Elegance with substance

Colignatus, Thomas (2009): Elegance with substance. Published in: Dutch University Press No. ISBN 978 90 3610 138 7 (12 June 2009): pp. 1-112.

Abstract

National parliaments around the world are advised to each have their own national parliamentary enquiry into the education in mathematics and into what is called ‘mathematics’. Current mathematics namely fails and causes extreme social costs.

The failure in mathematics and math education can be traced to a deep rooted tradition and culture in mathematics itself. Mathematicians are trained for abstract theory but when they teach then they meet with real life pupils and students. Didactics requires a mindset that is sensitive to empirical observation which is not what mathematicians are basically trained for. When mathematicians deal with empirical issues then problems arise in general. The stock market crash in 2008 was caused by many factors, including mismanagement by bank managers and failing regulation, but also by mathematicians and ‘rocket scientists’ mistaking abstract models for reality (Mandelbrot & Taleb 2009). Another failure arises in the modelling of the economics of the environment where an influx of mathematical approaches causes too much emphasis on elegant form and easy notions of risk but insufficient attention to reality, statistics and real risk (Tinbergen & Hueting 1991). Errors by mathematicians on realistic assumptions have important consequences for civic discourse and democracy as well (Colignatus 2007). The failure in math education is only one example in a whole range.

The discussion of mathematics in this book can be understood by anyone with a decent command of highschool mathematics. While school math should be clear and didactically effective, a closer look shows that it is cumbersome and illogical. (1) This is illustrated with some twenty examples from a larger stock of potential topics. (2) Additional shopping lists for improvement on both content and didactic method can be formulated as well. (3) Improvements appear possible with respect to mathematics itself, on logic, voting theory, trigonometry and calculus. (4) What is called mathematics thus is not really mathematics. Pupils and students are psychologically tortured and withheld from proper mathematical insight and competence. Other subjects, like the education in economics, biology or physics, suffer as well.

Application of economic theory helps us to understand that markets for education and ideas tend to be characterized by monopolistic competition and natural monopolies. Regulations then are important. Apparently the industry of mathematics education currently is not adequately regulated. The regulation of financial markets is a hot topic nowadays but the persistent failure of mathematics education should rather be high on the list as well. It will be important to let the industry become more open to society.

When you want to understand the underlying historical processes that cause the current state of the world then this is the book for you. Mathematics education must be tackled, both as a noble goal of itself and for the larger causes.

• Item Type: MPRA Paper
• Language: English
• Keywords: education; mathematics; economics; school; college; university; training; skill; ability; human capital policy; human development; capacity formation; remediation; lifecycle skill formation; software; ICT; computer algebra; textbook publishing; learning; teaching; efficacy; regulation; policy evaluation
• Subjects: A - General Economics and Teaching > A2 - Economic Education and Teaching of Economics > A20 - General; I - Health, Education, and Welfare > I2 - Education and Research Institutions > I20 - General; P - Economic Systems > P1 - Capitalist Systems > P16 - Political Economy

References

PM. Colignatus is the name of Thomas Cool in science. See http://www.dataweb.nl/~cool.

Anderson, J. R., L.M. Reder & Simon, H.A. (2000), “Applications and Misapplications of Cognitive Psychology to Mathematics Education”, Texas Educational Review, Summer

Angel, A.R. (2000), “Elementary algebra for college students”, Prentice Hall

Aronson, E. (1992), “The social animal”, 6th edition, Freeman

Barrow, J. (1993), “Pi in the sky. Counting, thinking and being”, Penguin

Baum, M. (2006), “Decimals Score a Point on International Standards”, http://www.nist.gov/public_affairs/techbeat/tb2006_1122.htm#decimal

Braams, B. (2001), “Research into K-12 mathematics education”, see http://www.math.nyu.edu/~braams/links/research0104.html and in general http://www.math.nyu.edu/mfdd/braams/links/

Colignatus (1999), “Beating the software jungle. Selecting the economics software of the future”, http://econpapers.repec.org/paper/wpawuwpgt/9904001.htm

