Primary students’ interpretation of maps : gesture use and mapping knowledge

Maps are used to represent three-dimensional space and are integral to a range of everyday experiences. They are increasingly used in mathematics, being prominent both in school curricula and as a form of assessing students understanding of mathematics ideas. In order to successfully interpret maps, students need to be able to understand that maps: represent space, have their own perspective and scale, and their own set of symbols and texts. Despite the fact that maps have an increased prevalence in society and school, there is evidence to suggest that students have difficulty interpreting maps. This study investigated 43 primary-aged students’ (aged 9-12 years) verbal and gestural behaviours as they engaged with and solved map tasks. Within a multiliteracies framework that focuses on spatial, visual, linguistic, and gestural elements, the study investigated how students interpret map tasks. Specifically, the study sought to understand students’ skills and approaches used to solving map tasks and the gestural behaviours they utilised as they engaged with map tasks. The investigation was undertaken using the Knowledge Discovery in Data (KDD) design. The design of this study capitalised on existing research data to carry out a more detailed analysis of students’ interpretation of map tasks. Video data from an existing data set was reorganised according to two distinct episodes—Task Solution and Task Explanation—and analysed within the multiliteracies framework. Content Analysis was used with these data and through anticipatory data reduction techniques, patterns of behaviour were identified in relation to each specific map task by looking at task solution, task correctness and gesture use. The findings of this study revealed that students had a relatively sound understanding of general mapping knowledge such as identifying landmarks, using keys, compass points and coordinates. However, their understanding of mathematical concepts pertinent to map tasks including location, direction, and movement were less developed. Successful students were able to interpret the map tasks and apply relevant mathematical understanding to navigate the spatial demands of the map tasks while the unsuccessful students were only able to interpret and understand basic map conventions. In terms of their gesture use, the more difficult the task, the more likely students were to exhibit gestural behaviours to solve the task. The most common form of gestural behaviour was deictic, that is a pointing gesture. Deictic gestures not only aided the students capacity to explain how they solved the map tasks but they were also a tool which assisted them to navigate and monitor their spatial movements when solving the tasks. There were a number of implications for theory, learning and teaching, and test and curriculum design arising from the study. From a theoretical perspective, the findings of the study suggest that gesturing is an important element of multimodal engagement in mapping tasks. In terms of teaching and learning, implications include the need for students to utilise gesturing techniques when first faced with new or novel map tasks. As students become more proficient in solving such tasks, they should be encouraged to move beyond a reliance on such gesture use in order to progress to more sophisticated understandings of map tasks. Additionally, teachers need to provide students with opportunities to interpret and attend to multiple modes of information when interpreting map tasks.

Co-thought gestures : supporting students to successfully navigate map tasks

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged 10–12 years) over a 3-year period as they solved map tasks that required spatial reasoning. The map tasks were representative of those typically found in mathematics classrooms for this age group and required route finding and coordinate knowledge. The results indicated that co-thought gestures were used to navigate the problem space and monitor movements within the spatial challenges of the respective map tasks. Gesturing was most influential when students encountered unfamiliar tasks or when they found the tasks spatially demanding. From a teaching and learning perspective, explicit co-thought gesturing highlights cognitive challenges students are experiencing since students tended to not use gesturing in tasks where the spatial demands were low.

Da crítica à relação sociedadenatureza no ensino de Geografia à crítica da questão ambiental na mídia

O ensino de Geografia defrontase com inúmeros desafios no que compete à formação de cidadãos com efetiva atuação social. Neste estudo, apontase, como um destes desafios, o raciocínio espacial, tendo como ponto de partida a compreensão multiescalar e multifacetada da questão ambiental por meio do reconhecimento dos diversos discursos e significados que permeiam essa questão. A mídia constituise, nos últimos tempos, em expressiva instância para a produção de sentidos e de representações acerca do que vem a constituir esse debate, tendo o docente um papel indispensável na mediação da prática educativa e na problematização dos processos que se pretendem hegemônicos. Considerando essas questões, este estudo discute o movimento a ser estabelecido da crítica à relação sociedadenatureza no ensino de Geografia à crítica da questão ambiental apresentada pela mídia. Para tal, desenvolveuse uma metodologia de pesquisa que, envolvendo professores e alunos, buscou confrontar as concepções e práticas enunciadas como as responsáveis pelo debate ambiental em sala de aula com a questão ambiental difundida pela mídia, sendo observados como principais aspectos: a persistente dicotomia sociedade versus natureza como a principal responsável pela dificuldade de professores e alunos na análise da questão ambiental; o não reconhecimento, por parte dos professores, de que essa dicotomia ainda se faz latente no pensar e no fazer geográfico na escola; a carência de uma mediação pedagógica entre o material da mídia e o conhecimento geográfico incorrendo na não problematização de importantes elementos concernentes à questão ambiental; as informações ambientais da mídia têmse sobreposto ao conhecimento geográfico do ambiente a ser pautado na relação sociedadenatureza; o reprodutivismo dos discursos e representações mediáticos sobre a natureza, o ambiente e o espaço pelos alunos. Portanto, a partir dessas constatações, concluise que as percepções da questão ambiental, deslocadas da compreensão analítica e crítica da relação sociedadenatureza na contemporaneidade, podem conduzir a interpretações fragmentárias e simplificadoras do espaço. Como contrapontos a essa perspectiva, são apresentados aspectos das teorias da complexidade (Edgar Morin) e da totalidade (na concepção geográfica de Milton Santos) como importantes alternativas analíticas para o combate da visão dicotômica homem (sociedade) versus meio (natureza) e, por conseguinte, para o fortalecimento da compreensão do espaço enquanto uma totalidade dialética.

