Prof. L. Verschaffel e.a. about Raf Feys Math War againt formalistic New Math and against constructivist & contextual Math Education in Searching for Alternatives for New Math in Belgian Primary Schools
Mijn lange en geslaagde strijd tegen zowel het extreem van de formalistische & hemelse Moderne Wiskunde
als tegen het andere extreem van de constructivistische, contextuele en aardse wiskunde
kwam ter sprake op een recent internationaal wiskundecongres in 2018.
In een publicatie met de verslagen wordt hier uitvoerig naar verwezen in een bijdrage van de Leuvense professoren Lieven Verschaffel, Dirk De Bock & Wim Van Dooren : Searching for Alternatives for New Math in Belgian Primary Schools. (In: International Reflections on the Netherlands Didactics of Mathematics Marja van den Heuvel-Panhuizen Editor. Ik citeer de belangrijkste passages
1. Critique on New Math: Raf Feys (1973-1998)
Although New Math was strongly criticised in international fora since the early 1970s (see,e.g., Kline, 1973),and in the Netherlands Hans Freudenthal (19051990) and his team had started the development of a realistic alternative for the teaching and learning of mathematics at the primary level (the Wiskobas project, see, e.g., Treffers,1993), the Belgian mathematics education community remained remarkably silent.
For about twenty years, ofﬁcial curricula in Belgium would follow faithfully the New Math or structural approach ( lager onderwijs: 1976-1998)
Obviously,several mathematics educators and mathematics teachers were sceptical about this approach, but criticisms were rarely voiced in public.
In 1982, this silence was suddenly broken by the Flemish pedagogue Raf Feys. In the Onderwijskrant nr. 24 an innovation-minded, independent and pluralistic journal on education, Feys wrote a virulent pamphlet (! Lees: gestoffeerde analyse van 48 paginas) in which he ﬁrmly criticised the starting points of New Math and the way it was introduced and dictated at the primary level (Feys,1982, Moderne wiskunde: een vlag op een modderschuit=modern mathematics: a ﬂag on a mud barge, 48 p.)
In his close contacts with schools, Feys did not see the appearance of a fascinating world, but artiﬁcial results in a fake reality, and also little enthusiasm in children, but more disgust, disorientation and desperation (Feys, 1982, p. 3).
He described New Math as upper-level mathematics which was in the ﬁrst place ballast, i.e. an enormous extension of the programs, concepts that were misunderstood,mechanical learning and pedantry(ibid.,p.6).
Moreover, it created an obstacle for the acquisition of traditional mathematics, which he described as mathematical-intuitive and practice-oriented lower-level mathematics.
He further stated that three-quarters of the reform involved the introduction of new terms and notations [
], a formal language primary-school teachers are unable to cope with and which complicated the application of mathematics (ibid., p. 8).
The pamphlet ended with a call for a large-scale counteraction, addressed to teachers, parents, inspectors with free hands, parents associations, labor movements, teacher training institutes, universities, centres for psychological, medical and social guidance (ibid., p. 37). In his pamphlet, Feys not only criticised New Math, he also suggested how mathematics education at the primary level should evolve.
Feys (1982, p. 37) wrote: When evaluating the renewed mathematics education, we should not only compare with the old mathematics, but also with alternatives like the ones that are, e.g., developed in the Netherlands by Wiskobas. We need the courage to examine the alternatives thoroughly. [
] We opt for an alternative reform along the lines of the Wiskobas approach of the IOWO, complemented, however, with a strong emphasis on the social-societal aspect of mathematical world orientation.
(We pleitten in 1982 en de erop volgende jaren vooral voor een herwaardering van het klassiek rekenonderwijs dat o.i. al lang zijn deugdelijkheid bewezen had aangevuld met enkele nieuwe elementen, o.m. i.v.m. ruimtelijke oriëntatie.)
Although Feys pamphlet enjoyed some resonance in the Flemish press and the author received some expressions of support by academics (e.g.,by Leen Streeﬂand, staff member of the IOWO, and by Lieven Verschaffel, whose letters were included in a subsequent issue of the Onderwijskrant), his point of view was not generally recognised and appreciated. Those responsible for primary mathematics education wrapped themselves in silence or disqualiﬁed Feys analysis as inﬂammatory language of irresponsible doomsayers (see,e.g.,Verschaffel, 2002). They argued that the innovation of mathematics education was a fact and that we, also asparents, ould better express our belief in the revised approach (quote from an interview of a member of the programme committee of the Catholic network as reported by Heyerick,1982,p.5).
The discussion had clearly been launched, but the tide had not yet turned! (O.i. was het tij wel gekeerd: na 1982 verschenen er geen bijdragen meer over de vele zegeningen van de moderne wiskunde.
An important follow-up event was the colloquium 'What Kind of Mathematics for 515' Year Olds? organised in 1983 by the Foundation Lodewijk de Raet, a Flemish socio-cultural organisation with apluralist scope (Stichting-Lodewijkde Raet,1983: een colloquium dat ik als lid van de stuurgroep onderwijs zelf had voorgesteld en mede ingericht en waarin ik ook als spreker optrad.)
At that occasion, proponents and opponentsof New Math defended their positions. A strong delegation from the Netherlands (in casu from Utrecht) participated, including Aad Goddijn and Hans Freudenthal, who not only gave a lecture, but also ﬁrmly intervened in the discussion afterwards, with signiﬁcant endorsement addressed to the opponents of New Math.
