The Effectiveness of Teaching Geometry to Enhance Mathematical Understanding in Children with Down Syndrome

ABSTRACT

It is widely known that people with Down syndrome have difficulties transitioning from a basic understanding of counting and cardinality to more advanced arithmetic skills. This is commonly addressed by resorting to the mechanical use of algorithms, which hinders the acquisition of mathematical concepts. For this reason some authors have recently proposed a shift in the focus of learning from arithmetic to more fertile fields, in terms of understanding. In this paper we claim geometry fits this profile, especially suited for initiating children with Down syndrome into mathematics. To support this we resort to historical, epistemological, and cognitive reasons: the work of Séguin and his intuition on the central role of geometry in the development of abstract thinking in the so-called idiot children, the ideas of René Thom about the role of continuum intuition in the emergence of conscious thinking, and finally the two strengths people with Down syndrome display: visual learning abilities and interest in abstract symbols. To support these ideas we present the main findings of qualitative research on elementary mathematics teaching to a group of seven children (3–8) with Down syndrome in Spain. The didactic method used, naturally enhance their naïve geometrical conceptions.     

基于图像的建模技术

与传统的基于几何的建模相比较，介绍了基于图像的建模（IBM）技术，重点介绍了IBM的新的研究进展和一些具有代表性的IBM方法，对各种方法进行了分析比较，最后介绍了IBM技术今后的研究方向。     

平面Bonnesen等周不等式的进一步加强

设欧氏平面R2中域D的面积为A,周长为L,r及R分别为D的最大内接圆半径及最小外接圆半径。利用参考文献中和分几何方法,给出了平面Bonnesen等周不等式的进一步加强,证明了L2-4πA≥π2(R-r)2(πR+πr-L)2.     

解析几何课程中重要数学思想方法探究

解析几何里蕴涵着丰富的数学思想方法,其为数学思想方法的教学提供了一个很好的知识平台。师专数学专业主干课程《解析几何》中的数学思想方法可按核心数学思想方法和一般数学思想方法来划分。     

理想元素及其应用

理想元素是欧氏几何过渡到射影几何的桥梁,是射影几何的基石。由于理想元素的"引入,"在欧氏几何的基础上开辟出一块全新的几何园地,使高等几何充满了创新意识和思想,其中理想元素还充满了创造性地综合应用。     

方位词“上”和“下”的空间定位

方位词“上”或“下”所表示的空间位置，主要由它们依附的名词所代表的物体的物理形状和几何形状来决定。物体的使用面和使用部位的不同，造成方位词所表示的空间位置和意义的不同。方位词“上”一般可以表示“上面”“下面”“里面”“表层”“深层”“方面”“上级”“上方”“角度”“范围”“部位”等空间位置和词汇意义。方位词“下”相对比较简单，可以表示“下方”“下部”“下面”等意义。     

Complex numbers and plane geometry

The representation of complex numbers as points of the Euclidean plane naturally leads to a two-way interaction between geometry and numbers. The geometry of the plane has a very deep influence in the study complex analytic functions. In this article, we illustrate the other way aspect by a few simple-minded application of complex numbers to give elegant solutions of problems in plane geometry, such as Ptolemy’s Theorem, Euler-line and Nine-point Circle Theorem. Anant R Shastri is a Professor at IIT, Bombay. His research inerests are in algebraic topology and algebraic geometry. He is also keen in math education and music. This article is based on a talk given to an audience consisting mainly students of class IX and X, at Nehru Science Centre under the aegis of Bombay Association for Science Education and Bombay Math. Colloq. on 25th Jan. 2003. An earlier version of this article was published in Bona Mathematica, Vol.14 Nos.1–2, 2003.     

Does the amount of on-screen text influence student learning from a multimedia-based instructional unit?

The present study examines how changes in the amount of on-screen text will influence student learning from a multimedia instructional unit on basic concepts of coordinate geometry. The relative effectiveness of two different versions (short-text and whole-text) of the instructional unit was examined for students who differed in terms of their ability to remember symbolic units, symbolic systems and symbolic interpretations. A total of 101 seventh graders were randomly assigned to work with either the whole-text or the short-text version. Student gains were analyzed using pre-test, post-test and retention test scores. Memory ability was assessed by the sub-tests of the Structure of Intellect-Learning Abilities Test. Results indicated no significant differences between groups who worked with short-text and whole-text versions. However retention scores of high and low memory groups who worked with the whole-text version showed significant differences. The whole-text version was observed to favor students with high memory for symbolic implications. Results suggest that workability of design principles for multimedia instruction may depend on the nature of the task and characteristics of the learner.     

仿射不变量在初等几何中的应用

简要叙述克莱因(F.Klein)几何观点,介绍几个仿射不变量,探讨如何利用仿射变换中的不变量解决一些初等几何问题,体现了高等几何对初等几何有重要的指导意义。     

沿直边简支环扇形薄板弯曲问题的辛几何法

由平面弹性与薄板弯曲问题的相似性,本文在辛体系中以径向模拟为时间,研究了两直边简支时的环扇形板弯曲问题。利用分离变量和本征函数展开等方法,给出其一个分析求解法,本文所得的结论为辛本征解的应用研究以及相关问题的解析求解提供了理论基础。