# Integrity of science in Dutch research in didactics of mathematics

I am sorry to report that Holland also fails on the integrity of science in the research on the didactics & education of mathematics. This is my letter (in Dutch) to the Scientific Integrity body LOWI of the Dutch Royal Academy of Sciences KNAW.

Earlier, in my book *Elegance with Substance *(2009), I made the empirical observation that mathematicians are trained for abstraction while education is an empirical issue. The training of mathematicians to become teachers of mathematics apparently can often not undo what has been trained for before. This basically means that many have lost the ability to *observe*. Math teachers tend to solve their cognitive dissonance by adhering to “mathematical tradition” that however is not very didactic, and that in fact collects the didactic debris of past centuries.

A key example here in Holland is the difference between Hans Freudenthal as the abstract topologist and Pierre van Hiele who as a mathematician and actual teacher however kept his ability to observe. We need only look at the debris in math textbooks to observe that the majority of math teachers aren’t like Van Hiele. See *Elegance with Substance *if you cannot identify the debris yourself.

An international example on statistics is the difference between Fisher and Gosset on “statistical significance”. Mathematicians tend to consider mathematical statistics only, and are little aware of empirical significance. Math educators who nowadays use statistics might fall victim to ‘garbage in, garbage out’ but nevertheless be praised as ’empirical’.

Now in 2014 that empirical observation comes with a sting. When abstract thinking mathematicians make statements about the empirical reality of didactics & education, they actually make statements out of their province, about something they haven’t studied: *which is a breach of research integrity.* This especially holds when they have been warned for this, say by my 2009 book (listed in the AMS *Book List*, Notices Vol 58, No 11, p1474), or perhaps even directly by me.

In Holland there now is the case of internationally known Jan Karel Lenstra, who did work in operations research, (linear) programming, scheduling and the traveling sales person, who was selected in 2009-2010 by theoretical physicist and KNAW President Robbert Dijkgraaf to chair a KNAW “Committee on Mathematics in Primary Education”. The Dutch complaint is that children don’t learn arithmetic so well anymore, e.g. aren’t trained on long division as a sure method. It often happens that a committee is chaired by a person who doesn’t know much about the subject beforehand, but then that person tends to be aware of this, and is willing to learn. In the case of Lenstra, he apparently thought that he knew enough about “Mathematics in Primary Education” so that he also understood the didactics & education itself.

Hans Freudenthal had a huge impact on arithmetic in Dutch primary education. Lenstra observes about the Freudenthal madness:

“The core is that we must get more evidence-based research [education ?]. The ‘realistic arithmetic’ has been adopted without the empirical evidence to make it obvious. And also the PABO [training of elementary school teachers] has been constituted on the base of beliefs instead of scientific research.” (my translation, comments in brackets)(Akademie Nieuws July 2011 p5)

But Freudenthal and his followers did claim that ‘realistic mathematics’ was scientifically warranted and based upon evidence. Thus professor in mathematics Lenstra observes a fraud with respect to empirical research, but doesn’t do anything about it. He doesn’t call for a repeal and annulment of earlier “research” that claimed empirical relevance but without such base. He is quite happy that his fellow abstract thinking mathematician Freudenthal invented a theory and let others suffer the consequences. Lenstra is another abstract thinking mathematician who now thinks that he has solved a problem and then lets others suffer the consequence – like the international community that still considers Freudenthal’s work “research”.

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. 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.)

One might say that Lenstra’s 2009 KNAW Report and recent June 30 2014 KNAW conference presentation (my report in Dutch) aren’t quite research themselves but rather evaluations on educational policy. It may well be that Lenstra’s texts here don’t register under scientific integrity in a strict legal sense, even though Parliament regards it as scientifically warranted. In another respect, Lenstra’s case is just an example, and it is a collective problem that abstract thinking mathematicians expound about empirical issues that they haven’t studied. Hence, my letter to KNAW-LOWI suggests a general exploration into the issue, so that the scientific community grows aware of the issue. Hopefully the specific issues on Freudenthal and his Institute are taken along, as explained here.

PM 1.

Above mentioning of Abstraction vs Empirics might cause the idea that those would be opposite, but these are rather separate axes. We might score the different professional groups on the study hours in each category, with mean and dispersion. I mention two example individuals for lack of an accepted term like “empirical mathematical statistics”. Since teachers teach they aren’t in research like other professions.

PM 2.

This weblog concentrates on failure on integrity within Dutch economic science, with the case at the Dutch Central Planning Bureau (CPB) concerning economic co-ordination and the example of unemployment. That censored analysis is relevant for the current crisis in the European Union, and for economic recovery in the United States, and for economic policy in the “emerging markets” too. My advice is to boycott Holland till the censorship of economic science here is resolved. KNAW-LOWI cannot officially tackle the case since its mandate concerns universities while the CPB falls directly under the national government.

But now there is a breach in integrity in research in math education as well. I have two academic degrees, one in econometrics and one in teaching mathematics, and it is disappointing to observe that my degrees open up to vista’s of non-integrity. It might soon become a personal thing. But, as Art Buchwald would advise us: while there is a whole country to blame we might as well take a look at the facts. And boycott that country till they get their act together.

The world chooses to use English rather than Dutch or Latin, and hence we fall in the Dutch language sink again. As my letter is in Dutch, we might need to look to whom in Belgium, South Africa or Suriname still understands the gibberish. I presume that the people in New York (“New Amsterdam”, if they only knew) would need a certified translator. There might be some expats living in Holland who have learned some Dutch but I am afraid that some issues are getting complex, and then even many Dutch people would not be able to follow things. Foreigners would have even more difficulty in understanding local conditions. Hence I am quite hesitant to translate that letter.

For comparison on KNAW-LOWI, we may look at the US bureau for research in education, IES, and the office of research integrity ORI of public health, and then also the ethical codes of AMS and MAA. There are a lot of ethics to look into.

But let us not forget about education itself, and thus let me also alert you to this issue of CF with *Forty Years of Radical Constructivism in Educational Research* and hope that they put students before method.