Pierre van Hiele and an interview in 2005

In 2005, Gerard Alberts (mathematician, historian) and Rainer Kaenders (mathematician, educator) interviewed Pierre van Hiele (1909-2010). The interview was published in the journal of the Royal Dutch Society for Mathematics, as G. Alberts & R. Kaenders (2005), “Interview Pierre van Hiele. Ik liet de kinderen wél iets leren”, NAW 5/6 nr. 3, september, p247-251. The publication is in Dutch and I will translate some parts into English.


The introduction to the interview is:

Pierre van Hiele is the silent force in didactics of mathematics in The Netherlands. He was teacher of mathematics and chemistry and never much stepped in the floodlights. His work receives broad international recognition and one cannot think about didactics of mathematics without it. His work is still studied, amongst others Stucture and Insight. Van Hiele is ninety-six. (Dutch: Pierre van Hiele is de stille kracht van de didactiek van de wiskunde in Nederland. Hij was wiskunde- en scheikundeleraar en is nooit veel op de voorgrond getreden. Zijn werk vindt brede internationale erkenning en is tegenwoordig niet meer weg te denken uit de wiskundedidactiek. Zijn werk, waaronder het invloedrijke Begrip en inzicht, werkboek van de wiskundedidactiek wordt nog steeds bestudeerd. Van Hiele is zesennegentig jaar.)

Hans Freudenthal (1905-1990) was supervisor to the 1957 thesis in which Van Hiele presented his levels of insight – see here for their crucial role in epistemology, comparable to the law of conservation of energy in physics. In 2014 I observed that Freudenthal committed fraud by misrepresenting Van Hiele’s work and by stealing elements for his supposedly “own” approach of “realistic mathematics education” (RME). This RME is a disaster because it doesn’t stick to Van Hiele’s proper didactics. Van Hiele was a teacher of mathematics and Freudenthal was an apparently jealous abstract thinking professor in topology. (Freudenthal’s wife Suus Freudenthal-Lutter was involved with pedagogy and perhaps this inspired him to similar efforts too.)

My discovery in 2014 of Freudenthal’s fraud happened in the context of discovering David Tall’s misconception, in which Tall reduces Van Hiele’s approach to geometry only. Tall claims to have found general epistemological applicability, which is correct and a useful confirmation of what Van Hiele already stated in his 1957 thesis, but which is incorrect in that Tall should not claim this general notion for himself and reduce Van Hiele to geometry only. It might be that Freudenthal was instrumental in Tall’s misconception. See Pierre van Hiele and David Tall: Getting the facts right (2014).

In all this, we have the Dutch language sink, in which Dutch readers have access to the local lingo that other language readers are barred from, except for still inadequate Google Translate and such.

The 2005 interview is important for understanding the situation but I have been hesitating to translate this myself. When I discovered the Freudenthal fraud, I felt that readers would better be served by translations that are independent from this discovery. Readers might all too easy think that such a discovery might be based upon wrong translations. See the Van Hiele & Tall paper for such translation issues. Thus, I asked Alberts & Kaenders whether they would be wiling to try to make such a translation. Up to now, there is no indication for this however.

Also, I recently discovered that Van Hiele has no page in the MacTutor History Archive, which is somewhat contrary to above observation by Alberts & Kaenders for his importance for mathematics education and its research. Notably, Gerard Alberts wrote an excellent and inspiring history booklet about David van Dantzig (1900-1959), who has an entry in the MacTutor archive. One would hope that something similar would be possible for Pierre van Hiele (only 9 years Van Dantzig’s junior).

My history comment caused some questions from the readership. These questions now cause me to give a translation of some key passages in the 2005 interview, selected on the Van Hiele – Freudenthal relationship, with the understanding that there should be an independent translation later on. I also provide the Google Translation, if only for fun.

NB. For vectors in primary education, see the pdf online: A child wants nice and no mean numbers(2015).

Page 247 on sabotage

“My relation with Freudenthal wasn’t so good, that I would go and drink coffee with him. Besides, Freudenthal has later frequently sabotaged my work, guys.”

Google: “So good was my relationship with Freudenthal not think I was going to drink coffee with him. Besides, Freudenthal has me later often put a heel, guys.

Dutch: “Zo goed was mijn relatie met Freudenthal niet dat ik met hem ging koffie drinken. Trouwens, Freudenthal heeft mij later nogal eens een hak gezet, jongens.”

Page 251 on Hans Freudental

What role did Freudenthal play in your life? “I did not mix well with Freudenthal. From the beginning. He was a bossy person. He did cause me to get ideas. That is rather all.”

Freudenthal used different descriptions of the process of abstraction. In the Vorrede zu einer Wissenschaft vom Mathematikunterricht he presented this process in terms of comprehension and apprehension. Did he also think differently about the role of levels of insight? “Yes, I believe actually that he did not really understand much about the levels of insight.”

