggör också att eleverna inte reflekterar kring sina val av metoder och strategier i samband med beräkningar av subtraktion. / The aim of this study is to investigate how nine pupils in schoolyear 5 experiences the subtraction sign. The study will present and reveal the pupils’ different perceptions and difficulties regarding the subtraction sign. This study has been performed through qualitative interviews by nine pupils describing how they comprehend the subtraction sign in different contexts. The theoretical point of view in this study is life-world phenomenology. When analyzing the study’s datasets, a number of themes has been formed that later are addressed in the result. The result of this study shows that the pupils considers the subtraction sign as to take something away or to decrease a number. The result also shows that the pupils considers subtraction to be difficult, and errors often occurs because of multiple steps during the calculations. Furthermore, the result reveal that the pupils are not aware of their choice regarding methods and strategies when making calculations in subtraction.

No intuito de transformar sistemas de angiografia convencionais em sistemas de subtração digital com angiografia foram implementados três métodos de subtração digital: subtração digital por complemento de um, subtração por comparação 1 e subtração digital por comparação 2 e dois métodos de processamento: \"threshold\" e equalização para aplicação em sistemas angiográficos (DSA). O estudo destes métodos foi realizado com a simulação em sistemas gráficos a partir do qual foram avaliados o realce das pequenas estruturas vasculares, a influência do ruído e a velocidade de operação na subtração das imagens. Os algoritmos desenvolvidos em linguagem Pascal, utilizando Borland Delphi 2.0 (32 bits) foram testados com imagens obtidas no Hospital das Clínicas de Ribeirão Preto e os resultados foram comparados por análise visual. / In the intention of transforming systems of conventional angiography in systems of digital subtraction with angiography three methods of digital subtraction were implemented, digital subtraction for complement of a, subtraction for comparison 1 and digital subtraction for comparison 2 two processing methods: threshold and equalize for application in systems angiographycs (DSA). The study of these methods was accomplished with the simulation in graphic systems statting from which were appraised it enhances it of the small vascular structures, the influence of the noise and the operation speed in the subtraction of the images. The algorithms developed in linguage Pascal, using Borland Delphi 2.0 (32 bits) they were tested with images obtained in the Hospital of the Clinics in Ribeirão Preto and the results were compared by visual analysis.

In this thesis we explore several algorithms for automatic real-time tracking of a tennis ball. We first investigate the use of background subtraction with color/shape recognition for fast tracking of the tennis ball. We then compare our solution with a cascade of boosted Haar classifiers [68] in a simulated environment to estimate the accuracy and ideal processing speeds. The results show that background subtraction techniques were not only faster but also more accurate than Haar classifiers. Following these promising results, we extend the background subtraction and develop other three improved techniques. These techniques use more accurate background models, more reliable and stringent criteria. They allow us to track the tennis ball in a real tennis environment with cameras having higher resolutions and frame rates. <p>We tested our techniques with a large number of real tennis videos. In the indoors environment, We achieved a true positive rate of about 90%, a false alarm rate of less than 2%, and a tracking speed of about 20 fps. For the outdoors environment, the performance of our techniques is not as good as the indoors cases due to the complexity and instability of the outdoors environment. The problem can be solved by resetting our system such that the camera focuses mainly on the tennis ball. Therefore, the influence of the external factors is minimized.<p>Despite the existing limitations, our techniques are able to track a tennis ball with very high accuracy and fast speed which can not be achieved by most tracking techniques currently available. We are confident that the motion information generated from our techniques is reliable and accurate. Giving this promising result, we believe some real-world applications can be constructed.

In this thesis we explore several algorithms for automatic real-time tracking of a tennis ball. We first investigate the use of background subtraction with color/shape recognition for fast tracking of the tennis ball. We then compare our solution with a cascade of boosted Haar classifiers [68] in a simulated environment to estimate the accuracy and ideal processing speeds. The results show that background subtraction techniques were not only faster but also more accurate than Haar classifiers. Following these promising results, we extend the background subtraction and develop other three improved techniques. These techniques use more accurate background models, more reliable and stringent criteria. They allow us to track the tennis ball in a real tennis environment with cameras having higher resolutions and frame rates. <p>We tested our techniques with a large number of real tennis videos. In the indoors environment, We achieved a true positive rate of about 90%, a false alarm rate of less than 2%, and a tracking speed of about 20 fps. For the outdoors environment, the performance of our techniques is not as good as the indoors cases due to the complexity and instability of the outdoors environment. The problem can be solved by resetting our system such that the camera focuses mainly on the tennis ball. Therefore, the influence of the external factors is minimized.<p>Despite the existing limitations, our techniques are able to track a tennis ball with very high accuracy and fast speed which can not be achieved by most tracking techniques currently available. We are confident that the motion information generated from our techniques is reliable and accurate. Giving this promising result, we believe some real-world applications can be constructed.

In this paper an overview is given on the application of directional basis functions, known under the name Curvelets/Contourlets, to various aspects of seismic processing and imaging, which involve adaptive subtraction. Key concepts in the approach are the use of (i) directional basis functions that localize in both domains (e.g. space and angle); (ii) non-linear estimation, which corresponds to localized muting on the coefficients, possibly supplemented by constrained optimization. We will discuss applications that include multiple, ground-roll removal and migration denoising.

