Thomas Colignatus, September 15, 2015, small update January 6 & March 13 2016
1. The gap between secondary and higher education *
2. Arithmetic in elementary school *
3. The period 2008-2015 *
4. Mathematical pronunciation of numbers *
5. Wilbrink - and Van de Craats again *
Appendix: Three emails *
Addendum September 22 2015:
Dutch readers may benefit from the diagram below, and this selection of screen shots.
In 2008, when I got my additional Leiden MSc degree for teacher of mathematics, I began writing about mathematics education, and concentrated on secondary education, though taking advantage of my experience in teaching mathematics, statistics, logistics and operations management at college level during 1997-2001. (Check out this TSOM textbook.)
Since my origin and main line of research is in econometrics and political economy, I also looked at the policy making process in the mathematics industry, and in 2008 gave the advice to a parliamentary enquiry on mathematics education, since that is the only solution to tackle the mess it is in (for each nation separately). The petition for Holland is here. The book Elegance with Substance (EWS) (2009) has a 2nd edition in 2015 here, again with PDF online, and explains the situation for countries in general.
There is a dirty math war in Holland between on one side the Freudenthal Head in the Clouds "Realistic Mathematics" Institute (FHCRMI) in Utrecht with their fraudulent "realistic mathematics education" (RME) and sect behaviour and scorged earth strategy, basically because they are incompetent and can only maintain their position by bullying the rest of the world, and on the other side professors of mathematics who however are at universities and who are not involved in or qualified for elementary or secondary education but who nevertheless look in dismay at what the students cannot do anymore when they enter higher education.
I take a third position in this. I criticise both RME and those math professors. The math professors are not qualified for earlier education, and use wrong arguments in their criticism of RME. They all misinform educators, the minister of education, parliament, journalists and the public. Whence a parliamentary enquiry is an unavoidable advice.
While my analysis is on my website since 2008, and has been further developed with articles and books, now in 2015, seven years later, we reach the point at which we cannot avoid the following observation on scientific integrity. Namely, the point is that people first get the benefit of the doubt, but once you have told them about a mis-state, then they should not neglect this information. An earlier observation in 2014 was about a collective failure, but specific breaches must be mentioned when they are observed.
Jan van de Craats (1944) (70+) is an emeritus professor in mathematics, formerly Leiden, KMA Breda, UvA Amsterdam, Open University (OU). Dutch readers may like this sympathetic though uncritical interview (2010). Jan van de Craats tends to write for higher education and since 2007 also about arithmetic at elementary school in Holland (here). In 2006-2007 Van de Craats was chairman of the Resonans committee, created by the minister of education to look into the problem that secondary school mathematics education doesn't prepare for higher education any more. Thus, the areas of activity of him and me don't overlap much, except on the 1-2-3 dependency, which is a factor in the explanation that it is only now in 2015 that I conclude that Van de Craats is in breach of scientific integrity. Addendum 2016-01-06, see also here: Van de Craats's appointment at KMA was for teaching math for tertiary education (military cadets), at UvA (till retirement around 2009) for "mathematics and society", and at OU (2004-07-01 till 2009-10-01) for "mathematics and in particular mathematics education". The latter does not specify whether it concerns primary, secondary or tertiary education, and whether it involves training of (math) teachers at such levels. Perhaps it is left to the professor's discretion to monitor his own competence ? When a mathematics professor writes about math education, then even universities might think that he or she is qualified for this and appoint him for such, but this is an elementary confusion (see the illustration in the diagram by Norma Presmeg). Without further proof by OU and Van de Craats, this memo will hold that he is not qualified for didactics at primary and secondary level, even though we can appreciate many of his comments. Addendum 2016-03-13: Van de Craats wrote the "Basisboek wiskunde" in collaboration with dr. Rob Bosch, qualified for secondary education who moved to KMA too. However, not all that Van de Craats stated has been in collaboration with Bosch.
Ben Wilbrink (around 1945) (70+) is a retired psychologist, particulary in testing. Van de Craats has an (A4 length) list of references on his website to Wilbrink's website. I discovered last month that Wilbrink maltreats the Van Hiele theory of levels of insight. Since Wilbrink refused to discuss and change this, I asked Van de Craats for mediation, see this entry on my weblog in English here.
Their breach in the integrity of science is:
they discuss mathematics education without proper qualification (a professor may have a teaching task at a university but not necessarily in primary or secondary education) (a psychologist should do psychology, and if meeting something that isn't psychology then respect it, e.g. mathematics education research (MER))
they neglect my criticism on their statements (and don't tell each other that they should look into this) (for Wilbrink especially on the epistemology w.r.t. his critique on Van Hiele levels)
they misinform educators, the minister of education, parliament, journalists and the public on this (and Van de Craats also the students of his textbook discussed below) (and not just desinformation by common human error but by deliberate and persistent neglect of criticism on that error).
These points come to the surface when we look in closer detail at the following five issues.
