Mathematics and Computer Science (original) (raw)
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Eurasia Journal of Mathematics, Science and Technology Education
The purpose of this study was to explore geometry spatial mathematical reasoning in Grade nine Annual National Assessments, South Africa. Conceptual Blending was the guiding theory. Document analysis within the exploratory case study was used to explore available data, the 2014 Annual National Assessment learners' scripts (n=1250). Results revealed that on average 70.5 percent of the total number of learners remembered and blended irrelevant prior knowledge not reflective to the contexts of the geometry problems. For learners who recalled the correct prior knowledge, its manipulation was either fragmented or irrelevant. The use of recalled information in wrong contexts could be due to the incorrect manipulation of the meaning of the problems. Also, responses reveal challenges on the quality of mathematics education on geometry. Therefore, the teaching and learning of geometry should focus on empowering learners with skills of recalling, blending and on manipulating problems in their contexts.
Demonstration in Euclidean Geometry
2014
Drawing out a model or a generalization in mathematic classes for cycle 3 – Grades 7,8 and 9 – is one of the major difficulties the learners face. However, exposing the learners to excessive practice and training on strategies and demonstrations through analysis and intermediate hints can lead to appreciable improvement in the learners’ abilities to solve mathematical problems which come to closure by carrying out a generalization. The aforementioned hypothesis was justified through conducting two examples on particular segments in a triangle in Grades 7, 8, and 9. Two theories support the approach of this action research. The theory of the Dutch researcher - Pierre Marie Van Hiele - who divided the Geometry learning into 5 sequential or linear steps: visualization, analysis, informal deduction, deduction, and rigor. On the other hand, the theory of the French researcher - Alain Kuzniak - who presented the Geometry learning as a back and forth navigation between three levels of Geom...
Integration of the data from electroanatomical mapping system and CT imaging modality
The International Journal of Cardiovascular Imaging, 2009
Purpose: Heart mapping systems allow approximate reconstruction of the heart chamber geometry which is used as a base for the representation of the spatial distribution of electrophysiological parameters. Main limitation lies in the difficulty of the reconstruction of the geometry of more complicated areas of the heart. Here, we propose a new method of representation of the spatial distribution of the electrophysiological parameters -an integration of the data points collected by a classical mapping system with the geometry reconstructed from a computed tomography (CT) image. Methods: CARTO maps of activation and bipolar viability of 7 patients undergoing atrial fibrillation ablation were integrated with the geometry of the left atria reconstructed from the CT image. Results: In all cases, integration was successful with the registration error measured as the distance between objects equal to 2.52±0.25 mm. Bipolar viability and activation maps were reconstructed on the CT geometry. Conclusions: Our method allowed us to create maps of electrophysiological parameters of anatomically complex structures without the need for their detailed mapping.
Visuospatial working memory in intuitive geometry, and in academic achievement in geometry
Learning and Individual Differences, 2013
A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and Spelke , which distinguishes between core, presumably innate, and culturally-mediated principles of geometry; and (3) a task measuring academic achievement in geometry. Path analysis models showed that some VSWM components support culturally-mediated principles of geometry, whereas no VSWM component is related to the core principles of geometry. A complex VSWM task requiring the manipulation of visual information as well as core and culturally-mediated principles of geometry directly predicted academic achievement in geometry. Our results are discussed in terms of the role of VSWM in learning geometry.
Point-line geometries with a generating set that depends on the underlying field
Suppose Γ is a Lie incidence geometry defined over some field F having a Lie incidence geometry Γ0 of the same type but defined over a subfield F0 ≤ F as a subgeometry. We investigate the following question: how many points (if any at all) do we have to add to the point-set of Γ0 in order to obtain a generating set for Γ? We note that if Γ is generated by the points of an apartment, then no additional points are needed. We then consider the long-root geometry of the group SLn+1(F) and the line-grassmannians of the polar geometries associated to the groups O2n+1(F), Sp 2n (F) and O + 2n (F). It turns out that in these cases the maximum number of points one needs to add to Γ0 in order to generate Γ equals the maximal number of roots one needs to adjoin to F0 in order to generate F. We prove that in the case of the long-root geometry of the group SLn+1(F) the point-set of Γ0 does not generate Γ. As a byproduct we determine the generating rank of the line grassmannian of the polar geometry associated to Sp 2n (F) (n ≥ 3), if F is a prime field of odd characteristic.
Tanagra: A mixed-initiative level design tool
2010
Abstract Tanagra is a prototype mixed-initiative design tool for 2D platformer level design, in which a human and computer can work together to produce a level. The human designer can place constraints on a continuously running level generator, in the form of exact geometry placement and manipulation of the level's pacing. The computer then fills in the rest of the level with geometry that guarantees playability, or informs the designer that there is no level that meets their requirements.