Pierre van Hiele and Michiel Doorman: Doorman misleads Indonesia too

Listening to Roy Orbison – Pretty Women

Let me give a clear and unbiased assessment of the qualifications and work of “dr.” Michiel Doorman at “Freudenthal Institute” at Utrecht University.

Let me first present four neutral points and then follow Sherlock Holmes.

(1) Michiel Doorman defended his “thesis” in 2005: “Modelling motion: from trace graphs to instantaneous change” (online), written under the supervision of P.L. Lijnse and Koeno Gravemeijer.

(2) He might best be introduced by his cv on p243 of his “thesis”:

“Michiel Doorman was born on 1 october 1962 in Eindhoven, the Netherlands. He completed his secondary education in 1981 at the Minkema College in Woerden. In1988 the Utrecht University awarded him a masters in Mathematics for his thesis on the extension of a proposition in intuitionistic logic for automated theorem proving. He minored in Computer Science. From 1988 he has been working at the Freudenthal Institute. Until 1992 he was mainly devoted to software development. During the following years he has been involved in curriculum and teacher training projects, mainly concerning the role of information and communication technology in mathematics education. Since 1994, this work concentrated on upper secondary (pre-university) mathematics education in a research project on the integration of the graphing calculator, in a curriculum development project (Profi), and in a project that aimed at guiding the Biology, Chemistry, Physics and Mathematics departments in schools to cooperate. In 1998 he started his PhD research study.” [my emphasis]

(3) There is also his Utrecht University webpage, that states:

“Interests are context-based mathematics education, modeling as a lever for learning mathematics, inquiry based learning and coherency between mathematics and science learning.”

(4) Michiel Doorman was also invited as one of the keynote speakers at the 3rd International Conference on Research, Implementation and Education of Mathematics and Science (ICRIEMS) at Yogyakarta, Indonesia, in May 2016.

• This is Doorman’s presentation pptx (on “inquiry based learning”) and
• this is the proceeding pdf: “What Can Mathematics Education Contribute To Preparing Students For Our Future Society?“.

Michiel Doorman fourth from left (Source: ICRIEMS website 2016)

Why does Doorman in 2016 claim success for RME while it failed ?

Around 2005 there was much discussion in Holland – a real math war – about arithmetic in elementary schools. The academy of sciences (KNAW) set up a committee to look into this.

Recall the graphical display of the math war between RME and TME, and the solution approach of NME. These abbreviations are:

• RME = realistic mathematics education
• TME = traditional mathematics education
• NME = neoclassical mathematics education

(i) This KNAW-committee concluded in 2009 (see the English summary on page 10 in the report) that pupil test scores for RME and TME did not really differ. Paraphrased: one cannot claim a special result for RME. Observe that many test questions contained contexts.

“Growing concern about Dutch children’s mathematical proficiency has led in recent years to a public debate about the way mathematics is taught in the Netherlands. There are two opposing camps: those who advocate teaching mathematics in the “traditional” manner, and those who support “realistic” mathematics education. The debate has had a polarizing effect and appears to have little basis in scholarly research.” [This neglects my third position with NME.]

“The public debate exaggerates the differences between the traditional and realistic approaches to mathematics teaching. It also focuses erroneously on a supposed difference in the effect of the two instructional approaches whereas in fact, no convincing difference has been shown to exist.” (KNAW 2009)

(ii) Doorman in Yogyakarta 2016 is unrepentingly for RME. He refers to key authors on RME, and takes a question of TIMMS 2003 with an international score of 38% and a Dutch score of 74% and claims, misleadingly:

“This cannot fully [be] attributed to the implementation of  RME, but it strengths [sic] the feeling that this approach contributes to the quality of mathematics education.” [my emphasis]

(iii) Subsequently, I criticised the KNAW report on these counts, and neither KNAW nor Michiel Doorman have responded to this criticism:

