IDEAS home Printed from
   My bibliography  Save this paper

Elegance with substance


  • Colignatus, Thomas


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.

Suggested Citation

  • Colignatus, Thomas, 2009. "Elegance with substance," MPRA Paper 15173, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:15173

    Download full text from publisher

    File URL:
    File Function: original version
    Download Restriction: no

    File URL:
    File Function: revised version
    Download Restriction: no

    File URL:
    File Function: revised version
    Download Restriction: no

    References listed on IDEAS

    1. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163.
    2. Colignatus, Thomas, 2009. "The Tinbergen & Hueting Approach in the Economics of Ecological Survival," MPRA Paper 13899, University Library of Munich, Germany, revised 09 Mar 2009.
    3. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Colignatus, Thomas, 2017. "Comparing votes and seats with a diagonal (dis-) proportionality measure, using the slope-diagonal deviation (SDD) with cosine, sine and sign," MPRA Paper 80965, University Library of Munich, Germany, revised 24 Aug 2017.
    2. Colignatus, Thomas, 2017. "One woman, one vote. Though not in the USA, UK and France," MPRA Paper 82513, University Library of Munich, Germany, revised 08 Nov 2017.
    3. Colignatus, Thomas, 2017. "Comparing votes and seats with a diagonal (dis-) proportionality measure, using the slope-diagonal deviation (SDD) with cosine, sine and sign," MPRA Paper 80833, University Library of Munich, Germany, revised 17 Aug 2017.

    More about this item


    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;

    JEL classification:

    • A20 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - General
    • I20 - Health, Education, and Welfare - - Education - - - General
    • P16 - Economic Systems - - Capitalist Systems - - - Political Economy of Capitalism

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:15173. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.