非言语学习不良青少年空间关系推理及其影响因素研究

It has reported that individuals with nonverbal learning disabilities (NLD) have deficits in visual-spatial organization and strengths in rote language abilities. At present, there are few studies on higher order cognitive abilities of adolescents with NLD, such as the reasoning about spatial relations. The study sampled three groups: a normal group (a control group, C), a nonverbal learning disabilities group (NLD), and a verbal learning disabilities group (VLD). The aim of this study was to examine spatial and nonspatial relation reasoning abilities in adolescents with NLD under figure and word conditions, and assessed the relative involvement of different working memory components in four types of reasoning tasks: reasoning about figure-spatial, figure-nonspatial, verbal-spatial, and verbal-nonspatial relations. Using the double-tasks methodology, visual, spatial, central-executive, and phonological loads were realized. We tried to find how working memory components impact on adolescents with NLD spatial and nonspatial reasoning. The main results of present research are as follows. (1) The NLD group didn’t differ from normal group on reasoning about figure-nonspatial relations. The NLD group scored lower than the C group in spatial problems. So, adolescents with NLD showed a dissociation between spatial and non-spatial relation reasoning. They scored higher in non-spatial problems than in spatial ones. Adolescents with VLD developed well in reasoning about figure-nonspatial relations, but showed deficits in other three tasks. (2) For each reasoning task, the difficult of four types of reasoning problem had different changing trend. For figure and verbal spatial problems, mental model approach can interpret performance of the four problems well. For verbal nonspatial problems, a logical rule approach can interpret performance of the four problems well. (3) Adolescents with NLD did not differ from adolescents with VLD and normal adolescents in phonological, central-executive, and visual dual tasks. But the NLD group had lower performance than the other two groups in spatial dual task. The results showed a dissociation between visual and spatial working memory in NLD group. The VLD group only experienced deficits in central-executive subsystem. (4) The studies found that spatial reasoning mainly loaded spatial working memory, whist the involvement of spatial resources in nonspatial reasoning was little. Visual working memory mainly involved in reasoning about spatial and figure-nonspatial relations, especially in figure-nonspatial problems, and had few impacts on verbal-nonspatial reasoning. Central executive system was involved in all reasoning tasks. The role of phonological loop in the reasoning tasks required further explored. (5) According to the findings, we concluded that the deficits in spatial working memory resulted in poor spatial reasoning abilities for teenagers with NLD, whist because of the limited central executive capability, teenagers with VLD showed poor reasoning abilities. (6) The three groups can used multiple strategies during the reasoning process. They didn’t differ from each other in reasoning strategies. They all used mental model strategy to solve figure and verbal spatial problems, and used logic rule strategy to solve verbal nonspatial problems.

Automatic Design of a Maglev Controller in State Space

We describe the automatic synthesis of a global nonlinear controller for stabilizing a magnetic levitation system. The synthesized control system can stabilize the maglev vehicle with large initial displacements from an equilibrium, and possesses a much larger operating region than the classical linear feedback design for the same system. The controller is automatically synthesized by a suite of computational tools. This work demonstrates that the difficult control synthesis task can be automated, using programs that actively exploit knowledge of nonlinear dynamics and state space and combine powerful numerical and symbolic computations with spatial-reasoning techniques.

A blackboard architecture for a hybrid CBR system for scientific software

This paper describes the use of a blackboard architecture for building a hybrid case based reasoning (CBR) system. The Smartfire fire field modelling package has been built using this architecture and includes a CBR component. It allows the integration into the system of qualitative spatial reasoning knowledge from domain experts. The system can be used for the automatic set-up of fire field models. This enables fire safety practitioners who are not expert in modelling techniques to use a fire modelling tool. The paper discusses the integrating powers of the architecture, which is based on a common knowledge representation comprising a metric diagram and place vocabulary and mechanisms for adaptation and conflict resolution built on the Blackboard.