Addendum 2016-01-06: The Code of Conduct for Scientific Integrity by All European Academies of Science (ALLEA) is deficient in dealing with issues of integrity. It is targetted at protecting employers of science against employees who manipulate, fabricate and plagiate, and it neglects other issues likely because these are legally more difficult. The following takes the wider view from science (other than employers).
Van de Craats & Rob Bosch present an exercise textbook (2005, 2009) about mathematics education, in Pearson's proper section of higher education that he is qualified for, in Dutch (excerpt pdf), English, German, French. We may compare it to Schaum's outline series but Schaum's tends to take smaller steps and give more theory and explanation. Van de Craats's argument for his book is:
"that it helps close the gap between secondary education and the required mathematics for higher education". (my translation from Dutch to English)
When there is a gap between secondary and higher education then this generally means that secondary education is deficient, as the very objective of level 2 is to prepare for level 3. (We may presume that higher education is already under pressure for lowering their standards ...)
Writing an exercise textbook is something that you might do. (1) Such a book helps students who suffered this deficient secondary education and who want to get into higher education, (2) It reminds educators, the minister of education, parliament, journalists and the public about the gap.
That is, if you really believe (2). Schools find some solution in redirecting "weak students" (failing education) towards less demanding diplomas, so that percentages on exam results are maintained. Problem (2) isn't in the media any more as it used to be. At the cost of students.
Overall, writing such a textbook is Kurieren am Symptom. Tinkering at the symptoms. The book distracts from properly informing educators, the minister of education, parliament, journalists and the public that something is wrong with secondary education. Students of his textbook should not have to pay for the book but should get a folder where to find a lawyer to sue their schools for deficient education. Van de Craats's approach is part of the process of deterioration. Writing such a book is not the reaction of an educator, but the reaction of a mathematician who has been trained on abstract thought and not on empirical science.
It is quite frustrating when you talk to a journalist, and explain about the sad state of mathematics education, that such a journalist may refer to Van de Craats as someone who does wonderful things such as writing this kind of textbook that solves a lot of problems for prospective students. This is bad journalism of course. Still, given the state of bad journalism that we are in, Van de Craats thus sabotages the flow of information. Undoubtedly, his intentions were good, but it is not thinking straight.
Apparently there is a market for this too, with reported 50,000 copies sold. It is unclear whether these buys were voluntary or mandatory - it is one of the suggestions at TU Delft - and whether its use caused success or failure. This is not evidence-based education (Dutch TIER). There are some student reviews that confirm that it is an exercise textbook, so that you need another book on theory. An online Dutch secondhand bookmarket shows 99 hits, which doesn't seem overly much for 50,000 copies sold, so readers might hang on to their copies, or there are message boards with (un-) successful users passing it on to future (un-) successful users.
The above is the main point that causes a breach in scientific integrity: neglect of a scientifically proper advice, in this case to a parliamentary enquiry, with a confused view on a "realistic" advice, and instead tinkering at the symptoms, and thus killing the true message. In this neglect, he assumes to be qualified for mathematics education research levels 1-2-3, but is only qualified for higher education, level 3. NB. At other points Van de Craats appears to keep in mind what he is qualified for, but at least in the neglect of said advice he forgets about that.
Policy makers are wary of the problems in education, and one of the policy measures is to create the "register of qualified teachers", mandatory now from 2017 onwards, unless the Dutch Senate would still block it. For teachers it becomes mandatory to follow courses to keep your license to teach. What courses that are, will be monitored. One supposes that the teachers unions will make sure that courses are at reasonable times and paid by schools. This may become the next straight jackett of bureaucracy, adding to the cost of education and reducing its quality. When the problems in mathematics education were caused by RME then the solution is not to create a register. But when policy makers and parliament do not get proper advice by professors like Jan van de Craats, then policy makers might feel excused for their erroneous path. (But see my letter to parliament, 2013.)
My supplementary problem with the textbook by Van de Craats & Bosch is:
[Addendum March 13 2016: Today, I discover that Bosch wrote his thesis in 2006 with Harrie de Swart and Jan van de Craats on social choice theory, see here. In the thesis we find a cv for Bosch. He was a secondary school math teacher in 1974-1987 (13 years). He graduated in mathematics in 1976, and he moved to KMA in 1987 where he met Van de Craats. Thus Bosch is formaly qualified for secondary education, and the responsibility of the didactics of the book falls basically on his shoulders. When I presented Van de Craats with criticism, it became Van de Craats's responsibility to check with qualified Bosch, and whether he allowed Bosch not to contact me.]
While the book is presented in the Pearson section of higher education, it is supposed to cover a gap in secondary education, which is what Van de Craats is not qualified for. Students who would study the book might be older than 18 but still at the level of competence in mathematics of perhaps 16 years of age, and thus be in need of secondary education instead of higher education. This has been covered by the qualification of co-author Rob Bosch (while corrections by Van de Craats might be only partly helpful).
