SMS Distinguished Visitor Programme (DVP) 2010
|Programme||Distinguished Visitor Programme (DVP)|
The Distinguished Visitor Programme was launched by the Singapore Mathematical Society in 1998. Through the visit of a distinguished mathematician/mathematics educator, who will interact with both mathematicians/mathematics educators at the universities as well as teachers and pupils at the schools here, the aim of the Programme is to expose as large and diverse an audience as possible to the excitement and relevance of mathematics, thereby enhance the awareness of mathematics in our society.
Professor Hung-Hsi Wu , University of California, Berkeley, USA
|Academic Talk|| Sense-making and problem-solving in math education in America
In America, sense-making and problem solving are two of the visible goals being actively pursued in mathematics education. A more dispassionate view is that the pursuits are done in isolation, taken out of the context of mathematics itself. The perceived failures in student learning should be understood as the inevitable consequence of the low level of the mathematics in the school curriculum.
|Teacher's Workshop|| The decimal expansion of a fraction
All middle school students learn that one can get the decimal equal to a fraction by long division (of numerator by denominator). The question is why. We will assume an intuitive knowledge of what an infinite decimal is, and use it to prove that any number (a point on the number line) is equal to an infinite or finite decimal. Then we analyze the process and reveal the fact that if the number is a fraction, the process in fact describes the long division algorithms. As a side remark, we observe that the decimal of a fraction is periodic. We will emphasize the fact that the non-triviality of this equality lies not in the periodicity of the decimal (which is the usual emphasis), but in the fact that we must first define precisely what a number is and what a fraction is, and only then can we assert that the two well-defined concepts are equal (i.e., same point on the number line). This is in part an advocacy to give precise definition of a fraction, even in elementary school, as a point on the number line.
|Teacher's Workshop||Geometry based on rigid motions
We begin with the informal introduction of rigid motions in the plane: rotations, translations, and reflections. "Informal" refers to the fact that strictly speaking one needs to first present the precise definitions of mappings, composite mappings, image, inverse image, etc. But we will be using these concepts essentially as axioms and the reasoning with them is rather primitive, so hands-on activities using transparencies can replace mathematical precision almost all the time. This is why this approach can be implemented in middle school. We start proving theorems right away assuming the abundant existence of rotations, and use these simple theorems to help define reflections and translations. In almost no time, we will prove SAS, ASA and SSS. At this point, the usual development can take over as far as congruence is concerned. If there is time, we pursue similarity by introducing dilations and, prove the Fundamental Theorem of Similarity: If D, E are points on AB and AC of triangle ABC, and if AD/AB = AE/AC, then DE//BC and DE/BC = AD/AB = AE/AC. After this, everything about similar triangles follows.
|Registration:||Online Registration (close on 18-8-2010)|
|Coordinator:||Dr Ng Kah Loon Tel: 65162751 Email: email@example.com|