David Tall: Perceptions, Operations and Proof in Undergraduate Mathematics

D. Tall, Perceptions, operations and proof in undergraduate mathematics. The De Morgan Journal 1 no. 1 (2011), 19-27. PDF file of the paper.

Professor David O. Tall (born 15 May 1941) is a mathematics education theorist at the University of Warwick. Personal homepageWikipedia.

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Roger Howe: Three Pillars of First Grade Mathematics

R. Howe, Three pillars of first grade mathematics. The De Morgan Journal 1 no. 1 (2011), 3-17. PDF file of the paper.

Abstract. This note presents a proposal for a coherent approach to mathematics instruction in first grade. The 3 pillars indicated in the title are

  1. a robust understanding of the operations of addition and subtraction;
  2. instruction in arithmetic computation that emphasizes place value issues;
  3. building a strong connection between arithmetic as used in counting, and as used in linear measurement.

The proposal is highly compatible with the recently published (in the US) Common Core State Standards for mathematics, but places more emphasis on connections between topics than might be evident from a casual reading of those standards.

Roger Evans Howe is the William R. Kenan Jr. Professor of Mathematics at Yale University. He is well known for his contributions to representation theory, and in particular for the notion of a reductive dual pair, sometimes known as a Howe pair, and the Howe correspondence. He has been a member of the National Academy of Sciences since 1994. He is also a member of the American Academy of Arts and Sciences. In 2006 he was awarded the American Mathematical Society Award for Distinguished Public Service in recognition of his “multifaceted contributions to mathematics and to mathematics education.”

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Augustus De Morgan: Mathematical Induction

The first  paper of our Blog is the famous Penny Cyclopedia article of 1838 by Augustus De Morgan which contains a description of mathematical induction in the form it is used now in mathematical textbooks. PDF file of the paper.

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician and a founder and the first President of the London Mathematical Society.  He formulated De Morgan’s laws and is seen as one of the creators of mathematical logic.

The paper was first published in The Penny Cyclopedia of the Society for the Diffusion of Useful Knowledge, vol. 12. London: Charles Knight and Co., 22, Ludgate Street, 1838. A scanned image of the original is available on Google Books, http://tinyurl.com/PennyCyclopedia

Please refer to this paper as A. De Morgan, Mathematical induction. The De Morgan Journal 1 no. 1 (2011), 1–2.