We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during...We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during their school and the degree development that shows in their performance when applied to specific fields of knowledge is a task to be elucidated. We place our study in the school stage in which it makes the transition from arithmetic to algebra and arithmetic problems we focus on in the underlying multiplicative comparison scheme. In this paper, we analyzed the responses of high school students to the translation of multiplicative comparison word problems to representation graphs. We have used the responses of 12 -14 year old students （freshman year of secondary school） to represent multiplicative comparison word problems to identify and categorize the students responses, which allowed us identify categories for each type of representation and hypothesize priority order and subordination between the categories. Results show that students are not familiar with building diagrams that integrate existing relations in word problems. Most of the students do not use all the quantitative information contained in the word problem, therefore draw diagrams referring to the subject or context of the problem without relating to the data in it. We describe in detail the quantitative diagram types produced by these students. We have identified four kinds of quantitative diagrams that the students used to represent the multiplicative comparison problems with inconsistent statements, and these diagrams correspond to the four strategies for tackling the construction of the diagram.展开更多
Due to the encephalic tissues are highly irregular, three-dimensional （3D） modeling of brain always leads to compli- cated computing. In this paper, we explore an efficient method for brain surface reconstruction fr...Due to the encephalic tissues are highly irregular, three-dimensional （3D） modeling of brain always leads to compli- cated computing. In this paper, we explore an efficient method for brain surface reconstruction from magnetic reso- nance （MR） images of head, which is helpful to surgery planning and tumor localization. A heuristic algorithm is pro- posed foi＂ surface triangle mesh generation with preserved features, and the diagonal length is regarded as the heuristic information to optimize the shape of triangle. The experimental results show that our approach not only reduces the computational complexity, but also completes 3D visualization with good quality.展开更多
文摘We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during their school and the degree development that shows in their performance when applied to specific fields of knowledge is a task to be elucidated. We place our study in the school stage in which it makes the transition from arithmetic to algebra and arithmetic problems we focus on in the underlying multiplicative comparison scheme. In this paper, we analyzed the responses of high school students to the translation of multiplicative comparison word problems to representation graphs. We have used the responses of 12 -14 year old students （freshman year of secondary school） to represent multiplicative comparison word problems to identify and categorize the students responses, which allowed us identify categories for each type of representation and hypothesize priority order and subordination between the categories. Results show that students are not familiar with building diagrams that integrate existing relations in word problems. Most of the students do not use all the quantitative information contained in the word problem, therefore draw diagrams referring to the subject or context of the problem without relating to the data in it. We describe in detail the quantitative diagram types produced by these students. We have identified four kinds of quantitative diagrams that the students used to represent the multiplicative comparison problems with inconsistent statements, and these diagrams correspond to the four strategies for tackling the construction of the diagram.
基金supported by the National Natural Science Foundation of China(No.61202169)
文摘Due to the encephalic tissues are highly irregular, three-dimensional （3D） modeling of brain always leads to compli- cated computing. In this paper, we explore an efficient method for brain surface reconstruction from magnetic reso- nance （MR） images of head, which is helpful to surgery planning and tumor localization. A heuristic algorithm is pro- posed foi＂ surface triangle mesh generation with preserved features, and the diagonal length is regarded as the heuristic information to optimize the shape of triangle. The experimental results show that our approach not only reduces the computational complexity, but also completes 3D visualization with good quality.
