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:
Specialisation is determined by the size of the market: Universities have their professors and Ph.D. students for primary education and pedagogy. My suggestion is that schools adopt the model of academic hospitals, with an integration of practice, research, and training. There is a special position for mathematics, since this deals with learning about abstraction. But this doesn't require professors of mathematics, who do research at the frontiers of mathematics.
ICT: Modern technology enters all levels of education, but what enters primary education has consequences for the rest. There is much confusion about "21st century skills", see here for a better perspective.
Mathematics: My books "Elegance with Substance" (EWS) (2009, 2015) and "A child wants nice and no mean numbers" (CWNN) (2015) clarify that mathematicians have been self-centered for say 5000 years, focusing on their own abstract understanding and neglecting the empirical issues of education and didactics. For the "trickling down" they only accepted the top-down process, and if kids did not get it, then supposedly these kids did not understand mathematics and better go back to the farm. Truth is that much of mathematics is rather crooked, and when kids don't easily get it, then they are right, and professors have to grow aware about the crookedness. Mathematics professors better stop meddling, see my comment in CWNN w.r.t. professor Hung-Hsi Wu (Berkeley) e.g. on fractions.
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 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 Gopher.nl and Mijnbestseller.nl.
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:
Like in American highschool, there can still be one building and one football team and one ceralbus, but classes can be different. In Holland, highschools are officially more segregated than in the USA. But in the USA segregation can arise via districts, with finance based upon property taxes. (In 1972-1973 I already debated on this topic in the US National Forensic League.)
Overall, the key decision is to allow more variety, and it is up to research to find out what works best.
I agree with HB 2013-04-05 that there is a crucial distinction:
conceptual error require a repeat or better explanation (retraining),
a mistake requires focus on accuracy, patience and motivation (e.g. redoing the question in a different fashion, so that there is a reward in finding the correction yourself).
that this distinction likely is not applied enough. The advice for retraining is given too often, with negative effect on motivation. Boonstra mentions: Benjamin Bloom (1913-1999), SRT, CITO, the Dutch textbook on arithmetic "Reken Zeker". (Unfortunately Bloom responded on Boonstra's message that this was a welcome addition instead of, acknowledging what it is: a fundamental critique & correction. There must have been others with the critique.)
that the score of 80% good and 20% wrong (for the very same type of question) may very well be a useful indicator for mere mistakes. Boonstra explains that there is a logical reason for this classification: someone without conceptual error is highly unlikely to be wrong for 80% on the same type of question. However, I tend to be more cautious: these numbers might require testing for particular cases. (Of course the 80% vs 20% split is also useful to test that these are indeed the same type of question.)
that the difference beween a score of 70% and 80% for different questions, say in the grade point average (GPA), may still indicate a key difference between motivation rather than conceptual understanding. This should also affect the focus of teaching (on motivation rather than retraining).
that answers must be split up into steps to check the difference. Boonstra: it is a common error by CITO that it scores answers only on good / wrong, while disregarding the steps. There must have been others with the critique. Perhaps an update on Boonstra: a "good" answer may still be arrived at by wrong methods, see this discussion (in Dutch) on "realistic mathematics education" (RME) and "traditional mathematics education" (TME). It is a key question for the tester what is being tested here, see the issue of validity.
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:
Boonstra refers to Caplan 1966 with distinction in prevention levels 1, 2, and 3.
Boonstra holds that "retardation" only exists in the mind of the testers, who use cross-section percentiles, rather than longitudinal advancement. His point isn't so much the differences between pupils, but rather what conclusion is attached to those differences: retraining (explaining theory again) or practice (what is already understood).
Boonstra suggests that individual advancement need not be forced with retraining (perhaps may require just more time in regular education or practice).
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:
Notation and pronunciation of numbers are important, and for many not learnt easily.
Teachers must be aware of this, monitor, and provide proper response.
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.
In the criticism of "Reken Zeker" and Van de Craats, this point of "one method" is not at issue. At issue is the overall lack of documentation and interest in evidence. For example, see how Van de Craats tortures kids with fractions.
A part of the scientific documentation must be an explanation how "realistic mathematics education" (RME) managed to go against this empirical finding from the practice of teaching, and ordained pupils to discover their own methods.
Holland currently has un unscientific and morally unacceptable experiment on children w.r.t. arithmetic, see here in Dutch.
At this time of writing, I haven't looked at the whole series by Boonstra on "Reken Zeker".