A aprendizagem musical como elemento de aperfeiçoamento de competências matemáticas

Tomando como ponto de partida a relação entre música e matemática, nesta investigação temos como principal objetivo estudar a influência da aprendizagem musical no desempenho matemático. Pretendeu-se ainda observar o efeito de um conjunto de preditores no referido desempenho, mais concretamente do nível socioeconómico, da inteligência e de variáveis cognitivo-motivacionais (motivação, expectativas de autoeficácia e atribuições causais). Numa primeira parte, delineámos as linhas teóricas desta investigação. Começámos por relatar a relação entre música e matemática no âmbito da musicologia histórica, da teoria e análise musicais, da acústica e das tendências na composição musical, evidenciando os mecanismos de ligação entre elementos e conceitos musicais e tópicos e temas matemáticos. Relatámos os benefícios da exposição musical ao nível do desenvolvimento cognitivo e intelectual, destacando o aumento do raciocínio espacial, do desempenho matemático e da inteligência com a aprendizagem musical. De seguida, descrevemos o impacto das aulas de música no aumento do desempenho académico a várias disciplinas, nomeadamente a Matemática, enfatizando a associação da duração da aprendizagem musical com o aumento das capacidades matemáticas; para além do efeito da aprendizagem musical, procurámos ainda explicação de um desempenho académico melhorado com base em variáveis potenciadoras da performance, tais como o nível socioeconómico e a inteligência. Nesta linha de abordagem, explorámos os efeitos de variáveis influentes do desempenho académico fora do contexto musical, reportando-nos ao nível socioeconómico, à inteligência e às dimensões cognitivo-motivacionais (motivação, expectativas de autoeficácia e atribuições causais), destacando o poder preditivo da inteligência, seguido do nível socioeconómico e da motivação. Por fim, referimo-nos à interação entre música e encéfalo por meio das temáticas da plasticidade neural estrutural e funcional, do efeito da aprendizagem e performance musicais, da cognição musical e domínios não musicais, bem como dos fatores genéticos; sublinhamos a possibilidade de ligações entre a cognição musical e os domínios espacial e matemático. Numa segunda parte, apresentamos a investigação que desenvolvemos em contexto escolar com 112 alunos do 7º ano de escolaridade provenientes de 12 escolas do Ensino Básico. Nove são do Ensino Especializado de Música e três são do Ensino Regular. No total, as escolas enquadram-se nas zonas urbanas de Braga, Coimbra e Lisboa. O estudo possui carácter longitudinal e abrange três anos letivos, do 7º ao 9º anos de escolaridade. Após explanação dos objetivos, das hipóteses de investigação, da caracterização da amostra, da descrição dos instrumentos de avaliação e respetiva validação empírica, relatamos os resultados que encontrámos. Estes permitiram, por um lado, validar a hipótese de que os alunos submetidos ao ensino formal de música apresentam um desempenho matemático superior comparativamente aos alunos que não frequentaram este tipo de ensino (H1) e, por outro, sustentar que o número de anos de aprendizagem musical contribui para o aumento do desempenho matemático (H3). Sublinha-se, ainda, que os alunos de instrumento de teclado revelaram desempenho matemático mais elevado em relação aos seus pares que estudaram outros instrumentos. Já no que se refere ao poder preditivo do tipo de ensino (Ensino Especializado de Música vs. Ensino Regular), apurámos que a formação em música prevê melhores desempenhos a matemática; destaca-se que as variáveis em estudo, tais como o nível socioeconómico, a motivação, as expectativas de autoeficácia e a inteligência adicionam capacidade explicativa do desempenho matemático, sendo que a presença da aprendizagem musical perdeu aptidão preditiva apenas na presença da inteligência. Contudo, após controlo estatístico da inteligência, foi possível concluir que a aprendizagem musical mantém o poder preditivo no desempenho matemático (H2). Os resultados permitiram identificar em que tópicos e temas matemáticos relacionados com os elementos e conceitos musicais os alunos com aprendizagem musical apresentam melhores desempenhos, evidenciando-se os tópicos no âmbito da Geometria (H4). Observámos, também, que é possível prever o desempenho matemático a partir do raciocínio espacial dos alunos (H5). Finalmente, referimos as limitações, refletimos sobre as implicações que estes resultados poderão trazer no âmbito do ensino da música em Portugal e apontamos pistas conducentes ao desenvolvimento de investigações futuras.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

