Some remarks w.r.t. Henk Boonstra's weblog,  elementary school and math & arithmetic

Thomas Colignatus
March 16 2016


Last week I discovered the books and weblog by Henk Boonstra, amply qualified for primary education. The following collects some of my (preliminary) comments. Part of my comments will be in English, part in Dutch. Boonstra also writes in French.

As a teacher of mathematics I am not qualified for primary education. I have noticed that professors of mathematics (Hans Freudenthal, Jan van de Craats) have been meddling in primary and secondary education while they were not qualified for these. I am not qualified to judge their views on primary education (other than on consistency and common sense), but the result for secondary education is rather disastrous. The reader thus is warned to evaluate my comments with care. Dutch readers are alerted to my Letter to Parliament of last week on the issue of education in mathematics and arithmetic. More comments in Dutch are here.


James Heckman has pointed to the importance of investment in early childhood. This message has arrived at the US White House (2014), see "The economics of early childhod investment". Conceivably, investment might be done with an increase in scale and scope of traditional education. At issue is that there can also be a different kind of investment.

Theory used to be developed at university, trickle down to highschool, and trickle further down to elementary school. While trickling down, the learning material was refitted as well. Anno 2016, there are some reasons why the process is in the reverse:

These developments aren't managed so well. Economic theory explains the vested interests and institutional inertia. A model with demand and supply is that of monopsony, with one powerful buyer (the government) and many suppliers. Subsequently, one can look at models of government and the behaviour of suppliers. See my analysis on the power void.

Boonstra's qualifications

Boonstra was born in Leeuwarden, 1939. He started as elementary school teacher in Leidschendam and Haarlem, and later graduated in Amsterdam in orthopedagogy. His official degrees are the "onderwijzersakte", "hoofdakte", "MO A & B", and university degree (MA, i.e. doctorandus and not doctor). He taught at college level for six years. Gopher: "Drs. Henk Boonstra is orthopedagoog, orthodidacticus en Gzpsycholoog. Hij was oorspronkelijk onderwijzer en werkte later aan het Medisch Opvoedkundig Bureau te Leiden, aan het Pedologisch Instituut/CED te Rotterdam en doceerde verschillende jaren aan de Nutsacademie te Rotterdam in de Algemene Orthopedagogiek en de Orthodidactiek."

Some books are at regular publishers. P.O.D. books are at and

Liberté, Egalité, Fraternité

I agree with HB 2010-01-26 that the variety of children requires a variety of education, whence elementary school must show the same variety as highschool.

It is fine that children learn at early age to deal with all variety in society, but this doesn't mean that their development must be forced. Boonstra's book "Geef me de (leer)tijd." 1990 is mentioned in ERIC and this German database. In Item / Response theory (IRT) or Elo rating (by wikipedia not recognised as the same mathematical model) or Csikszentmihalyi model: high competence and low challence causes boredom, low competence and high challenge causes stress, and a match causes "flow".

I agree with Boonstra that current educators who defend the current system, are inconsistent. The Dutch term for the current no-variety model is "leerstofjaarklassensysteem", I have not found the English translation yet (see this wiki).

I have not read Boonstra's book on continuous development (Dutch) (without jumping a "year" or having to redo one), but the approach merits attention by educators.

My own comments:

Benjamin Bloom and conceptual errors versus mistakes

I agree with HB 2013-04-05 that there is a crucial distinction:

I agree:

Prevention of remedial teaching (by using this expertise from the start)

The current system has a "normal" course, and subsequently for kids who fail a "remedial" course.

I agree with Boonstra (e.g. 2016-01-17 on Marcel Rufo), who proposes to move as much from the "remedial" course into the "normal" course. Why not offer the best available right from the start ? I don't have the background like Boonstra has:

Notation and pronunciation of numbers

Boonstra 2016-02-19 refers to his "De rekenfout nader beschouwd" (1980), and points to the issue of notation and pronunciation of numbers.

I agree with this. My comment: I find his experience as elementary school teacher a useful confirmation of my own analysis on pronunciation. See "A child wants nice and no mean numbers" (2015) and the references on that page. For pronunciation in English, French, German and Danish, see this proposal for an international standard (in research).

PM. Boonstra points to combinations of errors. Suppose that there was a series of sums with additions, and suddenly there is the question 47 - 9 = ? The student writes the "answer" 65. Apparently, the answer 47 + 9 = 56 was intended, but denoted in the wrong order. One issue is "perseverance" (not seeing the switch in type of question), another issue is the notation of numbers. Testers must see the two errors. Boonstra's points are:

"Reken Zeker" for arithmetic

Boonstra 2016-02-09 started some weblogs on the arithmetic textbook series "Reken Zeker" (2010).

I agree with Boonstra with his criticism of lack of documentation and scientific evidence for this method and its claims. See my criticism of Van de Craats & Wilbrink.

I agree with Boonstra that it may be accepted as an empirical finding from the practice of teaching, that pupils should learn (at least) one method that always generates a certain answer. This is one of the principles of Van de Craats.

Boonstra also observes that the documentation in 2016 does not provide a description of findings since 2010.

My comments:

At this time of writing, I haven't looked at the whole series by Boonstra on "Reken Zeker".