Department of Mathematics
Title : WHAT ARE WE THINKING IN MATHS WHEN WE SAY ALL (OR EACH OR EVERY)?
| Speaker: Prof. Ed Dubinsky Affiliation: USA: National Science Foundation & Alfred P. Sloan Foundation Time: 4pm Wednesday, 2 May, 2012 Location: Federation of Graduate Women's Suite, 1st Floor Old Government House |
Abstract
| This talk will explore the question of what is going on in the mind of an individual when he or she, in a mathematical context, uses an adjective such as all, each or every in a statement like all elements of the set S. This question relates to specific mathematical issues such as: potential vs. actual infinity, uncountable sets, and the relation between 0.99 and 1. Not surprisingly, the answer depends on whether the set S is very small, small, large, countably infinite, or uncountable. The presentation will describe how an APOS analysis of this question and related issues suggests an explanation of student difficulties with 0.99 and provides a pedagogical strategy that helps students overcome these difficulties. Unexpectedly, analysis of the data gathered in implementing this strategy leads to a possible revision of APOS Theory. Prof Ed Dubinsky is visiting us from the USA, where he is currently living in Miami, Florida. Although retired, he remains active in mathematics education research and curriculum development projects at the collegiate and secondary levels. He is co-PI on a US National Science Foundation grant to work with high school students from the lowest quartile of socio-economic status and academic performance and a co-PI on a grant from the Alfed P. Sloan Foundation to develop a new approach to assessing student understanding of mathematical concepts. |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
