Date: Oct 22, 2012 9:43 AM Author: Jerry P. Becker Subject: Symposium - Growth and Success of "mathe 2000" 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

http://www.mathematik.uni-dortmund.de/ieem/mathe2000/personen.html

] 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

http://www.mathematik.uni-dortmund.de/ieem/mathe2000/engl.html

. Information is given in German and in English

(by checking the flag above 'Short Info').

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From the Symposium "mathe 2000", September 21,

2012, Dortmund University, Dortmund, Germany. See

http://www.mathematik.uni-dortmund.de/ieem/mathe2000/neu.html

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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).

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.

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.

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).

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).

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.

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.

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.

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

http://www.edweek.org/ew/articles/2012/07/18/36schmidt.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

http://www.ed.gov/about/bdscomm/list/mathpanel/index.html.)

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.

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--

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: jbecker@siu.edu