Two-dimensional string notation for representing video sequences

Most current work on video indexing concentrates on queries which operate over high level semantic information which must be entirely composed and entered manually. We propose an indexing system which is based on spatial information about key objects in a scene. These key objects may be detected automatically, with manual supervision, and tracked through a sequence using one of a number of recently developed techniques. This representation is highly compact and allows rapid resolution of queries specified by iconic example. A number of systems have been produced which use 2D string notations to index digital image libraries. Just as 2D strings provide a compact and tractable indexing notation for digital pictures, a sequence of 2D strings might provide an index for a video or image sequence. To improve further upon this we reduce the representation to the 2D string pair representing the initial frame, and a sequence of edits to these strings. This takes advantage of the continuity between frames to further reduce the size of the notation. By representing video sequences using string edits, a notation has been developed which is compact, and allows querying on the spatial relationships of objects to be performed without rebuilding the majority of the scene. Calculating ranks of objects directly from the edit sequence allows matching with minimal calculation, thus greatly reducing search time. This paper presents the edit sequence notation and algorithms for evaluating queries over image sequences. A number of optimizations which represent a considerably saving in search time is demonstrated in the paper.

A utilização das tecnologias assistidas por computador como elemento de integração, pesquisa e desenvolvimento nas disciplinas de projeto para a engenharia e design

The use of technologies called computedassisted, such as CAD - (Computed Aided Design), CAM - (Computed Aided Manufacturing) and CNC - (Computed Numerical Control), increasingly demanded by the market, are needed in the teaching of subjects technical drawing and design courses for engineering and design. However its use findl barriers in the more conservative wing of the academy, who advocate the use of traditional drawing, for the settling of the concepts and the development of spatial reasoning. This study aimed to show the results obtained with the design and production of an apparatus for measuring a three-dimensional computer-aided milling machine, interaction, integration and consolidation of concepts, fully demonstrating that the learning of computer-assisted technology is possible, and its use is most appropriate, meaningful and productive, than the use of instruments in the classic design.

Image Quotient Set Transforms in Segmentation Problems

Image content interpretation is much dependent on segmentations efficiency. Requirements for the image recognition applications lead to a nessesity to create models of new type, which will provide some adaptation between law-level image processing, when images are segmented into disjoint regions and features are extracted from each region, and high-level analysis, using obtained set of all features for making decisions. Such analysis requires some a priori information, measurable region properties, heuristics, and plausibility of computational inference. Sometimes to produce reliable true conclusion simultaneous processing of several partitions is desired. In this paper a set of operations with obtained image segmentation and a nested partitions metric are introduced.

Connecting visual and analytic reasoning to improve students' spatial visualization abilities: A constructivist approach

Current reform initiatives recommend that school geometry teaching and learning include the study of three-dimensional geometric objects and provide students with opportunities to use spatial abilities in mathematical tasks. Two ways of using Geometer's Sketchpad (GSP), a dynamic and interactive computer program, in conjunction with manipulatives enable students to investigate and explore geometric concepts, especially when used in a constructivist setting. Research on spatial abilities has focused on visual reasoning to improve visualization skills. This dissertation investigated the hypothesis that connecting visual and analytic reasoning may better improve students' spatial visualization abilities as compared to instruction that makes little or no use of the connection of the two. Data were collected using the Purdue Spatial Visualization Tests (PSVT) administered as a pretest and posttest to a control and two experimental groups. Sixty-four 10th grade students in three geometry classrooms participated in the study during 6 weeks. Research questions were answered using statistical procedures. An analysis of covariance was used for a quantitative analysis, whereas a description of students' visual-analytic processing strategies was presented using qualitative methods. The quantitative results indicated that there were significant differences in gender, but not in the group factor. However, when analyzing a sub sample of 33 participants with pretest scores below the 50th percentile, males in one of the experimental groups significantly benefited from the treatment. A review of previous research also indicated that students with low visualization skills benefited more than those with higher visualization skills. The qualitative results showed that girls were more sophisticated in their visual-analytic processing strategies to solve three-dimensional tasks. It is recommended that the teaching and learning of spatial visualization start in the middle school, prior to students' more rigorous mathematics exposure in high school. A duration longer than 6 weeks for treatments in similar future research studies is also recommended.

Reasoning about natural language phrases for semantic goal driven exploration

This paper presents a symbolic navigation system that uses spatial language descriptions to inform goal-directed exploration in unfamiliar office environments. An abstract map is created from a collection of natural language phrases describing the spatial layout of the environment. The spatial representation in the abstract map is controlled by a constraint based interpretation of each natural language phrase. In goal-directed exploration of an unseen office environment, the robot links the information in the abstract map to observed symbolic information and its grounded world representation. This paper demonstrates the ability of the system, in both simulated and real-world trials, to efficiently find target rooms in environments that it has never been to previously. In three unexplored environments, it is shown that on average the system travels only 8.42% further than the optimal path when using only natural language phrases to complete navigation tasks.