Colignatus, Thomas (2015): Elegance with substance. Published in: mijnbestseller.nl No. ISBN 9789462540453 (7. August 2015): pp. 1139.
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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 (DeLong 1991, 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 

Original Title:  Elegance with substance 
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 
Item ID:  66012 
Depositing User:  Thomas Colignatus 
Date Deposited:  11. Aug 2015 15:29 
Last Modified:  11. Aug 2015 16:07 
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(2001), “Research into K12 mathematics education”, see http://www.math.nyu.edu/~braams/links/research0104.html and in general http://www.math.nyu.edu/mfdd/braams/links/ Colignatus, Th. (1981 unpublished, 2007a, 2011), "A logic of exceptions", (ALOE) 2nd edition, Thomas Cool Consultancy & Econometrics, Scheveningen (PDF of the book online at http://thomascool.eu/Papers/ALOE/Index.html) Colignatus, Th. (1999), “Beating the software jungle. Selecting the economics software of the future”, Legacy:EWS, http://econpapers.repec.org/paper/wpawuwpgt/9904001.htm Colignatus, Th. (2000), “The Disappointment and Embarrassment of MathML  update: Including Reactions and Answers”, http://thomascool.eu/Papers/MathML/OnMathML.html Colignatus, Th. (2000, 2005, 2011), “Definition & Reality in the General Theory of Political Economy” (DRGTPE), Dutch University Press, see http://thomascool.eu/Papers/Drgtpe/Index.html Colignatus, Th. (2001, 2007b, 2011g, 2014), “Voting Theory for Democracy”, 4th edition, see http://thomascool.eu/Papers/VTFD/Index.html Colignatus, Th. (2007c), “Why one would accept Voting Theory for Democracy and reject the Penrose Square Root Weights”, http://mpra.ub.unimuenchen.de/3885/ Colignatus, Th. (2008a), “Trig rerigged. Trigonometry reconsidered. Measuring angles in ‘unit meter around’ and using the unit radius functions Xur and Yur”, April 8, Legacy:COTP, http://thomascool.eu/Papers/Math/TrigRerigged.pdf Colignatus, Th. (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.unimuenchen.de/9661/ Colignatus, Th. (2008c), “Het Simon Stevin Instituut”, http://thomascool.eu/Thomas/Nederlands/ Wetenschap/Artikelen/20081111SimonStevinInstituut.pdf Colignatus, Th. 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URI:  https://mpra.ub.unimuenchen.de/id/eprint/66012 
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