• Before the report was published by alerting the committee chairman to Elegance with Substance (2009, 2015), that however is not included in the references.
• In 2014 explicitly for the collective breach of research integrity, for either neglecting or maltreating my books Elegance with Substance (2009, 2015) and Conquest of the Plane (2011) and Dutch Een kind wil aardige en geen gemene getallen (2012) notably on issues of arithmetic (the present subject): the pronunciation of numbers and notation of mixed numbers.
• In 2015 for neglecting the issue that TME prepares for algebra while RME doesn’t. The KNAW report uses the outcome of test questions and not the intermediate steps. Pupils who can only use RME will be very handicapped for algebra in secondary education.

See my 2016 letter and its supplement to the president of KNAW and director of CPB about the failure of the KNAW report and the neglect of criticism.

A repeat exercise that isn’t quite superfluous

I have explained, to boring repetition, that the Freudenthal Head in the Clouds Realistic Mathematics Institute (FHCRMI) should not be at a university. Please observe that first there was criticism on the failure of “realistic mathematics education” (RME) and only later it was discovered that Hans Freudenthal had actually abused the work by Pierre van Hiele. There also is a sound scientific explanation why it is a failure: namely a confusion of processes of learning with applied mathematics.

• Learning goes from concrete to abstract and from vague to precise.
• For the confusion by Hans Freudenthal on applied mathematics, see: Conquest of the Plane 2011, Ch. 15.2 Didactics, p 201, or A child wants nice and no mean numbers 2015, p 101.

Thus it holds:

There is little advantage in repeating this analysis,
neither for each and every individual working at FHCRMI.

For example, stating that Michiel Doorman works at FHCRMI should be sufficient. That he is at FHCRMI does not imply that he can indeed be at university and that his “thesis” and “PhD title” are proper.

However, the following points cause that it isn’t quite superfluous to look into Doorman’s qualifications and work.

• Michiel Doorman is member of the board of NVvW, the Dutch association of mathematics teachers. See my recent letter with a Red Card for this board. Thus it helps for the next annual meeting of NVvW in November 2016 to be specific.
• Also, there is my letter of April 15 2016 to NRO, the Dutch organisation for the distribution of funds for research in mathematics education. I advise them to stop subsidising FHCRMI. It so happens that Michiel Doorman did a project ODB08008 for them in 2009-2012 on the “digital mathematics environment” and “efficient exercising mathematics” (DWO). It will be helpful for NRO to see that, for example, Doorman is an ideologue and no scientific researcher. This is related to the following.
• There is the new impulse for “21st century skills” or in Holland “Onderwijs2032“. Part of the attention is for soft skills, part of the attention is for computer programming, part is elsewhere. ICT brings us to the work of Doorman too. There has already been a major disaster with the neglect of computer algebra since 1990. For example DWO at FHCRMI tends to present many Java applets that lack the flexibility of computer algebra. Don’t think that these issues are easy to resolve, but I do hold that the decisions have been driven by ideology and that the results are a disaster and a great waste of funds: penny wise pound foolish. See for example these two reports by the Inspectorate for Education: In 2002, mathematical topologist Hans Freudenthal is called a “pedagogue” while he had no education or training on this, and they assume that FHCRMI knows about ICT while the report doesn’t mention computer algebra but applets on “wisweb”. In 2006, the “waarderingskader” (inspection standards) doesn’t seem to realise that computer algebra can used in all subjects that use mathematics.

Above, I mentioned four neutral points. Following Sherlock “Google” Holmes I already debunked the event in Yogyakarta. Let us look at the other three points. Beware of confusion.

Ad 1. Doorman’s “thesis” of 2005

Michiel Doorman defended his “thesis” in 2005: “Modelling motion: from trace graphs to instantaneous change” (online), written under the supervision of P.L. Lijnse and Koeno Gravemeijer.

