Jan van de Craats tortures kids with fractions

Listening to Just like river water in the spring


Professor Jan van de Craats (University of Amsterdam, now emeritus) is in breach of integrity of science. In an email to me in 2008 he confirms some of my criticisms on mathematics education, but since then he has been effectively neglecting this and refusing to discuss matters. He founded and now advises a foundation SGR for better education in arithmetic, and they employ dubious methods, including neglect and refusal to discuss and refer to criticism. Their criterion on “good” must also contain “keep a closed mind”.

SGR was founded in 2008 and has a Committee of Recommendation. Perhaps that list requires a date, or must be updated, since SGR now supports a particular commercial product, the education method Reken Zeker at a particular publisher, and at least two persons on the list have joined the national council on education that is supposed to be impartial (Maassen van den Brink en Van der Werf at Onderwijsraad).

Let me given an indication how Van de Craats’ breach of scientific integrity also causes bad mathematics education. Let me take two screenshots from two instruction videos from this SGR website.

Two screenshots of videos at SGR

The first video discusses a division of mixed numbers, and the second video discusses the conversion of a square meter into square decimeters. The screenshots are such that you don’t need to understand Dutch. The issues are clear enough. The didactic problem lies in the presentation. An invitation to you is:

Assignment: Spot the problem in didactics of mathematics.

If you cannot spot the problem, try to draw the inference: that you need to brush up on your awareness of didactics, and that you ought to read my book Elegance with Substance, (EWS) 2009, 2nd edition 2015 (with pdf online since 2009, so that you don’t have the excuse of a paywall either).

Thus, if you hate to read EWS, and hate to drag professor Van de Craats to the courts of justice and have him hanged or drawn & quartered, to remain with the subject of fractions, then you will be encouraged to really think and spot the didactic problem that arises from comparing these two images. Clicking on the screenshots will bring you to the videos in Dutch, but only these screenshots are relevant now. Please scroll the computer window in such a way that you don’t see the discussion of the solution below till you have formulated your solution or give up.

Division by two mixed numbers at SGR (Source: website SGR)

Division by two mixed numbers at SGR (Source: website SGR)

Conversion of a square meter to decimeters at SGR (Source: SGR website)

Conversion of a square meter to square decimeters at SGR (Source: SGR website)


The didactic problem with these two screenshots

In the second screenshot 1m or 1 m represents multiplication, or 1 × m, without writing the multiplication sign. In the first screenshot 2 + ⅓ is written as 2⅓ = 2 × ⅓ = ⅔.

One might hold that it is “1 m” with a space and “2⅓” without a space, so that the notations are well defined. This is difficult to maintain in handwriting, especially for kids. It still is needlessly confusing, and thus didactically wrong.

One might also hold that the form a b/c can be recognised as a “number next to a fraction” so that kids should be able to spot the fraction b/c, and then understand that the whole expression would mean a + b/c. This is dubious. If you agree that 10 dm = m so that dm = m / 10, then above example gives a m / 10, so that kids would need to understand this as a + m / 10. Is that really your reasoning ?

If your response now would be that dimensions like m and dm must be treated differently, so that dm = m / 10 is wrong and must be dm = 1/10 m, then you are changing mathematics and introducing a second arbritrary rule just for the reason that you don’t want to admit that you were wrong. It means that you already tortured kids and don’t mind to torture more if it helps to maintain your ego and investments in textbooks full of errors.

The notation for mixed numbers was invented at some time deep in the past, but without proper didactic considerations, and the only reason to maintain it is that mathematicians don’t mind torturing kids.

See Elegance with Substance (EWS) (2009, 2015). I discuss this in 2008, Van de Craats refers to it in his email of 2008, and it could have been solved in 2009, so that it could have been in all methods that were put on the market in 2010, not only Reken Zeker.

In his other own “remedial book” Van de Craats prefers 5/2 over 2½ with the stated reason “because 5/2 is easier to calculate with”, which is a misrepresentation of the real didactic issue.

PM. The first video stops at 49/66, which might be justified since it cannot be simplified anymore or written in mixed number format. The small supplementary problem is that this should be checked and mentioned, which is’t done. The algorithm thus isn’t fully discussed. This is not the key issue here. It just surprises me since SGR puts such an emphasis on algorithms.

Van de Craats and Wilbrink on Pierre van Hiele

Van de Craats also refuses to look into and to refer to criticism w.r.t. the manner how psychologist Ben Wilbrink abuses the work by Pierre van Hiele, even though he has an extensive section with links to the site of Wilbrink. See my discussion of Van de Craats’ breach again.

One of Van Hiele’s suggestion was that fractions can be abolished. See the discussion here. Thus, SGR spends a lot of time on teaching kids fractions that can actually be abolished. Perhaps kids at some stage, when they understand the inverse of multiplication, must be instructed that old-fashioned people write mixed numbers in another fashion. But this is a short explanation. This would not obstruct the whole learning process of mastering arithmetic.


We spotted another case of the elementary sick Dutch mindset that requires a decent boycott.

In this case it is mathematics again. The key issue is that mathematicians are trained for abstract thought and not for empirical science. This is world problem.

The combination of this Dutch mindset with mathematics is especially disastrous.

The appeal to boycott Holland is targeted at the censorship of economic science since 1990 by the directorate of the Dutch Central Planning bureau. This example of the Dutch mindset confirms the analysis on the need of a boycott.

PM. For Dutch readers:

This is a petition on having a parliamentary enquiry into the censorship of economic science.

This is a petition on having a parliamentary enquiry into mathematics education.

How SGR teaches children fractions (Source: wikimedia commons on Dieric Bouts (1415-1475))

The medieval method how Van de Graats and SGR teach children fractions (Source: wikimedia commons on Dieric Bouts (1415-1475))


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