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Topic: Symposium - Growth and Success of "mathe 2000"
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GS Chandy

Posts: 8,307
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: Symposium - Growth and Success of "mathe 2000"
Posted: Oct 24, 2012 9:42 AM
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Jerry Becker posted Oct 22, 2012 7:13 PM (GSC's remarks precede and interspersed):

Thank you, Jerry Becker, for posting this fascinating piece. While awaiting most keenly the usual blasts about "PUT THE EDUCATION MAFIA IN JAIL!", "CLOSE DOWN THE DEPARTMENT OF EDUCATION!" and "BLOW UP THE SCHOOLS OF EDUCATION!" from the usual suspects, I provide my initial reactions interspersed.
> Hello --
> Below and attached is the talk given by Lieven
> Verschaffel on the occasion of the 25th
> anniversary of the elementary mathematics
> curriculum project "mathe 2000" at Dortmund
> University in Germany. During the turbulent
> international context of the last 25 years, Prof.
> Erich Wittmann, Prof. Gerhard Müller and the
> other members of the "Mathe 2000" project [see
> ersonen.html

Have not yet looked at this description of "Mathe2000" {with apologies to Robert Hansen (RH)}, but I do plan to do this in due course.
> ] have worked at the development of their own
> approach to elementary school mathematics
> education, in a way that may be considered quite
> unique and exemplary, for three reasons that are
> briefly elaborated below under the headings: A
> view of elementary school mathematics, the
> methodological approach, and the role of the
> teacher. The paper is a tribute to the project
> given by Lieven Vershaffel of the Center for
> Instructional Psychology and Technology,
> University of Leuven, Belgium.
> You can learn about the project at
> ngl.html
> . Information is given in German and in English
> (by checking the flag above 'Short Info').
> *************************
> From the Symposium "mathe 2000", September 21,
> 2012, Dortmund University, Dortmund, Germany. See
> eu.html
> *************************
> Growth and success of "Mathe 2000" - a privileged
> observer's view
> By Lieven Verschaffel
> [Center for Instructional Psychology and
> Technology University of Leuven, Belgium]
> It is a great pleasure and a great honor for me
> to represent the international community at the
> 22nd symposium "Mathe 2000", which is devoted
> to the 25th anniversary of this project.
> During the past three decades the international
> scene of mathematics education has witnessed, in
> various parts of the world, serious debates about
> the goals, the content and the methods of
> elementary school mathematics, which sometimes
> have evolved into true "math wars".
> For instance, in the US there have been, since
> the launch of the NCTM Standards in the 1980s
> (National Council of Teachers of Mathematics,
> 1989, 2000), highly emotional debates between
> opponents and advocates of the reform-based
> approach to elementary school mathematics;
> between traditionalists, who still believe that
> the emphasis of math education should be on the
> direct teaching of fixed, step-by-step procedures
> for solving various types of math problems, and
> reformers, who favor a more inquiry-based
> approach in which pupils are exposed to
> real-world problems that help them develop deep
> conceptual understanding, number sense, reasoning
> and problem-solving skills, and positive affects
> towards mathematics. Only in 2008, the National
> Mathematics Advisory Panel, created by president
> George Bush himself, succeeded, at least to some
> extent, in stopping that national war (United
> States Department of Education, 2008).
> In the Netherlands, another leading country in
> the international scene of mathematics education,
> we have seen a very similar development. Growing
> concern about Dutch children's mathematical
> proficiency in national and international
> assessments has led in recent years to a hot
> public debate about the way elementary
> mathematics should be taught. There were again
> two opposing camps: those who advocated teaching
> mathematics in the "traditional" manner, and
> those who supported realistic mathematics
> education, the reform- based type of mathematics
> education that has been conceived and further
> developed by Prof. Freudenthal (1983) and his
> colleagues and successors at the University of
> Utrecht (see, e.g., Van den heuvel, 2001).
> Because of the intensity of the debate, the Dutch
> Royal Academy of Sciences decided to install a
> Committee, which wrote a report that also
> succeeded in calming down, at least to some
> extent, the public debate about the quality and
> future of elementary school mathematics
> (Koninklijke Nederlandse Akademie van
> Wetenschappen, 2009).
> In this turbulent international context, Prof.
> Wittmann, Prof. Müller and the other members of
> the Mathe 2000 project have, during the past 25
> years, worked at the development of their own
> approach to elementary school mathematics
> education, in a way that I consider quite unique
> and exemplarily, for three reasons that I will
> elaborate in a necessarily brief and superficial
> way in this short tribute.
> View on elementary school mathematics
> In terms of its view on elementary school
> mathematics, one of the most important general
> characteristics of the "Mathe 2000" project is
> that it has, from the very beginning, refused to
> look at math education, and at its own position
> in the international scene, in extreme or
> polarized terms. I am aware that there exist more
> nuanced and sophisticated categorizations, but, I
> find it conceptually helpful to conceive of
> elementary mathematics education as a field
> consisting of roughly three major aspects, each
> of which has been central in a historically
> important tradition of elementary school
> mathematics: a mechanistic, a structuralistic,
> and a realistic aspect (Verschaffel, 1995).