Perhaps the standard of remedial teaching consists of presenting proper mathematics (finally after all these years !), but this "perhaps" indicates the uncertainty. I would rather look for a mixture of pen & paper and computer algebra, for example, as indeed is done by COTP (2011). A remedial book that uses only paper & pen doesn't guarantee gained competence for life. Familiarity with computer algebra would be useful to have a fall back position. It will always be around for help. The situation at higher education seems somewhat diffuse: having entry exams but with limited support, which might not be the optimal approach to remedial teaching either.
Van de Craats & Bosch stick to traditional mathematics, and
(a) my criticism on secondary school mathematics, as it fails to prepare for higher education, which is not only exercises but also theory, and indeed with exercises but in context of theory, and
(b) my criticism on traditional mathematics, as formulated in my books EwS (2009) and COTP (2011).
Van de Craats does not fully neglect my criticism, see the email of 2008 below, in which he reads my earliest statement on some issues, and expresses agreement. But he rejects the advice to a parliamentary enquiry with the curious argument of "unrealistic" (which is no argument for a scientific advice), and for all I know he hasn't looked at the later books EWS and COTP.
His 50,000 copies could have carried the message: "This book may solve your individual problem, if you study hard on it, but please observe that a parliamentary enquiry is required to solve the problem structurally, and that you may be the victim of this structural problem." When toothpaste comes with health warnings, why not mathematics exercise textbooks that are of much more importance for your future ?
[Addendum March 13 2016: In 2015 I wrote: "Perhaps co-author Rob Bosch is qualified for secondary education, but I cannot find a cv, and only that he has a doctorate and teaches at KMA, the Dutch national defence academy." This has now been resolved in 2016.] (There is the awkward situation of malconduct, and Bosch's involvement, here and as member of the team of editors of Euclides here, but that is not the current topic of discussion.)
Also, it leads too far for me to buy and look in their book, so my criticism has a hazy status. However, there is this excerpt pdf, and on page 17 we find a discussion on mixed numbers. Van de Craats holds that 2½ is less useful for multiplication than 5/2 and thus will hardly be used. My analysis however is that 2½ is a wrong notation, since it suggests multiplication, and that the proper notation is 2 + ½. The latter is useful so that you can know where it is on the number line. This example suggests to me that the exercise book has limited didactic scope. Other comments come to mind when I see other topics, but this is an excerpt only and one should look at the whole. Van de Craats may correct me if I am wrong about his view on adopting traditional mathematical presentations and neglecting my criticism on this.
Van de Craats observed that students entering his classes in KMA, and thus desiring to become officers in the Dutch military, had problems with mere arithmetic. This caused above article in 2007, and the subsequent "book of complaints" in 2008.
When the 2007 article by Van de Craats got national attention, he was approached by elementary school teachers Piet Terpstra and Arjen de Vries. (Be sure to read this key Dutch text.)
They had been distressed with Hans Freudenthal's "realistic mathematics education" (RME) since 1980, and had developed their own method, combining systematic methods with some useful aspects of RME. Up to then they had not been able to find a publisher because of the domination of RME in Dutch elementary schools. With support by Van de Craats, their work was "subjected to scrutiny" (their words) and 2008 gave a contract with the present publisher, for the new method "Reken Zeker" (RZ) ("Reckon Surely"). A foundation was created for good education in arithmetic (which apparently isn't done at Freudenthal Institute at the University of Utrecht), and educators of that foundations are editorial advisors to the method "Reken Zeker". The publisher's website states a satistfaction score of 8.2 on a scale of 10, in a survey of 744 elementary school teachers in 2013. As so often in education, the publisher's website presents the "method" and hides the names of the authors Terpstra & De Vries, so that others can take over without a fuss.
A Dutch text on Van de Craats's website might have given more laurels to the authors too: "Een nieuwe rekenmethode voor de basisschool. Noordhoff Uitgevers heeft in 2010 in samenwerking met de Stichting Goed Rekenonderwijs een nieuwe rekenmethode, genaamd Reken zeker, op de markt gebracht voor de groepen 3 tot en met 8 van de basisschool. De hoofdauteurs zijn Piet Terpstra en Arjen de Vries, maar (my emphasis / TC) Noordhoff heeft daarnaast een uitgebreid team van redacteuren, docenten, rekendeskundigen en vormgevers ingezet om er een aantrekkelijke eigentijdse methode van te maken. Voor de Stichting Goed Rekenonderwijs hebben Rob Milikowski en Liesbeth van der Plas zitting in de Redactieraad, en verder verlenen de Stichting Wiskunde Kangoeroe, de Technische Universiteit Eindhoven en de Universiteit van Tilburg medewerking aan deze uitgave."
Some remarkable points are:
The research & development of "Reken Zeker" has not been based upon the double blind randomized trial golden standard of empirical research - though the latter is a requirement by Ben Wilbrink, see here, and as far as I know Ben Wilbrink hasn't criticised this lack of scientific base, and Van de Craats does not refer to any such criticism by Wilbrink.
