Pierre van Hiele and Annie Selden

Tracing the confusions on Pierre van Hiele can be gratifying since you meet with all kinds of interesting research and the people doing this, but it also appears to be an arduous task since the number of possible confusions is amazingly large.

The day before yesterday, I discussed the review at MAA by Annie Selden of the book by Sacha la Bastide – van Gemert. Publisher Springer proudly quotes from this review. Indeed, the world will tend to rely upon professor Selden’s reputation. The MAA has an Annie and John Selden Prize. See also professor Selden’s impressive cv and statement at LinkedIn: “Specialties: Mathematics education,Qualitative research, Curriculum development, Editing”. Since I myself wrote a book on logic and looked at proofs for some mathematical theorems, like by Gödel and Cantor, I am looking forward to read, at some hoped for moment in the future, the Selden’s paper on teaching how proper proofs are constructed.

However: the Selden review missed Freudenthal’s fraud.

Let me restate the quote at Springer and give the two screenshots, and then discuss.


“It concentrates on the historical development of Freudenthal’s ideas on the didactics of mathematics. … it would primarily be of interest to mathematics education researchers, especially those who use RME as their theoretical framework and to those interested in the history and development of the field … .” (Annie Selden, MAA Reviews, June, 2015) QUOTED AT SPRINGER

Screenshot of the page at Springer

Screenshot of the page at Springer

Screenshot of the MAA John and Annie Selden Prize

Screenshot of the Annie and John Selden Prize at MAA


I informed professor Selden about the weblog text, and gave my estimate that it shouldn’t take too much time to confirm the fraud, once you know what to look for. I also informed her that historians would be interested in her confirmation. She replied succinctly:

Tue, 13 Oct 2015
Dear Mr. Cool,
I am not a historian of mathematics. I am also not a historian of mathematics education. I have no knowledge of the alleged fraud (on the part of Professor Freudendthal [sic]) that you mention in your email.  I cannot help you.
Also, I am very busy with my own work and concerns right now.
Sincerely yours,
Annie Selden
Math. Dept.

We should not guess a respectable lady’s age. Selden has a B.A. from 1959 and thus might have been born around 1938. We thus will not do the math but respect her need to prioritise. David Tall (1941) wrote me last year – then at age 73 – that he was in the autumn of his life and that he had to prioritise too. He considers his confusion about Van Hiele not his most urgent issue. I can only respect this. Henceforth I inform professor Mike Thomas of Auckland (NZ) who may filter points of relevance for Tall – such as the publication of the English translation of the LB-VG thesis.

Still, Selden’s reponse causes some questions, which I now transferred to the MAA Reviews editor together with the earlier ones.

  • There is no alleged fraud. I don’t allege. I don’t appreciate it when some suggests that I would allege something. I report on what I discovered and invite others to size up the evidence with the option to correct me. I can imagine that professor Selden has no time to look at the evidence but this doesn’t allow the inference that I only allege something. I presume that professor Selden is so pressed for time that she didn’t have time to think about a proper expression instead of “alleged”.
  • I didn’t ask for help but was trying to help her.
  • I never implied that professor Selden was a historian. I contacted her on her reviews (also the other on Freudenthal’s 1973 book).
  • Her review recommends the LB-VG book for “those interested in the history and development of the field”, and if professor Selden now feels that she is not qualified for such a statement, then this should be retracted from the review before the interview as a whole is removed as inadequate.
  • I did inform Selden that I copied my message to La Bastide – Van Gemert and some other historians. The fraud can be established by persons with the expertise also stated by Selden, which is also my expertise: mathematics education and its research. I am no historian either. Those who take it upon themselves to write or review the book should be able to establish it, who need not necessarily be historians. But I find it useful to involve historians as well, since they may have additional expertise, and since they write books on history. (Except Amir Alexander, who first selects the story and then selects some data that fit the story.)

This again shows how horrible fraud is. It wreaks havoc all over.

Originally La Bastide – Van Gemert spent years of her life investigating what she thought to be an important researcher on mathematics education. Last year it appeared that she was only tricked in believing such, and that she only made a record of mostly misrepresentation, nonsense and manipulation. When I informed her about this last year, she declined looking into this. Instead she proceeded with the English translation, which is deliberate neglect. It is a deliberate act with additional neglect of consequences for the publisher, the reviewers and the readers, and what they do further. The ebook comes at the hefty price of $139, and it depends upon the percentage for LB-VG whether she is cashing in on Freudenthal’s fame in the circles of mathematics education (or Van Hiele’s fame, with chapter 7).

