For IMU / ICMI: Integrity of science in Dutch research in didactics of mathematics

To: Professor I. Daubechies
From: Thomas Cool / Thomas Colignatus
Subject: For IMU / ICMI: Integrity of science in Dutch research in didactics of mathematics
Cc: secretary of the IMU, president of KWG, professor Andre Ran

To the president of the International Mathematical Union (IMU),
that has the International Commission on Mathematical Instruction (ICMI)

Dear professor Daubechies,

My email of July 16 can be updated integrally as follows, and I will put this present email on my weblog.

Let me invite you to read these two weblinks:

Let me invite you to also read this paper: “Pierre van Hiele and David Tall: Getting the facts right” (version 2, 2014-08-30) at

Let me invite you to keep the matter on your desk with priority, involve others in IMU / ICMI who could advise you on this, and aim at board decisions that result into proper resolution.

Since this email concerns research in didactics, your tendency would be to forward it to ICMI. My suggestion is not to give them total freedom but set up an overall IMU committee to monitor the process within ICMI on this. In itself it might be proper to hand the issue to ICMI, since when they succeed in resolving the issue, then it would meet with greater acceptance in their own circles. On the other hand, there will be a tendency to reject criticism. Hence my suggestion to keep the issue on your desk as well.

One of the problems is that ICMI has a “Hans Freudenthal Award / Medal“, which indicates that ICMI has not been able to detect the fraudulent nature of Freudenthal’s “research” and appropriation of ideas of Pierre and Dieke van Hiele. A related problem is that the Dutch representative to ICMI might not have transferred my earlier message on didactics in general.

Since your background is Belgian, I presume some knowledge of Dutch, and then let me also directly include the link to my letter to KNAW-LOWI, which is the Integrity of Research department of the Dutch Royal Academy of Sciences:

I imagine that IMU might not have the resources available at KNAW-LOWI. My suggestion is that IMU supports my suggestion to KNAW-LOWI to look into this, even though they have already declined my original suggestion. In that case I would hope that there is international monitoring of the investigation at LOWI too, since they might be less critical on what went wrong in Holland. There are some issues here, some of which seem quite local but that still would greatly benefit from international monitoring: (1) the habit of abstract thinking mathematicians and such teachers to forget about the real world and empirical methods, (2) Hans Freudenthal and his “work” (much in Dutch), (3) the renaming of the ICMI Award, say to a “Piaget & Van Hieles Award / Medal”, (4) the abolition of the Dutch “Freudenthal Head in the Clouds Realistic Mathematics Institute” (FI = FHCRMI) here in Holland. It would seem that the last would not be in the ballpark of IMU but it is important to be aware that the institutional drive of that institute is to defend Freudenthal’s “legacy”, and thus to oppose criticism on the other points too, at the detriment of IMU / ICMI. It is better to be straightforward on the logic from the outset, and have international monitoring.

I alerted the Presidents of MAA (Bob Devaney) and AMS (David Vogan) and the director of the US Institute of Education Sciences (IES, John Easton) on the two weblog links, but not on my recent paper on Van Hiele and Tall (yet). After putting this letter on my weblog, I will alert the board of NCTM (Diane Briars) to this. I now copy to the IMU secretary and the chair of the Dutch KWG, now professor Geurt Jongbloed but formerly Andre Ran. In my perception KWG has been seriously failing on this issue but if IMU would indicate that there is an issue indeed then they might perhaps be willing to help out, with some international monitoring.

My position in all of this is quite limited, and mainly described in my books “Elegance with Substance” (2009) and “Conquest of the Plane” (2011) and the Dutch “Een kind wil aardige en geen gemene getallen” (2012), see my website, where the PDFs of the first two can be found. I do not claim particular expertise on Freudenthal’s “work” but what I have read didn’t appear so practical, except for what he took from Pierre van Hiele. I am amazed both by RME’s adoption for education and the lack of interest to repeal it now that everyone can see that it doesn’t really give results, except for the part taken from Van Hiele. My main point is no 1 above: the habit of abstract thinking mathematicians and such teachers to forget about the real world and empirical methods. My suggestion is that we need “engineers in education” rather than such mathematicians, and that education requires the “medical school” model in which education and its research are attuned, see this other link:

Sincerely yours,

Thomas Cool / Thomas Colignatus
Econometrician (Groningen 1982) and teacher of mathematics (Leiden 2008)
Scheveningen, Holland


PM. Readers of this email may also be interested in: Elizabeth Green: Why Do Americans Stink at Math?, NY Times July 23 2014

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