This research & development is based upon experience from practice by two elementary school teachers, i.e. Terpstra & De Vries, supported by later other educators who don't rely upon statistical methods either, and of course supported by Van de Craats's "intuition" that algorithms are important, and of course exercises to master them. Please observe: also Pierre van Hiele started with practice, though later he turned his finding into a theory of epistemology. Ben Wilbrink rejects Van Hiele's method of using practice as gibberish (Dutch "zwamverhaal") but doesn't reject the same method by Terpstra, De Vries and Van de Craats.
The teachers hold for example (here p2) that learning goes "from concrete to abstract. Arithmetic is abstract". This is contrary to Ben Wilbrink who has a love affair with Stellan's Ohlsson's erroneous argument that learning goes from abstract to concrete, see here. Wilbrink wields Ohlsson's misconception to condemn Van Hiele's work. And Van de Craats refers to Wilbrink. But apparently both support RZ. Van de Craats and Wilbrink are hopelessly confused. Or criminally insane. It is a breach of scientific integrity that Van de Craats and Wilbrink do not react to my criticism on the maltreatment of the Van Hiele levels of insight, also concerning the direction of learning in those levels.
Moreover, Terpstra & De Vries state that their method is based upon a mix of traditional education (e.g. memorising the tables of addition and multiplication, that RME abolished) and some elements that they found useful in RME. They however do not specify what those elements are. It likely are the points that Hans Freudenthal stole from Pierre van Hiele. More clarity on this is needed.
NB. It is a no-brainer that you have to memorise the tables of addition and multiplication. Every scientist will acknowledge that you need to do this as a child if you want to do arithmetic. The RME sect that rejects this are no scientists. They say that they "agree with the principle" but "only use a different method", but their method doesn't lead to memorisation, so they are simply lying. The commission Lenstra who tried to mediate and "treat both parties with respect" was led by Jan Karel Lenstra who is a mathematician trained for abstraction and not empirical science, and Lenstra is in breach of scientific integrity by not responding to my criticism, see here.
We now see some kind of "survival of the fittest" experiment, which is not necessarily a properly controlled scientific experiment, and that does not satisfy the rules on experiments with human beings (see the KNAW-LOWI rules on those). There are two major education methods, RME versus RZ. The situation is a bit tricky, since the judge is the CITO score on arithmetic, and CITO arithmetic is a tool by the RME sect to exterminate all opposition. (One of CITO's employees is Ger Limpens who in his "review" of EWS 2009 showed that he doesn't know what science is, and started slandering me as an eccentric and Don Quixote though his final verdict was "okay, useful". His comment on the typing errors was correct, thus see the 2nd edition 2015, again PDF online.)
NB. An aspect in experiments on humans is that when you see that the "experimental" treatment works so well, e.g. in vaccination, then you stop the experiment, and give the treatment to all. It is a sickening story how RME got accepted and became the norm in Holland. (For example, the precursor to FHCRMI in Utrecht was abolished, its unemployed employees found employment all over Holland, and from there they started again, now seemingly as "experts from all over Holland".) Nevertheless, RME is the norm now, and RZ is the experimental treatment. If it is shown to be effective, stop with RME. But, will mathematics educators follow this rule ? Or will their ideology be more important than the future of the children ?
For example, in 2009 Kees van Putten of Leiden university compared RME with "traditional methods" and maintained (Trouw) that there are no differences for good or weak pupils, and that the middle group would be helped a bit more by traditional methods instead of RME. The major factor would be calculation on paper or not. Pupils who don't use paper would be worse off, and it would be a major improvement to encourage them to use paper. RZ was introduced in 2010, and Marian Hickendorff of Leiden repeated Van Putten's argument in 2014 (though argued in favour for the weaker students). See some of my questions on this, in Dutch 2014. Observe that these are psychologists and not researchers in mathematics education. They may know some statistics (as I do as an econometrician) but they lack practice and awareness of what mathematics is about (notably the notion of proof). See another example how neuro-psychologists do research that is obviously invalid. (Addendum 2016-01-06: See this weblog text for more.)
The cards seem against RZ. Fortunately, RME is such a miserable method that any decently competent alternative should gain the upper hand. The only worry for RZ is the quality of the teachers. Any method fails when teachers cannot do arithmetic themselves, which, unfortunately, is often the case. When RZ becomes so popular that the majority of elementary teachers, who used to work with RME, suddenly would have to use RZ, which they are not capable of, then RZ may well do worse, merely because pupils who are trained in RME might be more used to the silly manners by CITO arithmetic in RME fashion. In that case, the publisher of RZ would be forced to remove Terpstra & De Vries as authors, and introduce more RME in RZ, in order to maintain market share and profits. If the contracts would not allow this then the method would be stopped.