While awaiting the usual blasts from our usual suspects, I personally find the above unexceptionable.
> First, elementary school math has a lot to do
> with memorization of basic facts, automatization
> of techniques for doing mental and written
> arithmetic, routine mastery of rules for solving
> standard problems dealing with number and
> space... Historically, this "mechanistic" element
> has been emphasized a lot in traditional
> elementary school mathematics, and it is this
> element that has been re-emphasized in these
> anti-reform movements in the US and The
> Netherlands that I referred to before.

It does, indeed, and I for one stand firmly on the side that believes math should to be made "interesting" for the child to retain his/her interest in learning it. Of course, each teacher will find his/her own way to capture the individual interest of his/her wards.
> Second, elementary school mathematics is about
> structures and patterns. In the various
> manifestations in concrete mathematical
> statements or problems, there may be a common
> principle, a common pattern or structure, an
> underlying "big idea", that has to be discovered,
> explored, understood, expressed, formalized,
> generalized..., by the learner, and that should
> become part of his or her conceptual toolbox.
> This aspect was central in the structuralistic
> approaches to elementary school math, such as the
> New Math movement, that was dominant in the
> fifties to eighties of the previous century in
> various parts of the Western world, but is also
> emphasized in current approaches that emphasize,
> for instance, the role of pre-algebra in
> elementary school mathematics.

Much of the 'New Math' movement might not have succeeded - but I for one believe it was a needed process to try and 'discover' a way out of that 'by-rote mindless memorization' that was THE feature that led to generations of students fearing or loathing math.
> Third, mathematics is a human problem solving
> activity; it is about establishing links between
> real world situations and mathematics, in both
> directions; it is about seeing the mathematics in
> the real world and about using mathematics to
> make sense of this world, to understand and
> manipulate it, with a view to efficiently solve
> problems that arise in that world. This aspect of
> "mathematical modeling and applications" is
> prominently present in approaches, such as the
> Dutch realistic approach to mathematics education
> (although it would be too simple to reduce RME to
> that aspect).

I find all the three major points made to be unexceptionable - and I keenly await the response of our esteemed 'traditionalists' on them.
> Just as in the world-famous tale of a group of
> blind men each touching a part of the elephant to
> learn what it is like, but every single man being
> unable to get a complete picture of what it
> essentially is, each of these three aspects point
> to a truly essential feature of elementary school
> mathematics, but does not tell the whole story of
> what it is about. The great value of the "Mathe
> 2000" approach is that it departs from a view of
> elementary mathematics education that integrates
> in a well- balanced way all three aspects. It
> does so both in its theoretical foundations and
> in the concrete textbook pages and materials of
> its textbook, Das Zahlenbuch. To the best of my
> knowledge, there are few textbooks in the world
> that have been so successful in realizing this
> balance so subtly and so successfully as Das
> Zahlenbuch.