No intuito de transformar sistemas de angiografia convencionais em sistemas de subtração digital com angiografia foram implementados três métodos de subtração digital: subtração digital por complemento de um, subtração por comparação 1 e subtração digital por comparação 2 e dois métodos de processamento: \"threshold\" e equalização para aplicação em sistemas angiográficos (DSA). O estudo destes métodos foi realizado com a simulação em sistemas gráficos a partir do qual foram avaliados o realce das pequenas estruturas vasculares, a influência do ruído e a velocidade de operação na subtração das imagens. Os algoritmos desenvolvidos em linguagem Pascal, utilizando Borland Delphi 2.0 (32 bits) foram testados com imagens obtidas no Hospital das Clínicas de Ribeirão Preto e os resultados foram comparados por análise visual. / In the intention of transforming systems of conventional angiography in systems of digital subtraction with angiography three methods of digital subtraction were implemented, digital subtraction for complement of a, subtraction for comparison 1 and digital subtraction for comparison 2 two processing methods: threshold and equalize for application in systems angiographycs (DSA). The study of these methods was accomplished with the simulation in graphic systems statting from which were appraised it enhances it of the small vascular structures, the influence of the noise and the operation speed in the subtraction of the images. The algorithms developed in linguage Pascal, using Borland Delphi 2.0 (32 bits) they were tested with images obtained in the Hospital of the Clinics in Ribeirão Preto and the results were compared by visual analysis.

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The purpose of this study is to investigate how the teaching of mathematics is reflected in the students' understanding of the concept of the subtraction. The empirical data is based on observations in the classroom and student interviews. The understanding of the concept of the subtraction is shown through vocabulary and choice of examples and representations. The study used both qualitative methods and quantitative reports. The data is represented by one school and one classroom in grade three.  The theoretical framework is based on Liping Mas Subject Matter Knowledge and the variation theory of Marton and Booth and the relationship between these frameworks and concepts of variation, concretization, aids, subtraction and types of subtraction.  The results show that the impact of education is that subtraction is understood as the invers of addition. Complement and add to, is the type of strategy most frequently used, followed closely by the strategy remove and count down. The strategy compare is the least used. The observations in the classrooms shows several aspects and variations of the concept of the subtraction. Although the number line, and various forms of representation used in teaching has shown small effects of these aids in the students' own counting. The conclusions that can be drawn is that more and other metaphors and tools are needed in education to deepen students' understanding of the concept of the subtraction. They also need to be connected in the teaching. The language and the mathematical ideas discussed plays a critical role in the pupils’ acquisition of understanding.

The purpose of this qualitative study was to investigate how the progression appears in the teaching of subtraction between preschool class and grade 1. What was examined was whether the teaching in subtraction is interrelated be- tween these grades or whether it differs completely. In order to find this out, interviews were conducted with employed qualified teachers in pre-school class and grade 1. Through these interviews we got to learn about the teachers' stories about how they work and what influences their choices in their work on subtraction. A teaching media analysis was also carried out on the teaching materials that teachers stated they used in the teaching of subtraction. The re- sults show that teachers in pre-school class work very much with laboratory teaching materials in their teaching as well as in whole class or smaller groups, while teachers in grade 1 work less in whole class/groups but more with indi- vidual work. The work in grade 1 proves to be more focused on the fact that teachers want something to assess the students compared to the preschool class' work where much of the learning is done through play. The results show that preschool teachers work either very little with subtraction or not at all com- pared to primary school teachers in grade 1 where subtraction is practiced on a regular basis. In preschool the terminology that is used is both formal and informal, however, overall more informal words are used compared to grade 1 where more formal words are used. The results also show that preschool teach- ers prepare the subtraction strategy step-by-step calculations. In grade 1 the strategy step-by-step calculations are used as well as the numerical calculations strategy. / Syftet med denna kvalitativa studie var att undersöka hur progressionen ser ut i subtraktionsundervisning mellan förskoleklass och årskurs 1. Det som un- dersöktes var om undervisningen i subtraktion hänger samman mellan dessa årskurser eller om den ser helt olika ut. För att få reda på detta genomfördes intervjuer med verksamma behöriga lärare i förskoleklass samt årskurs 1. Ge- nom dessa intervjuer fick vi ta del av lärares berättelser om hur de arbetar och vad som påverkar deras val i sitt arbete med subtraktion. En läromedelsanalys genomfördes även på de läromedel som lärare uppgav att de använde sig av i subtraktionsundervisningen. Resultatet visar att lärare i förskoleklass arbetar väldigt mycket med laborativa läromedel i sin undervisning samt i helklasser eller mindre grupper medan lärare i årskurs 1 arbetar betydligt mindre del i helklass/grupper men desto mer med individuellt arbete. Arbetet i årskurs 1 visar sig vara mer inriktat på att lärare vill ha något som de kan bedöma ele- verna på jämfört med förskoleklassens arbete där stor del av lärandet sker ge- nom lek. Resultatet visar att lärare i förskoleklass arbetar väldigt lite eller inte alls med subtraktion till skillnad från årskurs 1 där subtraktion tränas regel- bundet. Terminologin som används i förskoleklass är en kombination av in- formella och formella ord, dock merparten informella ord till skillnad från årskurs 1 där det används mer formella ord. Resultatet visar att lärare i för- skoleklass förbereder subtraktionsstrategin stegvisa beräkningar och i årskurs 1 tränas strategierna stegvisa beräkningar samt talsortsvisa beräkningar.