Check what I wrote last year: "Lenstra’s solution to the arithmetic problem in Dutch primary education is not to retrain the 150,000 elementary school teachers, but shift the problem to the 4,000 math teachers in secondary education [Correction 2016-01-06: this number appears to be 12.000 (stamos.nl)]. The formula is that “arithmetic skills must be maintained” in the highschool curriculum. Lenstra suggests that it must be tested, but doesn’t quite specify how. The Dutch state secretary on education, Sander Dekker, wants mandatory arithmetic tests for highschool graduation. If you cannot calculate with pen and paper then you can’t get your highschool diploma. Lenstra thinks that this is too strict (see here) but doesn’t provide a practical alternative how to test whether arithmetic skills have been “maintained”. The state secretary apparently is quite happy that he doesn’t have to retrain the 150,000 elementary school teachers, many of whom are likely to fail too, and that it suffices to increase the burden for the 4,000 secondary school teachers, and of course the burden for the kids who turn 16 or 18 and discover that the educational system has given them a raw deal. (It is a bit too easy to blame them that they should have worked harder.)"
This is the harvest of Van de Craats's neglect of my advice in 2008 to have an enquiry by parliament.
My advice in 2008 didn't delve deep into issues of arithmetic at elementary school, but Van de Craats must have been able to make the inference, and rejected to do so. (Addendum 2016-01-06: see an update.)
Van de Craats's website shows him engaged in improvement in mathematics education. It would seem to be alright what one puts on one's website. I would not want other people to tell me what to put on my website. This section is no criticism. It is merely informative about what Van de Craats did not report about my contributions and criticism. This doesn't imply that he lived in a bubble. He may have studied my website every day but merely decided not to report on it. Let me list not all my texts from the period, but only the books, also the new ones.
My book Elegance with Substance (2009). Apparently Van de Craats feels no need to review it, or protest against the slander by Ger Limpens, mentioned above, here again. (Though Limpens is right on typo's, see the 2nd edition.)
My book Een kind wil aardige en geen gemene getallen (2012). Apparently Van de Craats feels no need to review it, or protest against the refusal by the editors of Euclides of reviewing it, since they don't like that I protest against slander, see here.
My book The simple mathematics of Jesus (2012) (or the Dutch version), idem dito.
The 4th edition of Voting Theory for Democracy (2014). Mutatis mutandis.
My book Foundations of mathematics. A neoclassical approach to infinity (2015). Mutatis mutandis.
The 2nd edition of Elegance with Substance (2015). Mutatis mutandis.
My book A child wants nice and no mean numbers (2015). Mutatis mutandis.
I still feel a bit unheimish by the neglect - as much as actually getting attention. When FHCRMI systematically neglects my work, even though they claim to monitor what happens in the world of mathematics education research, see their wiki, then this merely fits the diagnosis of sectarian behaviour. Van de Craats as an individual would not be a sect by himself. But perhaps he has created a network like this, sheltering him from criticism and telling him how wonderful it is what he is doing. One thing is certain: he did not give me a leg-up and he did not protect me in public against the abuse in Euclides. I don't know how hard he has been trying to do this behind the scenes, of course. Still, he stuck to traditional mathematics, his exercises textbook is sub-EWS-standard, and he was not open to the empirical observation that mathematicians are trained for abstraction and not for empirical methods.
I am not qualified for elementary school, and the following is only a suggestion for people who are qualified. What I do on this subject is only to elaborate the issue, and to facilitate easier research and decision making by those who are qualified. In my experience as a teacher it is an issue, there is international research on it, and it is eminently common sense. The Norwegian parliament (Storting) decided in 1950 to change the pronunciation of numbers and the Dutch didn't do so for silly reasons.
For English readers it may be a surprise to hear that twenty-one is pronounced in Germany, Holland and Denmark in the reverse order, say in Dutch as een-en-twintig (one-and-twenty). English readers may even be more surprised when they notice that there is the switch between nineteen and twenty-one. Shouldn't it be ten-nine ?
Readers of English are advised to look at A child wants nice and no mean numbers (2015), pdf online. Dutch readers may look at Tellen en rekenen met tig (2015), pdf online, reworked from 2012.
Van de Craats confirms that the Dutch pronunciation of numbers is awkward for arithmetic.
Dutch: "Met name de tientalpassering is een gevreesd struikelblok, terwijl ook de "onlogische" manier waarop wij in het Nederlands getallen van twee cijfers uitspreken (bijvoorbeeld vierendertig in plaats van dertig-vier) voor problemen zorgt. Wat dat betreft is het Engels in het voordeel (thirty-four)." (Didactief, August 31 2015)
But professor Fred Schuh of TU Delft already observed this in the 1940s and proposed a change to the minister of education around 1950 (Telegraaf, 29 maart 1952 page 3), and thus the text by Van de Craats should rather not be such a lacklustre observation, but inform his readership properly about this situation. He could also have referred to my book Een kind wil aardige en geen gemene getallen (2012).
Thus: Van de Craats is in breach of scientific integrity by not properly informing his readership about the true state of information.
