# Mathematics lessons and Competency orientation – an open letter

### To

### Dr Eisenmann, President of the Conference of Ministers of Education and Cultural Affairs

### Mrs Heiligenstadt, Minister of Education of Lower Saxony

### Prof Dr Wanka, Federal Minister for Education and Research

### Prof Dr Stanat and Mr Lorber, Institute for Quality Development in Education

### Prof Dr Köller, Prof Dr Heinze, and Mr Pigge, IPN Kiel

### Mr Rabe, senator for school and vocational training of the City of Hamburg

### Mrs Seiffert and Dr Busse, Head of the Department of Mathematics and Natural Science and Technology at the School of Vocational Education and Training, Free and Hanseatic City of Hamburg

### Mr Dietz, Ministry of Culture of the State of Hesse

### Prof Dr Röckner, President of the German Association of Mathematicians

### Prof Dr Biehler, Prof Dr Greefrath, Prof Dr Koepf, and Dr Langlotz Mathematics Commission, Transition School – College

### Prof. Dr. Dr. h.c. Hippler, President of the University Rectors‘ Conference,

### Ladies and Gentlemen,

The current situation in the run-up to the Hamburg Mathematics Abitur 2017 [HH] and the dispute over the Lower Saxony Abitur in mathematics of last year [BM] are alarming symptoms for the crisis of the mathematics education in schools. Within the framework of competency orientation, a requirement in the entire Republic in the form of educational standards [Bil], the mathematics school material has been thinned out to the extend that the mathematical knowledge of many university students is no longer sufficient for a WiMINT study.
Many university lecturers have already drawn attention to the new students’ deficiencies in mathematics: [Kn], [HP], [Bau], [Sch]. These beginners lack mathematics skills from the intermediate level [in Germany the intermediate level covers the 5th – 10th semester, editorial remark], actually already fractional arithmetic (!), power and root calculation, binomial formulas, logarithms, transformation of mathematical terms, elementary geometry, and trigonometry. These deficits have already long been difficult to catch up with – either in pre-courses or in bridging classes. Meanwhile, in the entry phase of studies almost everywhere mathematical literacy programs are carried out. This is frustrating for those students who arrive at the colleges with good grades and high expectations. In practice, the prior knowledge of many of the new students is far from the minimum requirement list of the universities of Baden-Wuerttemberg for studying WiMINT subjects [COSH].
Polaczek and Henn [HP] have shown through statistical surveys at the Aachen University of Applied Sciences that the command of the junior high material from the school period determines the success in MINT courses. We also refer to the statistical surveys at university entrance examinations in North Rhine-Westphalia [Kn] which show a decreasing mathematical level for new students over a period of 10 years.

The survey carried out by the IPN [MaLeMINT] asking university lecturers in mathematics teaching university entrance semesters about the requirements on mathematical knowledge when starting studies on a MINT subject is a clear demonstration that these reforms were implemented without sufficient involvement of experienced teachers of the schools and universities.

As part of the competency concept, proven mathematical phrasing and abstract excersises were replaced by bulky textures and artificial modeling tasks. The mathematical basics are taught only in a superficial way, a deeper content-related engagement doesn’t take place any longer. Accordingly, competency-oriented textbooks look like a kaleidoscope or a panorama where a new topic is started with each double page. You can see a lot of text and colorful pictures, but no longer a thread: [LS], [MB], [MW], [NW]. Mathematic topics are only „offered“ bit by bit and not sufficiently interlinked: this results in weakening of understanding, missing subject-matter knowledge, gutting of mathematics topics [RW], [Ban], [Mi].

The inadequate subject-specific depth is also reflected in the new A-level examinations. In all three areas (analysis, linear algebra, and stochastics), the Hamburg examinations have a (in some cases absurdly designed) “reference to reality”, ie a package with a lot of text and supplements, the student has to put aside in order to get to the mathematical core issue. This apparently causes the need for a working time of five hours plus an upstream read-in time of half an hour. This is definitely too long and nation-wide a peak value in the duration of the exam. From the viewpoint of those issuing the Hamburg A-level examination (German: Abitur), this style should assume a pioneering role for the whole of Germany. After the recent scandal this planned pattern will hopefully not be implemented!

In many publications, university professors have already pointed out that the “A-level examination” in this “modeling style” lowers the level of mathematical requirements and is counterproductive when preparing for studies in the MINT area; See Jahnke et al. [JK], Kühnel [Kü], Lemmermeyer [Lem], Klein [Kl], Bandelt/Matschull [BM], Walser [W].

The VERA tests, based on the new competency-oriented standard, test rather for everyday knowledge under the mantle of “mathematics” when testing the knowledge on the correctness of the statement “after Wednesday comes Thursday” or when testing the ability to read a bar graph in class 3 [VERA].

We ask you to take care, in your sphere of influence, that

- Germany ‚s schools can again return to a mathematical education oriented to subject –
- the responsibility to thoroughly exercise and repeat the above-mentioned intermediate grade subjects is again fully taken over by the schools,
- important basic contents such as fractional and root equations, powers with rational exponents, sufficient elementary geometry and trigonometry are included in the curriculi,
- the use of pocket calculators and computer algebraic systems (CAS) does not affect the important phase of teaching elementary and symbolic calculation techniques (in Hessen, for example, from class 7 onwards, it is mandatory to use a pocket calculator, disturbing routine retrieval,
- symbolic, formal and technical elements of mathematics and abstract content are weighted higher,
- the A-level exams shall instead of modeling tasks again contain tasks with content-oriented scope, as they are customary on an international level. •

[Ban] H.-J. Bandelt (2016). Entfachlichung durch Kompetenzorientierung (removal of subject specific topics) . Mitt. Math. Ges. Hamburg 36, p. 103–130