> Moreover, in realizing that subtle balance
> between these three major pillars of elementary
> school mathematics, it adheres to three
> principles that have been found in the curricula
> of the world's highest-performing countries,
> according to a recent study by Houang and Schmidt
> (2012) namely (1) coherence (the logical
> structure that guides students from basic to more
> advanced material in a systematic way); (2) focus
> (the push for mastery of a few key concepts at
> each grade rather than skim over dozens of
> disconnected topics every year); and (3) rigor
> (the level of difficulty at each grade level).

I find this to be an excellent overview - and keenly await the blasts of our esteemed 'traditionalists'.
> Methodological approach
> Closely related to the above-mentioned
> international debate between advocates and
> opponents of reform-based approaches to math
> education, there is an ongoing methodological
> fight about the kind of scientific research that
> is primarily suited and needed for improving
> elementary school mathematics. Stated again
> somewhat boldly, there are, on the one hand,
> researchers who adhere the so-called
> "evidence-based approach", which postulates that
> only effective type of research is the
> (quasi-)experiment, whereby one compares the
> effect on learners of two or more approaches to
> teach a given mathematical topic, with randomly
> selected classes, in well- controlled conditions,
> using only psychometrically adequate standard
> achievement tests; and, on the other hand, those
> who argue that this evidence-based approach is
> not and will never be able to capture the rich,
> complex and contextual nature of teaching and
> learning in a real mathematics classroom, and
> therefore argue that the only useful kind of
> research is of a more qualitative nature, that
> documents in detail how one arrived at the design
> of a new teaching/learning unit, how teachers and
> learners reacted to it, and what was learnt from
> it in view of the improvement of the design of
> that unit (Verschaffel, 2009). Also in this
> international methodological battlefield, the
> "Mathe 2000" project has always taken a nuanced,
> broad-spectrum view, by pleading, on the one
> hand, for the existence of "design experiments"
> as a central research method in the domain of
> mathematics education, but, on the other hand,
> also supporting more large-scale and systematic
> evaluation studies aimed at unraveling the
> relative strength and weaknesses of its newly
> designed instructional materials and approaches.
> As illustrations of the former, I refer to Prof.
> Wittman's paper "Mathematics education" as a
> design science", published in Educational Studies
> in Mathematics (1995), which has become an
> internationally recognized "classic" in the field
> of mathematics education, as well as Prof.
> Selter's exemplary design study about building on
> children's mathematical productions in grade 3,
> published in 1998 in the same journal.
> Illustrations of the latter are the evaluation
> studies by Moser Opitz (2002) and Hess (2003),
> both comparing teaching and learning in classes
> in which a traditional textbook was used with
> teaching and learning in classes which worked
> with (an adaptation of) the "Zahlenbuch", and
> both providing substantial empirical support for
> the "Mathe 2000" approach, particularly for the
> mathematically weaker children.