There is also this peculiar hypothesis. I don't know whether it is true, or how it can be tested or verified. Given the current wrong names of numbers, children, who grow up in language, experience problems in learning counting and the reading and writing of numbers, and the subsequent arithmetic. Perhaps this difficulty inspired Freudenthal to steal his notions of "realistic mathematics education" from Van Hiele (and misunderstanding and/or misrepresenting them, but that doesn't change the theft). In other words: there is an issue here, that calls for some change. But the proper change is not the introduction of RME but the introduction of a mathematical pronunciation.
I am no psychologist and perhaps Wilbrink is the perfect psychologist.
It will also be that empirical researchers commonly are not deep into epistemology. Daily practice in empirical science is to do your experiments and statistics, and jump in the air when you find something. Wilbrink would generally be excused when this daily practice is his frame of reference.
Wilbrink's critique that Pierre van Hiele relied on practice, and did not do double blind randomised trials, which is hardly a critique since Van Hiele explained so himself, would be run of the mill, in the spirit of the Cochrane Collaboration.
The situation changes however when you get a message that there is an issue in epistemology that shouldn't be overlooked.
For, now you know: this isn't run of the mill.
Now epistemology cannot be neglected anymore. Now you have to reply to the critique, dust off your Introduction to methodology, and ask a question when you don't understand something.
Wilbrink doesn't adhere to that ethic. He simply breaches scientific integrity.
He doesn't care about science, education, children, Pierre van Hiele and the fraud by Freudenthal. He just doesn't want to admit that he might have overlooked something. And he is too much in love with his newly found authority of Stellan Ohlsson that he can only see the rosy beauty of his own righteousness. And he will not accept that he applies a double standard for Van Hiele versus Terpstra & De Vries.
To clarify Wilbrink's malconduct, there are these entries on my weblog:
On Ohlsson, on Wilbrink's abuse of psychology, my email in English to Van de Craats (not listed below) asking to mediate w.r.t. Wilbrink, more clarification on epistemology.
The last entry in that series was from September 8 2015. Thus my email to Jan van de Craats of September 12 2015 below (in Dutch) gave both Wilbrink and Van de Craats ample time to look into the issue. Wilbrink didn't respond anymore and Van de Craats replied on September 13 2015 that he will not do so anymore, see below. For perspective, I include the email from November 12 2008 that indicates partial agreement on content and rejection of the scientifically based advice to an enquiry by parliament. Perhaps Van de Craats had no way of knowing about the quality of my work in econometrics and political economy. [Addendum March 13 2016: This appears to be more complicated. Bosch did his thesis with De Swart and Van de Craats. This is a connection that requires more attention. See here for starters, and wait for a later elaboration.]
Jan van de Craats and Ben Wilbrink are in breach of scientific integrity. The specific points have been mentioned in the Introduction above, and have been establised in above sections.
They are retired and not subjected to official rules at KNAW-LOWI.
They are advised to look for advice by others, in particular outside of their common network.
Still, the first edition of Basisboek Wiskunde dates from 2005, when Van de Craats was about 61 years of age, and might still have been at an official institution of higher education. This book is targetted at remedial teaching at secondary level, which he is not qualified for. Co-author is dr. Rob Bosch, currently at KMA. [Addendum March 13 2016: Bosch was secondary school math teacher in 1974-1987 (13 years), and the main responsibility w.r.t. the didactics falls on him. There is a crooked switch in qualification, when one student of 17 years of age may leave HAVO and go to college that Van de Craats is qualified for, and another student of 17 years of age may be at gymnasium and do more complicated mathematics that Bosch is qualified for. Overall, one would tend to be lenient to Van de Craats w.r.t. his qualification.]
Yet the point is that there are didactic omissions, and it is too simple to hold that Bosch would be responsible for all of those (because he has the only formal qualification). Not everything that Van de Craats states has been in collaboration with Bosch.
KNAW-LOWI is advised to reconsider the neglect of my earlier report in 2014 about the collective breach of scientific integrity in mathematics education research in Holland, and take along this particular case.
PM Disclaimer: Readers are advised to boycott Holland till the censorship of science since 1990 by the directorate of the Dutch Central Planning Bureau w.r.t. my analysis on unemployment is lifted. Many people make an invalid inference that being censored in the realm of economics makes it dubious what you say about mathematics education and its research. Even professors grow nervous about censorship and stop looking at only facts and reasoning. It would be better to have this confusion out of the way. President Putin of the Russian Federation boycotts Holland for the wrong reason.
Subject: RE: Simon Stevin Instituut (http://thomascool.eu/Thomas/Nederlands/Wetenschap/Artikelen/2008-04-17-WiskundeOnderwijs.pdf) (http://thomascool.eu/Thomas/Nederlands/Wetenschap/Artikelen/2008-11-11-Simon-Stevin-Instituut.pdf)
From: "Craats, J. van de"
To: "Thomas Cool / Thomas Colignatus"
Geachte heer Cool.