Freudenthal was your thesis supervisor (promotor). Did he also help you in stepping outside of the small circle – with contacts outside of The Netherlands? “The last thing definitely not. No, the situation was actually that I had to vouch for myself. For example I remember a conference in America, at which a speaker referred to my work and said: ‘Mr. Van Hiele whom I am mentioning now is actually present in this very lecture hall. Mr. Van Hiele, please rise (so that everyone can recognize you).” Someone in the audience, a German, asked where he could read about my work. I replied that there would appear a book of mine in English shortly. Then Freudenthal who was also present said: ‘You can also read about it in my book.’ Which wasn’t true. He just was sabotaging me again. Freudenthal was like this, yes.” He was sabotaging you all the time? “Actually yes. Freudenthal never was a friendly person for me, no.” Where can he have been sabotaging you? Didn’t you work in entirely different environments? “Yes, but he tried to pinch something from me all the time.”

Later you got more recognition for your work. Were you able to make peace with him then? “Well, peace? No, actually not. In that case you first would have made war. I don’t make war.”

You presume that Freudenthal did not fully understand your work. Did you understand him, conversely? “Yes, I understood what I knew of him. And I often agreed with it too. I wasn’t in constant quarrel with Freudenthal. From his side, he had very much respect for my ideas on vectors in primary education. He praised me very much for that.”

Page 251 Google Translation

What role does Freudenthal played in your life? “I did not like very much with Freudenthal. From the outset, not all. He was a bossy person. He gave me ideas. That was it really. “

Freudenthal wielded other descriptions of the process of abstraction. In Vorrede zu einer Wissenschaft vom Mathematik Unterricht he explained that process in terms of comprehension and apprehension. Did he think differently about the role of levels? “Yes, I actually believe he levels that do not understand much.”

Freudenthal was your promoter. He did he nevertheless helped to come out – outside the Netherlands? “The latter certainly do not. No, it was just that I had to defend myself. Example, I remember a conference in America, where a speaker referred to my work and said, “Van Hiele what I am now, sitting here in the audience. Mr. Van Hiele state momentarily. “Someone in the audience, a German, asked where he could read my work. I replied that soon a book of mine would appear in English. Then Freudenthal said who was also present: “You can read them with me in my book.” That was not true. He just sat cross me again. Freudenthal was so, yes. “Was he can cross all the time? “Actually, yes. Freudenthal has never been a nice guy to me, no. “Wherever he may well have been bothering you. You still worked in very different environments? “Yes, but every time he tried to steal me something off.”

Later did you find more recognition for your work. Do you then can make peace with him? “Well, peace? Not really. Then you must first make war. I do not make war. “

You assumes that Freudenthal your job did not quite understand. You knew him, conversely, is it? “Yes, what I knew of him that I understood. And I was also often agree. I was not in permanent quarrel with Freudenthal. On his side, he had a lot of respect for my ideas of vectors in elementary school. There he has given me much to praise.”

Page 251 Dutch original

Welke rol heeft Freudenthal in uw leven gespeeld? “Ik had niet zo erg veel op met Freudenthal. Van begin af aan al niet. Hij was een bazig iemand. Hij bracht me wel op ideeën. Dat was het eigenlijk.”

Freudenthal hanteerde andere beschrijvingen van het proces van abstractie. In de Vorrede zu einer Wissenschaft vom Mathematikunterricht zette hij dat proces uiteen in termen van comprehensie en apprehensie . Dacht hij ook anders over de rol van denkniveaus? “Ja, ik geloof eigenlijk dat hij van die denkniveaus niet veel begrepen heeft.”

Freudenthal was uw promotor. Hij heeft hij u toch ook geholpen naar buiten te treden — buiten Nederland? “Dat laatste beslist niet. Nee, het was juist zo dat ik voor mijzelf moest opkomen. Ik herinner mij bijvoorbeeld een congres in Amerika, waar een spreker naar mijn werk verwees en zei: ‘die Van Hiele waar ik het nu over heb, die zit hier in de zaal. Meneer Van Hiele staat u even op.’ Iemand in het publiek, een Duitser, vroeg waar hij over mijn werk kon lezen. Ik antwoordde dat er binnenkort een boek van mij in het Engels zou verschijnen. Daarop zei Freudenthal die ook aanwezig was: ‘U kunt het ook bij mij in mijn boek lezen.’ Dat was dus niet waar. Hij zat mij gewoon weer dwars. Zo was Freudenthal, ja.” Zat hij u de hele tijd dwars? “Eigenlijk wel, ja. Freudenthal is nooit voor mij een leuke man geweest, nee.” Waar kan hij u nou dwars hebben gezeten. U werkte toch in heel andere omgevingen? “Ja, maar hij probeerde iedere keer mij iets af te snoepen.”

Later hebt U meer erkenning voor uw werk gevonden. Heeft U toen vrede met hem kunnen sluiten? “Nou, vrede? Eigenlijk niet. Dan had je eerst oorlog moeten maken. Ik maak geen oorlog.”

U gaat ervan uit dat Freudenthal uw werk niet helemaal begreep. Begreep U hem, omgekeerd, wel? “Ja, wat ik van hem kende dat begreep ik. En daar was ik het ook vaak mee eens. Ik verkeerde niet in permanente ruzie met Freudenthal. Van zijn kant had hij erg veel respect voor mijn ideeën van vectoren op de lagere school. Daar heeft hij mij erg om geprezen.”


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