There was already David Tall as a victim in 2014, since I asked her to look into this in that context. With Springer as a second victim, we now find a third victim in a respectable lady who thought to do well with a review, relying upon the reputation of others, relying about the “scientific process in Holland”, and who is in the autumn of her life too and who doesn’t know where to find the time to restore the error when the bad news arrives. Can we consider it mathematically proven that LB-VG is harrassing senior citizens ?

We can only hope that the MAA Reviews editor has more resources and deals with this properly.

Intermezzo: On the brighter side

In the wonderful world of Google, tracing the above generated a paper by Norma Presmeg in Fried & Dreyfus (2014), also at Springer.

First there is the following diagram, useful for who wants to judge upon expertise, such as on who would be qualified for issues of fraud in mathematics education research. I agree with the diagram, except that I propose to regard the diagram as per Van Hiele level and math topic. There could be needless confusion when researchers on higher education make statements on primary education that they are not qualified for, as well.

Diagram by Norma Presmeg p 46 with "Topic !" amendment

Diagram by Norma Presmeg in Fried & Dreyfus (2014:46) with “Topic !” amendment

Secondly, Presmeg recollects, complimenting Van Hiele but restricting it to geometry, instead of emphasizing the general applicability (like the law of conservation of energy), and the work was done in the 1950s, with the two theses by Dina and Pierre in 1957:

Norma Presmeg (2014), p52-53

Norma Presmeg in Fried & Dreyfus (2014:52-53)

Intermezzo: Return to dismay

As happy we were in discovering the Presmeg article, as great is the dismay again to again see the article by David Tall in the same volume, in which he states his confusion on page 225, as if Van Hiele didn’t state the general applicability of his theory (and focused on geometry only).

David Tall, in Fried & Dreyfus (2014:225)

David Tall, in Fried & Dreyfus (2014:225)

The Fried & Dreyfus volume was available in January 2014 and my discovery was in July 2014. See this article later in August for Tall’s misreading of his reference to Van Hiele (2002). There is no deliberate misrepresentation on Tall’s part, just a significant error. Though Tall will not correct, I still advise Springer to put a health warning there.

While Sacha la Bastide – van Gemert has the inconsistent report that both Van Hiele and Freudenthal would be the originators of the idea of the general applicability of the theory of levels, readers may now observe that David Tall claims it for himself: not only misreading Van Hiele (2002) but also unaware of Freudenthal’s earlier claim and misrepresentation. You can be famous without being read well.

Email to the MAA

Date: Thu, 15 Oct 2015
To the MAA, executive director Michael Pearson
CC Book Reviews editor [..], professor Selden, dr La Bastide – van Gemert, historians
Subject: Urgent: wrt two reviews by Annie Selden who didn’t notice the fraud by Hans Freudent[h]al

Dear dr. Pearson,

Let me urge you to do your best to preserve professor Annie Selden’s health and reputation, in what has become a sordid matter, due to fraud, incompetence and deliberate negligence in Holland.

Yesterday I informed MAA Book Reviews editor […] on this, giving him a head start. As I told him, I just reworked my message to him into a weblog text, available here:


I copy to professor Selden, but with hesitation: She stated that she has no time for this. Yet, it are her two reviews that cause a problem. Given her age she is less subject to the illusion of youngsters that there is ample time to choose what to do. I want to respect that, but, in that case the human invention of “organisation” would have to take over. I urge you to do so.

I copy to dr. Sacha la Bastide – van Gemert, whom I subsequently will report to her authorities. I discovered the existence of the 2015 English translation only a few days ago, and this puts matters of 2014 into a different light. Seeing the consequences not only for David Tall in 2014 but also Annie Selden in 2015 proves to me that this unavoidable.

I also copy to the historians who I copied to earlier, so that they can see both professor Selden’s reply to me and that I try to deal with this in the best way possible.

I also copy to two Dutch historians of science, […] and Danny Beckers. Beckers earlier wrote a review in Dutch of the Dutch thesis by LB-VG, and he missed the fraud by Freudenthal too. Given the existence of the English translation, I have asked him to translate his review into English, and also look into the Freudenthal fraud.

Earlier I copied to Gerard Alberts and Rainer Kaenders, who interviewed Pierre van Hiele in 2005. I have come to the conclusion that Kaenders may well be in breach of scientific integrity as well. While Alberts has no background in mathematics education research, Kaenders has. He should be able to spot the Freudenthal fraud when it is pointed out to him. But he doesn’t react to this. He might be on holiday now and not read his emails. But there may also be more to this. I will inform him about this problem and will copy to you too.

I will put this email into above weblog text, turning names anonymous where needed.

Sincerely yours,

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


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