Dank voor uw mail. Uw artikel "De wenselijkheid van een parlementair onderzoek ..." heb ik met belangstelling gelezen (ik was er nog niet eerder aan toegekomen). Er staat veel in waar ik het volledig mee eens ben, bijvoorbeeld uw aanval op de `gemengde' breukennotatie, decimale punt versus decimale komma, uw pleidooi voor vectoren in het voortgezet onderwijs, standaardnotatie voor de vergelijking van een rechte lijn, functienotatie, uw opmerkingen over de kansrekening, `zuivere dobbelsteen', uw kritiek op de grafische rekenmachine, etc., etc. Ook uw opmerkingen over de bestaande kaste van vrijgestelde, goed verdienende wiskunde-didactici heb ik met instemming gelezen.
In een aantal gevallen heeft u theoretisch wel een punt, maar staan praktische bezwaren realisatie in de weg, gewoon omdat bestaande praktijken niet gemakkelijk radicaal te veranderen zijn. Het onderwijs moet leerlingen op de bestaande praktijk voorbereiden, en die is nu eenmaal niet in alle gevallen logisch en optimaal. Het is net als met de spelling van het Engels (ook een ramp) of de gangbare muzieknotatie. Als we het opnieuw mochten ontwerpen, zouden we het anders doen, maar dat gaat nu eenmaal niet.
Ik vrees ook dat uw suggestie voor een parlementair onderzoek veel te zwaar is aangezet en geen kans van slagen heeft. Ik probeer de zaken op een minder radicale manier de goede richting op te sturen. Met wisselend succes, dat wel, maar met kleine stapjes kun je ook een eind komen.
Met hartelijke groeten,
Jan van de Craats
Korteweg - De Vries Instituut
Universiteit van Amsterdam
Plantage Muidergracht 24 1018 TV Amsterdam homepage: www.science.uva.nl/~craats
To: "Craats, Jan van de"
From: Thomas Cool / Thomas Colignatus
Subject: (A) Stand van zaken t.a.v. Ben Wilbrink, (B) Uw eigen inbreuk op de integriteit van wetenschap
Cc: "Henk Tijms", "Ben Wilbrink", enkele anderen
Geachte professor Van de Craats,
Ik schrijf u nu t.a.v. twee verwante zaken omtrent integriteit van wetenschap t.a.v. onderwijs in wiskunde (en rekenen):
(A) De situatie t.a.v. Ben Wilbrink is:
(1) Ik heb hem voorgesteld een bemiddelaar aan te wijzen, en hij reageert daar niet op.
(2) Hieronder is een advies van Henk Broer, voorzitter van de sectie wiskunde van de KNAW, cc Ben Wilbrink, om te praten, maar het effect op Wilbrink is dat hij blijft niet-reageren.
(3) Ik heb Ben Wilbrink nog eens de epistemologie uitgelegd, maar daar reageert hij niet op:
(4) En ik heb heel specifiek aangegeven wat er op zijn website verkeerd staat, maar daar reageert hij niet op:
Nu kan iemand menen dat kritiek vervelend is. Wanneer je in het publieke domein treedt, dan is het toch ongepast om kritiek te negeren, juist ook wanneer die kritiek onderbouwd is en terecht blijkt.
U zelf heeft een pagina-onderdeel "Ben Wilbrink over realistisch rekenen". Op zichzelf is het een correcte stelling dat u alleen verwijst naar wat Ben Wilbrink schrijft. Toch is diens beschrijving t.a.v. de positie van Van Hiele in het MORE onderzoek onjuist, zoals ik heb beschreven. Door kritiekloos naar Wilbrink te verwijzen, draagt u bij tot de verwarring:
Ik beschouw het als een ernstige misstand dat Ben Wilbrink niet reageert. Mijn verzoek is of u bij hem kunt aandringen om wel te reageren t.a.v. het bovenstaande.
In ieder geval wil ik u verzoeken om bij uw verwijzing op uw pagina ook wilt linken naar mijn kritiek op Wilbrink t.a.v. diens presentatie van MORE.
(B) Ik verzoek u om te zien dat mijn kritiek specifiek is: betekenis van Van Hiele, uitspraak getallen, specifieke kwesties t.a.v. breuken, e.d., en met vervolgens een overkoepelende analyse t.a.v. het verschil tussen een opleiding tot abstract denkende wiskundige en de empirie van onderwijs. Het zou m.a.w. onjuist zijn wanneer gedaan wordt alsof het maar een grabbelton is.
Inmiddels dateert mijn boek "Elegance with Substance" uit 2009, met het advies tot een parlementair onderzoek naar het onderwijs in wiskunde (en rekenen).
U heeft deze analyse tot op heden genegeerd. Of er wel naar gekeken, tegenargumenten gehad, en het naast u neergelegd, zonder mij van die argumenten te laten weten. [correctie: althans wel het oppervlakkige argument in bovenstaand email van 12 november 2008]
Het is niet zo, dat u alleen naar het rekenen kijkt. U heeft ook een "Basisboek Wiskunde" geschreven "om de kloof tussen de wiskunde op school en de wiskunde op hbo en universiteit te overbruggen".