[Bau] A. Baumann (2013). Mathe-Lücken und Mathe-Legenden – Einige Bemerkungen zu den mathematischen Fähigkeiten von Studienanfängern (Gaps in mathematical knowledge and other legends) . Die Neue Hochschule, volume 5, p. 154–157. www.mathematikinformation.info/pdf2/MI55Baumann.pdf

[Bil] Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife (basic knowledge in mathematics with regard to a general matriculation standard) (18.10.2012), vs. p. 9. www.kmk.org/fileadmin/Dateien/veroeffentlichungen_beschluesse/2012/2012_10_18-Bildungsstandards-Mathe-Abi.pdf

[BM] H.-J. Bandelt, H.-J. Matschull (2016). Denken darf hier nur der Taschenrechner (Thinking allowed only by the pocket calculator). “Frankfurter Allgemeine Zeitung” from 28. May 2016. www.faz.net/aktuell/feuilleton/forschung-und-lehre/streit-um-das-mathe-abitur-in-niedersachsen-14256230.html

[COSH] COSH – Cooperation Schule - Hochschule lehrerfortbildung-bw.de/bs/bsa/bk/bk_mathe/cosh_neu/
[HH] NDR.de (11.1.2017): Ärger um miese Probeklausur (Trouble with a dinky pretest). www.ndr.de/nachrichten/hamburg/Zentral-Abi-Aerger-um-miese-Probe-Klausur,abitur282.html

[HP] G. Henn; C. Polaczek (2007). Studienerfolg in den Ingenieurwissenschaften (Success in studying Engineering sciences) . In: Das Hochschulwesen, 55. Jg./volume 5, p. 144–147. www.hochschulwesen.info/inhalte/hsw-5-2007.pdf

[JK] Th. Jahnke; H.-P. Klein; W. Kühnel; Th. Sonar und M. Spindler (2014). Die Hamburger Abituraufgaben im Fach Mathematik. (the Hamburg A-level test in Mathematics) In: MDMV, Bd. 22, volume 2, p. 115–121. https://www.mathematik.de/ger/presse/ausdenmitteilungen/artikel/dmvm-2014-0046.pdf

[Kl] H. P. Klein (2016). Vom Streifenhörnchen zum Nadelstreifen. Das deutsche Bildungssystem im Kompetenztaumel. zu Klampen, Springer

[Kn] H. Knospe (2012). Zehn Jahre Eingangstest Mathematik an Fachhochschulen in Nordrhein-Westfalen. (10 years of Entrance exam in Mathematics on universities of applied science) Proceedings to 10th “Workshop Mathematik in ingenieurwissenschaftlichen Studiengängen”, Hochschule Ruhr-West, Mülheim an der Ruhr, p. 19–24. www.nt.th-koeln.de/fachgebiete/mathe/knospe/10jeingangstest_knospe.pdf

[Kü] W. Kühnel (2015). Modellierungskompetenz und Problemlösekompetenz im Hamburger Zentralabitur zur Mathematik. (Modelling competence and problem solving competence in Hamburg A-level exams) Math. Semesterberichte 62, p. 69–82

[Lem] F. Lemmermeyer (2016). Abituraufgaben und Kompetenz (A-level exams and competence). MDMV 24, p. 170–173

[LS] Lambacher Schweizer 5 (mathematical textbook) (NRW), Klett, ISBN 978-3-12-734411-0

[MaLeMINT] Mathematische Lernvoraussetzungen für MINT-Studiengänge – eine Delphi-Studie mit Hochschullehrenden (Prerequisits for learning mathematics in MINT topics) www.ipn.uni-kiel.de/de/das-ipn/abteilungen/didaktik-der-mathematik/forschung-und-projekte/malemint

[MB] Das Mathematikbuch 9 (mathematical textbook) , Klett-Verlag, ISBN 978-3-12-700391-8

[Mi] F. Milde (2016). Offener Brandbrief zum verschlechterten Mathematikunterricht (Open letter of a deteriorating teachning in mathematics . Mathematikinformation 65, p. 64–66. www.mathematikinformation.info/pdf2/MI65LeserbriefMilde.pdf

[MW] Mathewerkstatt 5 (mathematical textbook), Cornelsen-Verlag, ISBN 978-3-06-040230-4

[NW] Mathematik Neue Wege 7 (mathematical textbook) (Hessen G9), Schrödel-Verlag, 978-3-507-85664-6

[RW] Remus, D., Walcher, S. (2016). Die Entkernung des Mathematikunterrichts (The gutting teaching of mathematics (PROFIL July-August 2016, p. 19–21

[Sch] A. Schwenk-Schellschmidt (2013). Mathematische Fähigkeiten zu Studienbeginn (Mathematical skills when starting at university), Symptome des Wandels – Thesen zur Ursache. DNH 1, p. 26–29

[VERA] https://www.iqb.hu-berlin.de/vera/aufgaben/map (Briefe von Wittmann zu VERA 3_M 2010 vom 31.5.2010 und 7.6.2010: http://www.mathematik.uni-dortmund.de/ieem/mathe2000/vera3.html)

[W] H.Walser (2011). Die Modellierung des schönen Scheins (modelling beautiful appearance). Mathematikinformation 55, p. 3–14

www.mathematikinformation.info/pdf2/MI55Walser.pdf.

*cc*. This open letter is signed as a first signatory by more than 130 university lecturers and teachers, especially in mathematics and natural sciences. 150 further personalities have now joined the group.

The initiators of the letter aim to increase the number of signatures to at least 500.

The list of the existing signatories of this letter and the possibility of signing it can be found on the website of “Gesellschaft für Bildung und Wissen”, https://bildung-wissen.eu.