Colignatus, Thomas (2018): The Math War between traditional and “realistic” mathematics education and its research. An analysis in institutional economics on research on education in arithmetic and algebra, with a focus on long term memory of pupils and using a causal model for valid testing on competence.

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Abstract
Institutional economics investigates how institutions affect empirical events. The term "institution" can be taken widely, and may also represent engrained mental conceptions by organised groups of actors. There is a curious but counterproductive combination of three groups also at universities in Holland w.r.t. research on education in arithmetic and algebra: (1) adherents of "realistic" mathematics education, an ideology that compares to astrology or homeopathy, (2) traditional mathematicians, who have no expertise on the empirical science of didactics of mathematics either, (3) psychometricians, who look at statistical data but who have no expertise on the empirical science of didactics of mathematics either. This combination needs deconstruction and the present paper focuses on (3), though with influence from (1) and (2). Some psychometricians seem to have a sound dislike of both the ideologues from (1) and the discussion between (1) and (2), but they are less aware that (2) are ideologues too. Some psychometricians also throw away the child with the bathwater by disregarding (4) the proper science of didactics of mathematics. Measuring competence in arithmetic and algebra requires consideration of long term memory of students. What you learn in elementary school tends to stay with you for the rest of your life. What you learn in highschool has the property of "use it or lose it". Algebra in highschool requires competence in the traditional algorithms of arithmetic, best learned in elementary school. "Realistic" mathematics education has reduced the competence of students at elementary school which affects them not only for algebra in highschool but also for the rest of their lives in both arithmetic and algebra. Inadequate testing by psychometricians allows this detrimental state to continue. The paper presents a causal model that identifies the engrained mental conceptions by psychometricians and where they would have to accept insights from didactics of mathematics. There is also a role for the Dutch Academy of Sciences KNAW that supported an inadequate report in 2009.
Item Type:  MPRA Paper 

Original Title:  The Math War between traditional and “realistic” mathematics education and its research. An analysis in institutional economics on research on education in arithmetic and algebra, with a focus on long term memory of pupils and using a causal model for valid testing on competence 
Language:  English 
Keywords:  education; elementary; mathematics; arithmetic; highschool; algebra; economics; memory; training; skill; ability; human capital policy; human development; capacity formation; lifecycle skill formation; software; ICT; computer algebra; textbook publishing; learning; teaching; efficacy; regulation; policy evaluation; Institutions: Design, Formation, Operations, and Impact; methodology and didactics; 
Subjects:  D  Microeconomics > D0  General > D02  Institutions: Design, Formation, Operations, and Impact I  Health, Education, and Welfare > I2  Education and Research Institutions > I20  General O  Economic Development, Innovation, Technological Change, and Growth > O1  Economic Development > O17  Formal and Informal Sectors ; Shadow Economy ; Institutional Arrangements P  Economic Systems > P1  Capitalist Systems > P16  Political Economy 
Item ID:  88810 
Depositing User:  Thomas Colignatus 
Date Deposited:  12 Sep 2018 09:08 
Last Modified:  12 Sep 2018 09:09 
References:  PM 1. Colignatus is the name in science of Thomas Cool, econometrician (Groningen 1982) and teacher of mathematics (Leiden 2008). PM 2. References in footnotes need not be mentioned here. PM 3. Commentary by anonymous researchers is acknowledged and has contributed to the quality of the present analysis. Colignatus (2001, 2014), “Voting Theory for Democracy”, https://zenodo.org/record/291985 Colignatus (2009, 2015), “Elegance with Substance”, mijnbestseller.nl, https://mpra.ub.unimuenchen.de/66012/ and https://zenodo.org/record/291974 Colignatus (2014, 2015), "Pierre van Hiele, David Tall and Hans Freudenthal: Getting the facts right", http://arxiv.org/abs/1408.1930 Colignatus (2015, 2018), “A child wants nice and no mean numbers”, https://doi.org/10.5281/zenodo.774272, 2nd edition 2018 forthcoming Colignatus (2015c), "Het rekenexperiment op kinderen moet en kan worden beëindigd" http://www.wiskundebrief.nl/721.htm#5 Grift, W.J.C.M. van de (2010), “Ontwikkeling in de beroepsvaardigheden van leraren”, https://www.rug.nl/education/lerarenopleiding/onderwijs/oratievandegrift.pdf Hickendorff, M. (2011), "Explanatory latent variable modeling of mathematical ability in primary school : crossing the border between psychometrics and psychology", https://openaccess.leidenuniv.nl/handle/1887/17979 Hickendorff, M., T.M.M. Mostert, C.J.van Dijk, L.L.M. Jansen, L.L.van der Zee, & M.F. Fagginger Auer (2017), “Rekenen op de basisschool. Review van de samenhang tussen beïnvloedbare factoren in het onderwijsleerproces en de rekenwiskundeprestaties van basisschoolleerlingen”, https://www.nro.nl/wpcontent/uploads/2017/12/40517920010RapportNROReviewRekenenen.pdf KNAW (2009), "Rekenonderwijs op de basisschool", https://www.knaw.nl/nl/actueel/publicaties/rekenonderwijsopdebasisschool Plas, L. van der (2009), “Rekenvaardigheid in relatie tot wiskunde”, Orthopedagogiek (TvO), may 2009 (no 5), 48, 205211, http://www.liesbethvanderplas.nl/rekenvaardigheidinrelatietotwiskunde/ Putten, C.M. van (2008), "De onmiskenbare daling van het prestatiepeil bij de bewerkingen sinds 1987", http://media.leidenuniv.nl/legacy/putten_reactie%20op%20Treffers%20in%20PPost.pdf Putten, C.M. van, M. Hickendorff (2009), “Peilstokken voor Plasterk: Evaluatie van de rekenvaardigheid in groep 8”, Tijdschrift voor Orthopedagogiek, 48, 184194 Slavin, R.E., and C. Lake (2008). Effective programs in elementary mathematics: A best evidence synthesis. Review of Educational Research, 78(3), 427–455 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/88810 