Colignatus (2000), “The Disappointment and Embarrassment of MathML - update: Including Reactions and Answers”, http://www.dataweb.nl/~cool/Papers/MathML/OnMathML.html

Colignatus (2005), “Definition & Reality in the General Theory of Political Economy” (DRGTPE), Dutch University Press, see http://www.dataweb.nl/~cool/Papers/Drgtpe/Index.html

Colignatus (2007a), “A logic of exceptions” (ALOE), see http://www.dataweb.nl/~cool/Papers/ALOE/Index.html

Colignatus (2007b), “Voting theory for democracy”, 2nd edition, see http://www.dataweb.nl/~cool/Papers/VTFD/Index.html

Colignatus (2007c), “Why one would accept Voting Theory for Democracy and reject the Penrose Square Root Weights”, http://mpra.ub.uni-muenchen.de/3885/

Colignatus (2008a), “Trig rerigged. Trigonometry reconsidered. Measuring angles in ‘unit meter around’ and using the unit radius functions Xur and Yur”, April 8, http://www.dataweb.nl/~cool/Papers/Math/TrigRerigged.pdf

Colignatus (2008b), “Review of Howard DeLong (1991), “A refutation of Arrow’s theorem”, with a reaction, also on its relevance in 2008 for the European Union “, July 22 2008, MPRA 9661, http://mpra.ub.uni-muenchen.de/9661/

Colignatus (2008c), “Het Simon Stevin Instituut”, http://www.dataweb.nl/~cool/Thomas/Nederlands/Wetenschap/Artikelen/2008-11-11-Simon-Stevin-Instituut.pdf

Colignatus (2009), “The Tinbergen & Hueting Approach in the Economics of Ecological Survival” (draft), http://mpra.ub.uni-muenchen.de/13899/

Dijksterhuis, H. (1990), “Clio’s stiefkind. Een keuze uit zijn werk door K. van Berkel”, Bert Bakker

Doelman, A. et al. eds. (2008), “Masterplan wiskunde”, NWO, http://www.nwo.nl/nwohome.nsf/pages/NWOA_7P7KRY

Elgersma, S. and W. Verdenius (1974), “Voortgezette analyse”, syllabus Mathematical Institute, Rijksuniversiteit Groningen

Ernest, P. (2000), “Why teach mathematics?”, chapter is published in J. White and S. Bramall eds. (2000), “Why Learn Maths?”, London University Institute of Education; http://www.people.ex.ac.uk/PErnest/why.htm

Freudenthal, H. (1978), “Weeding and sowing. Preface to a science of mathematical education”, Reidel

Freudenthal, H. (1991), “Revisiting mathematics education. China Lectures”, Kluwer

FU wiki (2008), “Pierre van Hiele”, Freudenthal Institute, http://www.fi.uu.nl/wiki/index.php/Pierre_van_Hiele

Gill, R.D. (2008), “Book reviews. Thomas Colignatus. A Logic of Exceptions: Using the Economics Pack Applications of Mathematica for Elementary Logic”, NAW 5/9 nr. 3 sept., http://www.math.leidenuniv.nl/~naw/serie5/deel09/sep2008/reviewssep08.pdf

Gladwell, M. (2000), “The tipping point”, Back Bay Books

Gladwell, M. (2008), “Outliers. The story of success”, Little Brown

Goffree, F., M. van Hoorn and B. Zwaneveld eds. (2000), “Honderd jaar wiskunde-onderwijs”, Leusden (NVvW)

Groen, W. (2003), “Vier decennia wiskundeonderwijs”, Nieuw Archief Wiskunde, NAW 5/4 nr. 4 december 2003

Hattie, J. (1999), “Influences on student learning”, Inaugural Lecture: Professor of Education, University of Auckland, see http://www.education.auckland.ac.nz/staff/j.hattie/

Hiele, P. van (1959), “Development and learning process. A study of some aspects of Piaget’s psychology in relation with the didactics of mathematics”, Acta Paedagogica Ultrajectina XVII, Wolters Groningen

Hornby (1985), “Oxford advanced learner’s dictionary of current English”, Oxford

Hughes-Hallett, D. and A. Gleason et al. (2000), “Calculus. Alternate Version”, 2nd edition, John Wiley & Sons

