Over the Christmas holidays 2000/2001 I was in the Netherlands and visited the Freudenthal Institute, the home place of Realistic Mathematics Education (RME). This report, from Jan 2001 with minor stylistic changes since, was originally written for my colleagues at the Courant Institute. Some later addenda are marked by square brackets in the main text [...]; see also the bottom of the page. A Dutch translation of the report is here. --BJB

See the Education Page of Bas Braams - Links, Articles, Essays, and Opinions on K-12 Education - for related matter.

Dear Colleagues:

The Freudenthal Institute (FI) in Utrecht, the Netherlands, has been mentioned in connection with the constructivist plans for education reform in our District 2. I visited them recently. This is an informal report. I talked with Marja van den Heuvel, Koeno Gravemeijer, Truus Dekker, and Henk van der Kooij. I also brought back some publications and reports, including dissertations of van den Heuvel, Gravemeijer, and de Lange. (Professor Jan de Lange is Director of the institute.)

The FI's website is http://www.fi.uu.nl. They are affiliated with the Mathematics Department of the State University at Utrecht, but they are geographically separate and have independent funding. Their work covers K-12 mathematics education, with an emphasis on primary school and the lower branches of secondary education.

The educational philosophy of the Freudenthal Institute is Realistic Mathematics Education (RME). Part of this philosophy is to emphasize mathematical problems posed as small realistic stories, a step beyond word problems. Another part is "guided reinvention"; the pupils are to re-invent mathematics under the well-considered guidance of the teacher. They also advocate group learning processes in heterogeneous environments over individualized instruction (the latter has, through Montessori, a stronger tradition in the Netherlands than here). In details it is a developing philosophy -- I think they were more radical in the 1980's than now, but this impression has only a flimsy basis in conversations about the philosophy with respect to testing and assessment. Probably I should read de Lange's 1987 dissertation more carefully.

The FI's curriculum development has been very influential at the primary school level during the past 15 years. A report of the independent dutch educational testing agency (CITO) on the status of primary education (PPON-1997) remarks that almost all schools now use textbook material based on RME, when 10 years earlier this was still a minority. At the level of the secondary school education the Freudenthal Institute is influential, but not as much as for the primary schools. In the implementation of the RME principles at grade school level I think I see an appreciation for mental arithmetic, a depreciation of pencil and paper arithmetic, an appreciation of electronic calculators, an interest in practical, pictorial geometry, and much interest in the ability of students to verbalize their thinking for each other's benefit.

There are plenty of things that struck me in the discussions and in reading their web site and various reports, not all positive.

The principles of realistic mathematics education are often expounded in the work of the Freudenthal Institute, but I don't recognize that the effectiveness is backed up by much research. On the contrary, there appears to be no real interest in the development of careful studies comparing the outcome of different educational strategies. Gravemeijer explained to me that they have a philosophy, RME, and their research is focussed on support for curriculum development on that basis. So they will try out various elements of some curricular unit, observe classroom practice, and see how the classroom processes match the desires of RME theory; this then guides the further development and refinement of the curricular unit.

I was quite struck by this acceptance of Realistic Mathematics
Education as a revealed philosophy. The one review that I know of
occurs in the PPON-1997 report of CITO. That review, on my first
reading, appears to be piggy-backed onto the regular end of school
tests administered by CITO; the study compares performance of schools
using different textbooks, without other correlations, and finds on
one hand that schools that use RME methods do better than other
schools, and on the other hand that the general performance has
decreased as RME methods became more widely used. I found a reaction
by Professor Treffers of the Freudenthal Institute to these
conflicting findings
[http://ublad.warande.uu.nl/ubladen/31/11/11treffers.html] and it is
in essence that he shrugs his shoulders. Methodologically the
research does not seem to amount to much anyway, so I sympathise with
his reaction. [**Addendum January 2003**: see the bottom of the
page for a correction and further information regarding the PPON
study.]

