After my short stint as expert on national security in 2005, I now had another short stint, now as expert on mathematics education, STEM and the role of mathematics education in the whole curriculum. First Jos Tolboom of SLO had hinted that I could be invited for an expert meeting, but then this invitation didn’t actually materialise.
This is a bummer. I wrote several books and articles on the subject. One of the reasons why there is so little progress in the field is that there isn’t enough attention for my novel analysis.
The November event
This concerns the following event:
22 – 23 November 2016
CIDREE STEM (science, technology, engineering, mathematics) Expert Meeting
Utrecht, The Netherlands
Hosted by Freudenthal Institute and SLO
Topic: The position of mathematics education and informatics education in a coherent STEM curriculum
This meeting aims to create an international overview of innovations in mathematics education and informatics education, their relationship and the coherence from the STEM perspective, with a special interest in computer based mathematics and its relation with computer science (informatics). This goal has been determined with other CIDREE members as a follow up on the expert meeting in June 2015 in Trondheim, Norway.
The announcement in Dutch is here. Three questions for the meeting are (in my translation):
- How can we create more coherence in STEM education overall ?
- How can we create a mathematics curriculum with a strong component in computer based (mathematics) education ?
- How can we create a curriculum for computer science (“informatica”) as part of the STEM curriculum ?
Cambridge Mathematics will be represented at this event as we explore innovations in mathematics education and how we can plan for the future of the mathematics curriculum.
Key warning for STEM researchers
(1) Researchers on STEM should be aware that the researchers on STE may have little knowledge or interest in both Mathematics education (ME) and its research (MER). Every field tends to focus on itself, and coherence is secondary.
(2) A key difference is:
- STE fields have empirics as a judge of what works. This empirical mindset is also applied to the education in these fields.
- Mathematics is directed at non-empirics (abstraction). There is no external judge but only personal opinion. Thus mathematicians tend to regard power play and “math wars” as acceptable methods to get views accepted. (Examples of such thinking in Holland are mathematicians Jan van de Craats and Henk Broer.)
- See this discussion about the math war between “realistic mathematics education” RME and traditional ME (TME), and the scientific alternative of neoclassical NME. Look also for the explanation that the name “Freudenthal Institute” does not convey the true meaning of the institute, and that it is better to speak about “Freudenthal Head in the Clouds Realistic Mathematics Institute” (FHCRMI). Namely, RME is like astrology or homeopathy.
(3) In combination: STE are willing victims of “realistic mathematics education” (RME) ideology. STE provide “contexts” and they apparently appreciate the interest. However, it really requires a study of ME and MER to get rid of the RME ideology and their unscientific narratives.
Let me mention my qualifications as expert for this topic and these questions, and observe that my books are online:
- I developed four books within Mathematica, a system for doing mathematics on the computer: Voting Theory for Democracy (2001), A Logic of Exceptions (2007), Conquest of the Plane (2011), and The Economics Pack. (since 1993). These books provide the coherence that the expert meeting is looking for, with text, formulas, graphs, tables, routines, programming (informatics) and interaction. (A missing element is assessment.) There is also the book Transport Science for Operations Management (2000) that has been supported by routines in Mathematica. It is likely the “not invented here” syndrome at Dutch universities that these books are not being used regularly in matricola. (There is also the breach of scientific integrity w.r.t. a “review” of COTP.) (The distinction between the popular vote for Clinton and the Electoral College for Trump might cause more attention for voting theory nowadays, but my expectation is that Dutch universities will continue to neglect VTFD.)
- I also discussed “Beating the software jungle”, included in Elegance with Substance (2009, 2015). This explains about the current chaos in software for education and what an effective and proper approach would be to resolve this. (The STEM researchers at this meeting might not have enough background in economics to understand the argument on market structure.)
- I clearly explained the failure by the Dutch organisers of the event, both SLO and the Freudenthal Head in the Clouds Realistic Mathematics Institute (FHCRMI), in their dealing with these issues before. Thus the organisers would know that inviting me would give scope for a discussion that goes to the heart of matters (and not beating about the bush again). Let me discuss this in the subsequent sections. (If these institutes would be scientific, then not-inviting me amounts to blocking me, since I would like to attend. Blocking me is an abuse of power, made possible by the current power void in mathematics education and its research, see here. But these institutes might also argue that they are not scientific.)