Jolles J. et al. (2006), “Brain lessons”, Neuropsych publishers, http://www.brainandlearning.eu/

Krantz, S. (2008), “Through a Glass Darkly”, arXiv:0807.2656v1, http://arxiv.org/abs/0807.2656

Landa, L. (1998), “Landamatics Instructional Design Theory and Methodology for Teaching General Methods of Thinking”, paper presented at the Annual Meeting of the American Educational Research Association (San Diego, CA, April 13-17, 1998), Landamatics International, http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/ content_storage_01/0000019b/80/15/7f/c2.pdf

Mandelbrot B., and N. Taleb (2009), “A focus on the exceptions that prove the rule”, Financial Times, January 29, http://www.ft.com/cms/s/0/bc6e6148-ee26-11dd-b791-0000779fd2ac.html?nclick_check=1 or http://www.fooledbyrandomness.com/FT-1.pdf and http://www.fooledbyrandomness.com/FT-2.pdf

Palais, R. (2001a), “π Is wrong!”, The mathematical intelligencer, Vol 23, no 3 p7-8

Palais, R. (2001b), “ The Natural Cosine and Sine Curves”, JOMA, http://mathdl.maa.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=483

Partidge, E. (1979), “Origins”, Routledge & Kegan Paul

Saari, D. (2001a), “Chaotic elections”, AMS, 2001, www.ams.org; or

Saari, D. (2001b), “Decisions and Elections. Explaining the unexpected”, CUP

Salmon, F. (2009), “Recipe for Disaster: The Formula That Killed Wall Street”, Wired, March, http://www.wired.com/techbiz/it/magazine/17-03/wp_quant

Scheelbeek, P.A.J. and W. Verdenius (1973), “Analyse”, syllabus Mathematical Institute, Rijksuniversiteit Groningen

Streun, A. van (2006), “In memoriam de onderwijsman A.D. de Groot”, Euclides 82, Nr. 3

Struik, D. (1977), “Geschiedenis van de wiskunde”, SUA. Translated from “Concise history of mathematics”, Dover 1948

Sullivan, M. (1999), “College algebra”, Prentice Hall

Taleb, N. (2009), “Ten principles for a Black Swan-proof world”, Financial Times, April 7, http://www.ft.com/cms/s/0/5d5aa24e-23a4-11de-996a-00144feabdc0.html

Tall, D. (2002), “Three Worlds of Mathematics”, Bogota, Columbia, July 2–5, 2002, see http://www.warwick.ac.uk/staff/David.Tall/themes/procepts.html

Tinbergen, J. and R. Hueting (1991), “GNP and Market Prices: Wrong Signals for Sustainable Economic Success that Mask Environmental Destruction”, (with Jan Tinbergen). In (R. Goodland, H. Daly, S. El Serafy and B. von Droste zu Hulshoff (eds)), “Environmentally Sustainable Economic Development: Building on Brundtland”, Ch 4: 51-57, United Nations Educational, Scientific and Cultural Organization, Paris, 1991. Also published in R. Goodland et al. (eds), “Population, Technology and Lifestyle: The Transition to Sustainability”, Ch. 4: 52-62. Island Press,  The International Bank for Reconstruction and Development and UNESCO, Washington, D.C., 1992. Also published in R. Goodland et al. (eds), “Environmentally Sustainable Economic Development: Building on Brundtland”, Environment Working Paper 46, The World Bank, Washington, D.C. See also www.sni-hueting.info

Waerden, B.L. van (1975), “Science Awakening I”, 4th edition, Kluwer

Waerden, B.L. van (1983), “Geometry and algebra in ancient civilizations”, Springer

Waerden, B.L. van (1985), “A history of algebra”, Springer

Wallace, D.F. (2003), “Everything and more. A compact history of ∞”, Norton

Watkins, C. (1995), “Follow Through: Why Didn’t We?”, Effective School Practices, Volume 15 Number 1, Winter 1995-6, http://www.uoregon.edu/~adiep/ft/watkins.htm

Yates, F. (1974), “The art of memory”, University of Chicago