With regard to the New York District 2 projects and constructivist teaching the Freudenthal Institute seems to be on the border. They participate in Catherine Fosnot's "Mathematics in the City" project but not in the more heavily constructivist "Reconceptualizing Mathematics Teaching ..." thing that has been the object of most attention here. The RME pillar of guided reinvention becomes radical constructivism in the limit that the guidance goes to zero, but the FI does stay well away from that fringe. On the other hand, they don't volunteer any misgivings about the constructivist side to Catherine Fosnot's projects.

The Freudenthal Institute is participating in the development of an alternative to TIMSS, which is seen as boring and lacking in realism. The alternative is the PISA project, sponsored by the OECD. The project is described in the FI web pages and under http://www.pisa.oecd.org. International tests are to take place in a three-year cycle, and the first took place in 2000. Look for a report in 2001.

The Freudenthal Institute is also a major partner in the Wisconsin "Mathematics in Context" project. I did not pay attention to this work. See the FI web pages.

Bas

--

Bastiaan J. Braams
- braams@math.nyu.edu

Courant Institute, New York University

251 Mercer Street, New York, NY 10012-1185

Additional (later) remarks:

I refer to my note About the Mathematics in PISA for related comments. Professor Jan de Lange, Director of the Freudenthal Institute, was head of the mathematics experts group for PISA, and I believe that the math component of the PISA test offers a revealing view of the philosophy of the reform mathematics movement with regard to mathematics content, assessment, and mathematics education research.

For further comments related to the collaboration between the Freudenthal Institute and New York's Community School District 2 see my Letter to the NYC Board of Education and my note on Shelley Harwayne and Mathematics.

With regard to the PPON study of 1997 I received additional information and corrections from the project leader Dr. Frank van der Schoot (email of Jan 15, 2003). His comments, translated and reduced in length, follow.

The PPON is a project similar to NAEP in the United States. For the mathematical domain more than 20 topics are distinguished, and for each topic a test is created that is given to a sample of pupils at the end of primary education (and there are similar tests halfway in primary education and for special populations). This provides a very detailed measurement of pupil skills. The tests are assigned to pupils using matrix sampling, with each pupil tested in three topics. The mathematics PPON took place in 1987, 1992, and 197, and results are compared over the years.

The study also obtains information regarding the pupils' language background, age, gender; the population background of the school, and the curricular method used in the school. The statistical analysis then looks at the effect of any variable while controlling for the effects of all the other variables.

Concerning the effect of the year (1987, 1992, or 1997) this implies that in the analysis it is controlled for other effects, including the shift in the choice of curricular methods. In the earlier two years we classified the methods broadly: traditional method, realistic method, and a method "Operatoir Rekenen" that was popular at the time and was said to occupy an intermediate position. In the analyses Operatoir Rekenen quite often seemed best.

In the most recent study we decided to compare specific curricula. From this we learned, for example, that the effect sizes within the category of realistic methods were larger than the effect size between different categories of methods. So there certainly is not a definite positive effect of realistic methods. However, we did learn that two (at the time) relatively new methods (Pluspunt en Wereld in Getallen (revised)) were quite often among the better ones.

That was my translated and shortened version of a description by Frank van der Schoot. It is seen that my description of PPON in the main text of 2001 is incorrect in several points and to say that methodologically the research does not amount to much is unfair: the study is not piggy-backed onto the regular end of school CITO test, and a large number of correlations is considered in the analysis. At the same time it is apparent that this PPON study does not give much guidance to the relative quality of different curricula. A problem with PPON (as with NAEP in the United States) is that one does not have data on the development of individual test subjects over multiple years, so that it is not possible to perform value added analysis to investigate, for example, the effect of the different curricula. If a value added evaluation were possible then the effect of different curricula or other influences might be visible more clearly.

References for the PPON study (in Dutch): PPON in General and Evaluation of the third PPON mathematics study (1997).