Freudenthal Head in the Clouds Realistic Mathematics Institute (FHCRMI)
I find myself repeating again. This isn’t good.
The actual argument is quite elaborate. When I would fall into the trap of using one-liners, then readers might think that I am being simplistic and that I (over-) generalise. Let me refer to Elegance with Substance, Chapter XIII and the note on p114.
A new phase in the discussion is the breach of research integrity by psychometricians at Leiden University. They actually expose the unscientific nature of RME / FHCRMI ideology but they don’t do so adequately.
Let me also refer to the abuse of so-called “21st century skills”. This label is deliberately used as a Trojan horse for re-introducing “realistic mathematics education” (RME) ideology. The true revolution is computer algebra. See here.
News on Michiel Doorman
A new element – on which I am not repeating myself – is that I have now collected my documentation about the unscientific and ideological performance by Michiel Doorman, one of the employees of FHCRMI on STEM and one of the key organisers of above event. Much of this documentation is in Dutch, but I provided an overview in English.
Two elements are relevant for STEM:
- Doorman maltreated the new algebraic approach of the derivative. Obviously, for physics education it is a key discovery that it is a false mathematical argument that limits would be required. For the derivative, it suffices to use algebra.
- Doorman promoted Java applets instead of computer algebra.
A google on Doorman also generated this diagram within the EU project of Mascil. I regard this as simsalabim, a phrase used in magic tricks, with flash and smoke that hide what is really happening. For example, there are “inquiring minds” and there is reference to a “collaborative classroom culture”, but these RME / FHCRMI “experts” clearly close their minds and use their elbows.
SLO – Dutch expertise center on curriculum
SLO would be the Dutch national expertise center on the curriculum. It started as a foundation and initiative by researchers, and it is gradually absorbed by government regulations, with work packages and subsidies. This particular QUANGO has no longer a transparant structure. Best would be a decent government body, with accountability, but at some distance of political decision making because of the scientific base. For mathematics education, each nation should have a national organisation with a key role for teachers and researchers, and this organisation would also supervise the curriculum. For Holland my suggestion is a Simon Stevin Institute, and it would give directions to SLO (instead of SLO telling teachers what to do).
The traditional approach in pedagogy looks at the triad of student, material and teacher. In this approach, the student features with both a personality and personal development. SLO however derives from the world of “education studies” that are at a distance of the traditional development of pedagogy. “Educational studies” tend to overlook the student. In the Van den Akker diagram about learning, students who would do the learning are not mentioned themselves. They are regarded as learning machines, and the personalities of students might only be considered from contacts w.r.t. “other students”, see the “spider diagram”, at the SLO “Europe: Mathematics and Science knowledge” and SECURE project page. Potentially SLO exports this spider diagram to other countries, and foreigners cannot check whether they listen to criticism. Dutch readers / viewers will benefit from this video interview with professor emeritus in traditional pedagogy Jan Dirk Imelman. (Interviewer Ad Verbrugge is an ideologue too, but Imelman makes it a useful interview.)
Letter to Dutch Parliament, September 27 2016, on Onderwijs2032
I wrote this letter in English to Dutch Parliament, about much of the same thing. As stated in the letter, I chose for the use of English because I wanted that OECD and CIDREE would be able to read the argumentation.
The minister of education is considering a transformation of Dutch education to “21st century skills” (“Onderwijs2032”). This would involve the abolition of traditional subjects (like physics or economics) and merging those into common labels (like nature or society). The idea is that education should increase understanding that surpasses the various subjects. This is also known as the “transfer” problem. However, the traditional approach is: one must first master a subject before one can surpass it. Thus Onderwijs2032 is created from rosy dreams.