1. In the “thesis”, Doorman basically refers to Paul Drijvers at FHCRMI for computer algebra, but Drijvers is no light on this either. For the subject of the thesis (“Furthermore, it has been examined what role computer tools could play in learning mathematics and physics.”) it would have made much sense to look deeper into computer algebra.
2. Also check my analysis that Koeno Gravemeijer is no scientist but an ideologue for “realistic mathematics education” (RME) who misrepresents issues on “21st century skills” (in Holland “Onderwijs2032“), and who doesn’t see the revolution by computer algebra. (Dutch readers can look here too.)
3. On p58-59 Doorman critically adopts RME, and remember that this was in 2005, while RME was under discussion, see (a) the discussion in 2006 between Robbert Dijkgraaf (who has no qualification for math ed at this level) en Kees Hoogland (a RME ideologue, see below), which report was written by RME supporter Martinus van Hoorn, and (b) while Jan van de Craats (who has no qualification for math ed at this level) was protesting about RME, and published “Waarom Daan en Sanne niet kunnen rekenen” in 2007. See my criticism w.r.t. Jan van de Craats (fighting his math war on the side of TME and neglecting NME since 2008).
4. Doorman refers to Freudenthal for “guided reinvention”, but this is a wrong reference (he may only have coined the phrase but not the concept), and Doorman’s thesis does not refer to the true inventor of the concept (guide through levels of insight) Pierre van Hiele at all.
5. I will not look at this “thesis” in detail because there is really no reason to so so now.

Ad 2. Curriculum vitae

Doorman’s cv shows that he got a mathematics degree and continued at Freudenthal Head in the Clouds Realistic Mathematics Institute (FHCRMI), thus without a teaching degree in mathematics and without proper training in research of mathematics education.

• The KNAW report of 2009 showed that FHCRMI doesn’t do research on arithmetic education, and one should not suppose that this is different for other areas.
• Thus Michiel Doorman is neither a teacher of mathematics nor a researcher in the education of mathematics.
• We find no qualification for teaching and research, but immersion into ideology, and while he is involved in programming and the role of ICT for (mathematics) education, there are only perfunctory statements on computer algebra (for all subjects that use mathematics).

Ad 3. Webpage

Observe that “context-based mathematics education” is a rephrasing of “realistic mathematics education” (RME). Also “inquiry based learning” is basically RME, with contexts as the starting point for the “inquiry” (constrained by learning goals).

Someone really interested in didactics and RME would also have been interested in my analysis that shows that RME is a confusion and an ideology.

Observe also that the sciences are easy victims of RME. The sciences do not care much about mathematics education, and when RME people flock in to assist in the learning of the sciences, and when student learning time for mathematics is actually spent on the sciences, then professors of physics or biology might hardly object. For RME the sciences are useful window dressing, since those provide both contexts and an aura of respect and acceptance, and an argument that “students are learning something” (even if it isn’t mathematics). There is a curious historical link-up of mathematics with the beta sciences while there are also the humanities (alpha) and social sciences (gamma), see here. But is it really curious, and isn’t there a method, that the human and social scientists who know the techniques and who also do research by observation are kept out from this association between “mathematics education” and “science education” ?

Possible confusions that are triggered immediately

Stating the above might immediately trigger some confusions.