With due apologies to RH, I need to study the above with more care before I comment on it.
> Role of the teacher
> Referring back to the two reports that tried to
> stop the math wars in the US and The Netherlands,
> it is interesting to see that according to both
> reports the key to improving children's
> mathematical proficiency does not lie in the
> textbook in itself, but in the competencies of
> the teachers who have to use it. And, by these
> competencies, they do not only mean their
> mathematical content knowledge, but also, and
> according to some even primarily, their
> "Fachdidaktische Kompetenz", or, in Shulman's
> (1986, 1987) terminology, their pedagogical
> content knowledge (PCK). Many studies and surveys
> have indicated the importance of this PCK. In a
> recent German study (COACTIV project - see,
> Baumert et al., 2010), it has been shown that
> students taught by teachers with a high PCK
> showed better PISA results than those of other
> students, mainly because teachers with a high PCK
> design their teaching so that the students are
> more actively cognitively engaged. Further
> analyses revealed that PCK has greater predictive
> power for student progress and is more decisive
> for the quality of instruction than their content
> knowledge (Baumert et al., 2010, p. 164).
> Moreover, the available international research on
> mathematics teachers' knowledge and professional
> development (as nicely summarized in a recent
> publication by the Education Committee of the
> European Mathematical Society (2012) headed by
> prof. Konrad Krainer), indicates the positive
> impact of "collaboration" among teachers and of
> teachers' collegial learning, i.e. of teachers
> belonging to "communities" consisting of experts,
> teachers and researchers and improving their
> teaching actions and upgrading their professional
> theory through unfolding their learning process
> in cooperation with the other members of the
> community. Clearly, the "Mathe 2000" project has,
> from the very beginning, deeply endorsed the idea
> that the teacher is the critical factor in the
> curriculum implementation process, and that,
> therefore, a textbook series project without a
> parallel well-established supportive system for
> its teachers, is doomed to fail. This is not only
> evidenced by the two excellent volumes of the
> Handbuch produktiver Rechenübungen (Wittmann &
> Müller, 2000-2002) that accompany the textbook
> Das Zahlenbuch, and that provide the teachers
> with the PCK and the accompanying beliefs needed
> to implement the textbook in a proper way; but
> also by the organization of the annual meetings
> of the "Mathe 2000" community allowing intensive
> exchanges of ideas, findings and experiences
> between teachers, researchers and other kinds of
> experts.

KEENLY await the blasts of our esteemed traditionalists while I study the above with the care it deserves.
> As a scholar from abroad, it was a great
> privilege to observe from close-by, through my
> long-standing and intensive contacts with the
> members from the Dortmund "Institut für
> Entwicklung und Erforschung des
> Mathematikunterrichts" (IEEM), the development of
> the "Mathe 2000" project. The project can be
> really proud of what it has accomplished during
> the past 25 years and the impact it has had on
> the research on and practice of elementary school
> mathematics, in Nordrhein-Westfalen, in Germany,
> and abroad. I wish you all very nice and
> stimulating conference celebrating this 25th
> anniversary.

I've not studied what they've done, but I most keenly look forward (with profound apologies to RH) to studying what they had achieved over the past 25 years AND the impact it has had on 'elementary school math'.

("Still Shoveling Away!" - with the usual profound apologies to Barry Garelick for any tedium caused; and with the observation that it is VERY EASY to avoid ALL this tedium by the SIMPLE expedient of not opening any messages purporting to originate from GSC)