What is crucial to know is that RME already belonged to that stream of rosy “21st century skills” way of thinking, and that it failed miserably. This is also why it is so curious that the Leiden psychometricians failed in reaching the proper analysis, even though they did show that RME claims are exaggerated. See this submission to the integrity board and this link on algebra as a troubling word.
Curiously, SLO has been supporting this Onderwijs2032 project. Though they oversee the curriculum, they did not notice that you need traditional algorithms in arithmetic in elementary school because you need those for algebra in secondary education.
News on Jos Tolboom
At SLO, Jos Tolboom (LinkedIn) is the other key organiser of the November event. He informs me that he read Elegance with Substance this last Summer and is impressed by its quality and relevance. I hope that he finds time to express this in a public statement that others can check (and that I would include on the EWS website). It is still possible that there are misunderstandings though, for we haven’t had a discussion on particulars. I also hope that he finds time to read COTP and then will protest against the abuse by Jeroen Spandaw in the journal Euclides in 2012.
Tolboom also alerted me to this CIDREE event and hinted at the possibility that he might invite me to attend. I am wondering now why he doesn’t. He gave me a reason but in my expert view not a convincing one, and lacking in respect for science. (Perhaps though he doesn’t regard SLO as a scientific organisation.)
I observed that Tolboom is giving video presentations on the new Dutch national exam on mathematics. A key element in the exam renewal are the “mathematical think-activities” (MTA). When I evaluated this MTA notion last month, I found it deficient. (1) MTA is severely confused w.r.t. didactics and testing, (2) MTA is a disguise of RME, (3) MTA is not proper mathematics (which would have a development towards deduction with definitions, theorem, proof). Another suggestion for Tolboom is to state a reply to this criticism. Hopefully, Holland finds a way to rewrite the national exam regulation.
The revolution is computer algebra
Let us return to the November event and the revolution of computer algebra. The problem with this revolution is that mathematicians are riding their hobby horses and creating chaos, e.g. by creating that software jungle. Perhaps there must be a jungle for a survival of the fittest, but in the past organised efforts like for Algol seem to have worked better.
Looking at the schedule, I don’t see a presentation that will explain that computer algebra forms the common core. Suggestions for a common core are “drawings” and “modeling”. You can check how the sessions of November 23 are geared to such a conclusion. Such a (prepared) inference would be deficient in understanding of didactics. Apparently Jos Tolboom didn’t read Elegance with Substance well enough. (Potentially, for mathematics, the “modeling” can be translated as MTA ?)
There will be a presentation on November 22nd by “Computer Based Maths” (CBM). This organisation was founded by Conrad Wolfram, and thus CBM is personally related to Wolfram Research Inc. (WRI), the makers of Mathematica, created by Stephen Wolfram. WRI apparently decided that it would not do to simply advertise the use of Mathematica. This might come across as a commercial enterprise. Conrad Wolfram set up CBM, and I suppose that they use more resources than only Mathematica (for example on assessment). See my earlier comments on computer algebra and Conrad, here.
Still, I find the situation needlessly complex and disinformative. The proper analysis is that computer algebra is the revolution, and that this provides the common core in education with the computer, not only for STEM but also for languages and the arts. There are other computer algebra implementations than Mathematica, but this remains the best system, consistently since at least 1993 when I started using it. We can allow for various implementations but as long as the same computer language is used for doing mathematics. The commercial venue by WRI is somewhat of a distraction. The creation of CBM is evidence of this too, and an admission by WRI too. It would be better that WRI is turned into a public service utility. The true question is what arguments would cause WRI to agree on this.
My impression is that it would help a great deal when the community of educators would agree that the common core can be found in mathematics itself, and, when the computer is used, in computer algebra. It is easier (also for CBM and WRI) to agree to help out when you are lauded than when your accomplishments are misunderstood and when you feel that you have to put in an effort to get recognition. If WRI would make Mathematica free for elementary and secondary education, then they can still earn their income on universities and research institutes as they are doing now.
When these CIDREE conference “experts” would arrive at the “STEM common core” of “modeling” then they do not understand didactics of mathematics and then their conference result is caused by an abuse of power by excluding a proper expert, duly signed, yours truly.