• As member of the NVvW board Doorman might argue “not to look into the criticism on FHCRMI because of an interest there”. Instead, he should rather take the initiative and make sure that this criticism was answered in decent manner rather than burked. If his interest is so large that he cannot speak freely on science then he should rather not be in the board.
• Doorman in a 2015 text in Euclides, the journal of NVvW, referred to (intellectually stealing) Freudenthal and not to (victim) Van Hiele. When asked to correct, he didn’t reply to this very question (see page 8) but talked around it, see my deconstruction of his “reply”. Potentially Doorman just didn’t have the relevant knowledge about didactics, for his “thesis” refers to RME but not to Van Hiele. If Doorman had looked into this criticism of mine, he could have been a bridge of understanding for the other members of the NVvW board and readers of Euclides, but he wasn’t.
  PM 1. I don’t understand either why these people didn’t see that he dodged the question.
  PM 2. Doorman in Indonesia sheets 44-49 on RME repeats the reference on anti-didactic inversion to (intellectually abusing) Freudenthal at the cost of (victim) Van Hiele.  Thus I asked a correction, he dodged the question, and proceeds as if there would be no problem (and likely not informing the audience about the criticism).
• Thus Doorman is neither teacher nor researcher: so what is he doing in the board of NVvW ? From qualifications, actually their lack, and work, actually the lack of answers, it is a small step towards wondering about motivation. A good hypothesis is: he is spreading the gospel of RME and blocking criticism. If Doorman wants to become professor at FHCRMI he must show that he is a true sectarian of RME. He is polishing up his cv and can now claim that he has been involved in the community of teachers, even when it was dodging questions. This is a hypothesis only, and one might also offer other explanations like blindness.
• I wonder who paid for this trip to Yogyakarta. It is also known that Freudenthal Head in the Clouds Realistic Mathematics Institute (FHCRMI) still is busy in establishing footholds over the world even though RME has failed. See also FIUS.org, who apparently neglect the KNAW report or my criticism.
• Yes, there is also NRO-project supervisor Frits Beukers, but he is professor of mathematics also without qualification for mathematics education research. Beukers presently is chairman of the Platform Wiskunde Nederland (PWN)-education committee, but would represent the universities since he has no qualification for primary or secondary education or the trade colleges. In that committee we also see Kees Hoogland, who abused the biography by John Allen Paulos for RME, and who has not corrected yet and who refuses to give an English translation of the key section.

Disclaimer: Can I be unbiased ?

I stated that I would give an unbiased assessment. Can I really do so ? Undoubtedly the reader will make up one’s own mind, but my perception is that I have been fair and unbiased.

Doorman’s “thesis” of 2005 is closely related to the education on the derivative. There was ample scope for a meeting of minds. When Doorman sticks with RME and Java applets, instead of NME and computer algebra, it is all of his own choosing. The differences in positions can be mentioned:

• Check my proposal since 2007 for an algebraic approach to the derivative, see e.g. Conquest of the Plane (2011).
• COTP was also programmed in Mathematica – a system for doing mathematics on the computer (a.k.a. “digital environment”) .
• Also, I am a user of computer algebra since 1993, while Doorman tends to use other programs that don’t have the flexibility of computer algebra.
• Doorman was editor of TD-Beta when I submitted a short note in 2012 on my invention of the algebraic approach to the derivative. This was maltreated. See here anonymised  and see here with full names (it is a scientific discourse and no private exchange).

At the NVvW annual convention of 2015 when Doorman was elected to the board, I had my doubts but opted still mildly optimistically for the benefit of the doubt. I had no experience with this TD-Beta journal and perhaps everything was an unfortunate misunderstanding. It doesn’t happen so very often that someone can propose a new approach to the education on the derivative. The performance of last eight months however gives evidence of the mindset of an ideologue.

Conclusion: Doors of perception

Any link to Doorman’s name is coincidental, and it is also a coincidence that the Dutch family name “Doorman” indeed is related to the English “doorman” (at least according to the Meertens institute).

The phrase “doors of perception” comes to mind when looking at Doorman’s presentation sheet “Aim of Primas” that states:

“A question not asked is a door not opened!”

1. This implies that an opened door is a result of a question. (This need not be an open door.)
2. This doesn’t imply that asking a question will open a door. (The question might e.g. be ignored.)

The message of this present weblog is, amongst others, that there are some crucial questions that Michiel Doorman refuses to look into and apparently doesn’t want to answer. He is employed at the Freudenthal Head in the Clouds Realistic Mathematics Institute, that should not be at a university. Apparently Doorman did not inform his hosts in Indonesia about the existing critique either.