> References
> Baumert, J., Kunter, M., Blum, W., Brunner, M.,
> Voss, T., Jordan, A., Klusmann, U., Krauss, S.,
> Neubrand, M., & Tsai, Y.-M. (2010). Teachers'
> mathematical knowledge, cognitive activation in
> the classroom, and student progress. American
> Educational Research Journal, 47, 133-180.
> De Corte, E. & Verschaffel, L. (2006).
> Mathematical thinking and learning. In Damon, W.,
> Lerner, R., Sigel, I & Renninger, A. (eds.)
> Handbook of child psychology. V. 4: Child
> psychology in practice, pp. 103-152. New York:
> Wiley.
> Education Committee of the European Mathematical
> Society (2012). It is necessary that teachers are
> mathematically proficient, but is it sufficient?
> Solid findings in mathematics education on
> teacher knowledge. Newsletter of the European
> Mathematical Society, March 2012, 46-50.
> Freudenthal, H. (1983). Didactical phenomenology
> of mathematical structures. Dordrecht, The
> Netherlands: Reidel.
> Hess, K. (2003). Lehren - zwischen Belehrung und
> Lernbegleitung. Einstellungen, Umsetzungen und
> Wirkungen im mathematischen Anfangsunterricht.
> Bern: h.e.p. Verlag.
> Koninklijke Nederlandse Akademie van
> Wetenschappen (2009). Rekenonderwijs op de
> basisschool. Analyse en sleutels tot verbetering.
> Amsterdam: KNAW.
> Moser Opitz, E. (2002). Zählen, Zahlbegriff,
> Rechnen. Theoretische Grundlagen und eine
> empirische Untersuchung zum mathematischen
> Erstunterricht in Sonderschulklassen. 2. Auflage.
> Bern: Verlag Paul Haupt.
> National Council of Teachers of Mathematics.
> (1989). Curriculum and evaluation standards for
> school mathematics. Reston, VA: National Council
> of Teachers of Mathemetics.
> National Council of Teachers of Mathematics.
> (2000). Principles and standards for school
> mathematics. Reston, VA: National Council of
> Teachers of Mathematics.
> Schmidt, W. (2012). Seizing the Moment for
> Mathematics. Education Week [American Education's
> Newspaper of Record], Wednesday, July 18, 2012,
> Volume 31, Issue 36, pp 24-25. See
> .h31.h
> tml?cmp=ENL-EU-SUBCNT
> Selter, C. (1998). Building on children's
> mathematics - A teaching experiment in grade 3.
> Educational Studies in Mathematics, 36, 1-27.
> Shulman, L. S. (1986). Those who understand:
> Knowledge growth in teaching. Educational
> Researcher, 15, 4-14.
> Shulman, L. S. (1987). Knowledge and teaching:
> Foundations of the new reform. Harvard
> Educational Review, 57, 1-21.
> United States Department of Education (2008).
> Foundations for success. The final report of the
> National Mathematics Advisory Panel. (Retrieved
> January 17 2009 from
> tml.)
> M. van den Heuvel-Panhuizen (Ed.) (2001).
> Children learn mathematics. Utrecht, The
> Netherlands: Freudenthal Institute, University of
> Utrecht.
> Verschaffel, L. (1995). Ontwikkelingen in de
> opvattingen over en de praktijk van het
> reken/wiskundeonderwijs op de basisschool. In: L.
> Verschaffel & E. De Corte (Red.), Naar een nieuwe
> reken/wiskundedidactiek voor de basisschool en de
> basiseducatie. Deel 1. Achtergronden (pp.
> 95-128). Brussel: Studiecentrum voor Open Hoger
> Afstandsonderwijs (StOHO).
> Verschaffel, L.. (2009). ''Over het muurtje
> kijken': Achtergrond, inhoud en receptie van het
> Final Report van het 'National Mathematics
> Advisory Panel' in de U.S. Panama-Post - Reken-
> wiskundeonderwijs: Onderzoek, ontwikkeling,
> praktijk, 28(1), 3- 20).
> Verschaffel, L., & Greer, B. (in press).
> Domain-specific strategies and models:
> Mathematics education. In Spector, J. M.,
> Merrill, M. D., Elen, J. & Bishop, M. J. (eds.)
> Handbook of research on educational
> communications and technology. 4th ed. New York:
> Springer Academic.
> Wittmann, E. Ch. (1995). Mathematics education as
> a design science. Educational Studies in
> Mathematics, 29, 355-374.
> Wittmann, E. Ch., & Müller, G. R. (2000-2002).
> Handbuch produktiver Rechenübungen (Bd.1, Vom
> Einspluseins zum Einmaleins, und, Bd.2, Vom
> halbschriftlichen und schriftlichen Rechnen: Vom
> halbschriftlichen zum schriftlichen Rechnen).
> Stuttgart: Ernst Klett Schulbuchverlag.
> *********************************************
> --
> Jerry P. Becker
> Dept. of Curriculum & Instruction
> Southern Illinois University
> 625 Wham Drive
> Mail Code 4610
> Carbondale, IL 62901-4610
> Phone: (618) 453-4241 [O]
> (618) 457-8903 [H]
> Fax: (618) 453-4244
> E-mail:

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