Colignatus, Thomas (2009): Elegance with substance.
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Subject: The education in mathematics, its failure and costs, and how to redesign this market. The political economy of mathematics education.
Method: We do not require statistics to show that mathematics education fails but can look at the math itself. Criticism on mathematics itself can only succeed if it results into better mathematics. Similarly for the didactics of mathematics. Proof is provided that the mathematics that is taught often is cumbersome and illogical. It is rather impossible to provide good didactics on what is inherently illogical.
Basic observations: We would presume that school mathematics would be clear and didactically effective. A closer look shows that it is cumbersome and illogical. (1) This is illustrated here with some twenty examples from a larger stock of potential topics. (2) It appears possible to formulate additional shopping lists for improvement on both content and didactic method. (3) Improvements appear possible with respect to mathematics itself, on logic, voting theory, trigonometry and calculus. The latter two improvements directly originate from a didactic approach and it is amazing that they have not been noted earlier by conventional mathematics. (4) What is called mathematics thus is not really mathematics. Pupils and students are psychologically tortured and withheld from proper mathematical insight and competence. Spatial sense and understanding, algebraic sense and competence, logical sense and the competence in reasoning, they all are hindered and obstructed. Mathematics forms a core element in education and destroys much of school life of pupils and students in their formative years.
Basic analysis: This situation arises not because it is only school math, where mathematics must be simpler of necessity, but it arises because of the failure of mathematicians to deliver. The failure can be traced to a deep rooted tradition and culture in mathematics. Didactics requires a mindset that is sensitive to empirical observation which is not what mathematicians are trained for. Psychology will play a role in the filtering out of those students who will later become mathematicians. Their tradition and culture conditions mathematicians to see what they are conditioned to see.
Higher order observations: When mathematicians deal with empirical issues then problems arise in general. The failure in education is only one example in a whole range. 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 and insufficient attention to reality, statistics and real risk (Tinbergen & Hueting 1991). Improvements in mathematics itself appear possible in logic and voting theory, with consequences for civic discourse and democracy, where the inspiration for the improvement comes from realism (Colignatus 2007). Economics as a science suffers from bad math and the maltreatment of its students – and most likely this is also true for the other sciences. Professors and teachers of mathematics – or at least 99.9% of them – apparently cannot diagnose their collective failure themselves and apparently ‘blame the victims’ for not understanding mathematics. The other scientific professions are advised to verify these points.
Higher order analysis: Application of economic theory helps to understand that the markets for education and ideas tend to be characterized by monopolistic competition and natural monopolies. Regulations 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 would rather be high on the list as well. It will be important to let the industry become more open to society. Without adjustment of regulations at the macro-level it is rather useless to try to improve mathematics education and didactics at the micro level. Mathematical tradition and culture creates a mindset, and mathematicians are like lemmings that are set to go into one direction. Trying to micro-manage change with some particular lemmings will not help in any way. An example layout is provided how the industry could be regulated.
Conundrum: Mathematicians might be the first to recognize the improvements in mathematics and didactics presented here. Mathematical tradition clearly is an improvement from alchemy and astrology. Most people will also tend to let the professors and teachers decide on whether these items are improvements indeed. It is tempting to conclude that the system then works: an improvement is proposed, it is recognized, and eventually will be implemented. This approach however takes a risk with respect to potential future changes. With the present failure and analysis on the cause we should rather be wary of that risk. We better regulate the industry of mathematics education in robust manner. The mathematical examples presented here can be understood in principle by anyone with a highschool level of mathematics. They are targetted to explain didactically to a large audience how big the failure in the education in mathematics actually is.
Advice: The economic consequences are huge. National parliaments are advised to do something about this, starting with an enquiry. Parents are advised to write their representative. The professional associations of mathematics and economics are advised to write their parliament in support of that enquiry.
|Item Type:||MPRA Paper|
|Original Title:||Elegance with substance|
|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 - Economics Education and Teaching of Economics > A20 - General
I - Health, Education, and Welfare > I2 - Education and Research Insititutions > I20 - General
P - Economic Systems > P1 - Capitalist Systems > P16 - Political Economy
|Depositing User:||Thomas Colignatus|
|Date Deposited:||14. May 2009 00:11|
|Last Modified:||11. Feb 2013 21:13|
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
Baum, M. (2006), “Decimals Score a Point on International Standards”, http://www.nist.gov/public_affairs/techbeat/tb2006_1122.htm#decimal
Barrow, J. (1993), “Pi in the sky. Counting, thinking and being”, Penguin
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
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/
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
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
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
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