Dat laatste is natuurlijk een kromme redenering.
Havo en vwo moeten voorbereiden op hoger onderwijs. Wanneer het daarin fout gaat, moet het parlement ingrijpen, en moet je geen boek schrijven om de kloof te overbruggen.
Vervolgens heeft u het boek "Vervolgboek Wiskunde", met voortzetting van de onhandige didactiek die ik juist bekritiseer in "Elegance with Substance" en het latere "Conquest of the Plane". U moet me vergeven dat ik deze boeken niet in detail ga lezen en bekritiseren, want dat lijkt me een herhaling van zetten. Maar u mag me corrigeren wanneer u in zo'n boek wel degelijk gebruik maakt van mijn kritiek.
Uw idee van kritiek op Freudenthal lijkt te zijn om terug te keren naar traditionele wiskunde die geen zicht heeft op de empirie van onderwijs. U negeert dus kritiek dat dit wetenschappelijk onjuist is.
Laat ik derhalve helder stellen dat uw opstelling sinds 2009 onderdeel van het probleem is gebleken.
Het is mooi dat u recentelijk in het AD van 29 aug 2015 nog eens uitlegt dat je de tafels tot (en met) 10 uit je hoofd moet kennen, maar, u draagt zo bij tot stagnatie en verwarring, doordat u de journalisten niet vertelt dat u onderdeel bent van het probleem t.a.v. het onderwijs in wiskunde (en rekenen). U spreekt bijv. over de tafels van 10 maar ik zie geen tig genoemd. Mutatis mutandis voor die Engelse uitgaven.
Tevens heb ik op 18 maart 2013 de president van de KNAW en wiskundigen, waaronder u, geschreven over de laster door Jeroen Spandaw t.a.v. "Conquest of the Plane" (2011), welk boek een "proof of concept" is van "Elegance with Substance" (2009). Ik schreef niet zomaar, want het was n.a.v. de tekst van Christiaan Bourdri. Wellicht heeft u ernaar gekeken, maar u heeft dan niet doorgegeven wat uw bevinding was.
Het is onjuist dat u mij niet de bescherming heeft geboden die je van een wiskundige toch zou moeten kunnen verwachten, juist ook bij zo'n helder onderwerp als de afgeleide op het vwo.
Zoiets schept denkelijk ook verwarring voor anderen, zoals wellicht Ben Wilbrink of Rob Milikowski die dan wellicht denken dat Spandaw wel gelijk zal hebben of zo. Ik doe beiden genoemden kopie, zodat ze eventueel kunnen melden wat ze ervan denken. De situatie t.a.v. Jan Bergstra is een verhaal apart, en bewaar ik voor een ander kader.
Het lijkt me nuttig dat ik u helder laat weten hoe ik over deze situatie denk. Ook u pleegt een inbreuk op de integriteit van de wetenschap, m.n. t.a.v. onderwijs en didactiek van wiskunde. Men kan niet zomaar informatie negeren.
U heeft kritiek op de rekentoets, en legt de verantwoordelijkheid bij anderen en uiteindelijk de staatssecretaris. Maar u heeft zelf deze staatssecretaris nadere informatie onthouden, door niet in te gaan op mijn kritiek in "Elegance with Substance" e.d.
Ik verzoek u mij te laten weten of deze toelichting heeft geholpen om het inzicht te vergroten, en wat u daar dan aan wilt gaan doen. Een nieuwe opening is geboden door de 2e editie van "Elegance with Substance", 2015, pdf op mijn website.
Het is mogelijk dat ik dit email op mijn website plaats.
Met vriendelijke groet,
Thomas Cool / Thomas Colignatus
Econometrist en leraar wiskunde
From: "Henk Broer"
Date: Sun, 6 Sep 2015
Cc: Jan Bergstra,
"Ben Wilbrink", "Henk Broer"
To: Thomas Cool / Thomas Colignatus
Geachte heer Cool
Het is mijns inziens beter als u uw problemen met de heren Bergstra en Wilbrink rechtstreeks met henzelf bespreekt.
Met vriendelijke groet,
Prof dr Henk W Broer
Johann Bernoulli Institute
for Mathematics and Computer Science
University of Groningen
From: "Craats, Jan van de"
To: "Thomas Cool / Thomas Colignatus"
Cc: "Henk Tijms", "Ben Wilbrink", enkele anderen
Subject: RE: (A) Stand van zaken t.a.v. Ben Wilbrink, (B) Uw eigen inbreuk op de integriteit van wetenschap
Geachte heer Cool, beste Thomas, Ik wil je verzoeken op te houden met het zenden van emails naar mijn adres. Ik zal er niet op reageren. Jan van de Craats Korteweg - de Vries Instituut Science Park 105-107 1098 XG Amsterdam