Obviously, the colloquium elicited opposite points of views, but also strong dissatisfaction with the current situation (no one wants to continue this way; Stichting-Lodewijk de Raet,1983, p.29
At the end of the colloquium, again a call for action was launched, but there response to this call was minimal. In the subsequent years,no signiﬁcant changes in the Flemish mathematics educational landscape occurred .
Although interest in the Instituut voor de Ontwikkeling van het Wiskunde Onderwijs (Institute for the Development of Mathematics Education).
(Commentaar: aan tafel over de middag met prof. Hans Freudenthal maakte ik hem wel toen al duidelijk dat ik de Wiskobas-standpunten van de periode 1978-2004) wel interessant vond, maar dat m.i. de recente ontwikkeling binnen de groep Freudenthal te weinig belang hechtte aan de klassieke wiskunde, de wiskunde als cultuurproduct.)
2 Searching for Alternatives for New Math in Belgian
& kritiek van Feys op constructivistische en contextuele wiskunde à la Freudenthal Instituut
Dutch alternative did not disappear and the RME-approach (Realistic Math Education) received strong consideration in academic circles (Verschaffel,1987) as well as insome so-called alternative schools (based, for example, on the Freinet pedagogy), ofﬁcial curricula were not adjusted.
But since the late 1980s, the RME model (van het Freudenthal Institut) was not only praised in Flanders, but critical questions and doubts about the value and feasibility of that model were also raised, and, strikingly enough.
It was again Raf Feys who played a pivotal role in these criticisms. Feys critique focused, among other things,
on the neglect of the mechanistic aspects of learning,
on the lack of guided construction of knowledge,
on the excessive freedom that is given to students to construct their own solution methods,
on the limited attention for the process of de-contextualising,
and on insufﬁcient recognition of the value of mathematics as a cultural product (Feys, 1998).
When comparing new RME methods with traditional Flemish (pre-New Math) methods, he esteemed the latter as superior to the ﬁrst (Feys, 1989, 1993).
Although not all mathematics educators in Flanders agreed with Feyss criticisms, it is likely that his judgments have contributed to the fact that particularly the more extreme elements and aspects of the RMEvision were not implemented. Second and complementary to the ﬁrst element, comparative international research of that period revealed the very high quality of Flemish mathematics education.
Actually, Flanders outperformed the Netherlands, not only inlarge-scale international studiessuch as TIMSSc(Mulliscc Searching for Alternatives for New Math in Belgian
55et al., 2000), but also in some small-scale comparative studies only involving the Netherlands and Flanders (see, e.g., Luyten, 2000; Torbeyns et al., 2000). These results not only increased the self-conﬁdence of Flemish mathematics educators,but also strengthened their hesitation to implement a more radical version of the Dutch RME model.
The negative reaction with respect to the value of the RME model, initiated in Flanders by Raf Feys in the late 1980s, is akin to the position o fone of the parties in the Math Wars that emerged around the same time in the United States. These Math Wars refer to a vehement debate held between reformers and traditionalists about mathematics education.
This debate was triggered by the publication of the(reform-minded) Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) and the widespread adoption of a new generation of mathematics curricula inspired by these Standards. The vision of the American Standards had much in common with the RME philosophy with, for example, much attention for self-discovery learning via rich interactions between teachers and students and between the students themselves, mathematical connections between the different mathematical domains, continuous vertical learning trajectories (from kindergarten to high school), multiple and ﬂexible problem representations and solutionstrategies, a meaningful integration of new technologies and a plea to pay less attention to paper-and-pencil calculations and isolated skills.
Especially from the side of the professional mathematicians, ﬁerce criticism and even a real counter movement was initiated, blaming the Standards for dumping, without good reason, a number of traditional and tested values of the past, such as the memorisation of facts, the automation of skills and learning through direct classroominstruction. The opposite views between reform-basedmathematics educators (of the NCTM) and traditionalists were the basis of the Math Wars in the United States (the further development of which is beyond the scope of this chapter, but which has been discussed by, e.g., Klein, 2007).
The Math War crossed the ocean, and in the Netherlands there also was a heated debate about the quality of mathematics education and its didactical approaches. The debate polarised between two groups that both partly relied on the (interpretation of) results of the Cito-studies of the PPON5 (see, e.g.,cJanssen, Vander Schoot, & Hemker, 2005) used to assess mathematics achievements of primary students in the Netherlands (Ros,2009).
The Dutch Math Wars were launched by Jan van deCraats, mathematician at the University of Amsterdam and co-founder of the action group Stichting Goed Rekenonderwijs (Foundation for good arithmetic education). Vande Craats (2007) stated that children in the Netherlands are no longer able to calculate, that the RME approach created chaos wherever good mathematics needs calm and abstraction, and that standard algorithms (such as long division) and automatismswhich are, according to the traditionalists, especially helpful for children with medium and weak abilitieshave totally disappeared from arithmetic education in the Netherlands.
Commentaar: Vande Craats prees mijn tijdige kritische analyse van de contextuele en contextuele aanpak van het Freudenhtal Instituut en het leerplan wiskunde lager (katholiek) onderwijs waarvan ik een van de opstellers was en waarin geenszins gepleit wordt voor de Freudenthal-aanpak. Intussen leidde de constructivistische aanpak in tal van landen als Canada, Schotland,
tot een sterke niveaudaling.
Verschaffel en Co slaagden er wel in de constructivistische aanpak te laten doordringen in het leerplan wiskunde eerste graad-1997 secundair onderwijs. Het leidde tot veel kritiek vanwege de leerkrachten en tot een niveaudaling.