Mathe durch Deutsch (or Vorsprung durch Geometrie)Author(s): Andrew FlemingSource: Mathematics in School, Vol. 32, No. 4 (Sep., 2003), pp. 4-5Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30212283 .

Accessed: 06/10/2013 13:50

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access toMathematics in School.

http://www.jstor.org

This content downloaded from 147.8.31.43 on Sun, 6 Oct 2013 13:50:02 PMAll use subject to JSTOR Terms and Conditions

Mathe durch Weutsdt) (or Vorsprung durch Geometrie)

by Andrew Fleming

The Mountbatten School is a designated Language College in Romsey, Hampshire. The 'Mathe durch Deutsch' project is an experiment in 'immersion' teaching: teaching in other curriculum areas in schools

in a language other than the majority mother tongue.

'Geometry is hard enough already - but in German!' This was the headline produced by our cub reporters in the school for the local newspaper a couple of weeks before the project ran. For many, two of the 'hardest' subjects of our schooldays are mathematics and languages and here they were in one package, a double whammy.

The year 8 guinea pigs in this experiment gasped suitably when I announced that they were going to be at the hard end of four hours of mathematics teaching in German, but when the four hours were up their faces were beaming with pride and a sense of success as well, no doubt, as relief that the ordeal was over.

As the Language College Co-ordinator in this school which teaches French, German, Italian, Spanish and Japanese, I had been looking for a way into this 'immersion' teaching. In many countries children learn most of their school subjects through the medium of foreign languages. In France there are 'sections bilingues', in Canada many English-speaking Canadian children learn through the medium of French. On a perhaps less obvious note many children attend British schools every day and are exposed, in every lesson they attend, to a language not spoken at home.

It was my colleague in the mathematics department who came up with the idea of year 8 'Angle' as a body of work that might lend itself to being taught in another language. The more I looked at the content, the more I realized that one way or another pupils would have to learn a foreign language to deal with this material with its prevalence of Latin-based vocabulary, and that, of the languages I knew, German was the absolutely obvious choice because of its lack of classical civilization language influence on its mathematical, technical and scientific language. 'Isosceles', 'equilateral', 'circumference', 'heptagon' are more difficult than many 'foreign' words to learn, yet in German they are the products of simple building blocks: isosceles becomes gleichschenkelig, or equal-legged, equilateral becomes gleichseitig, or equal-sided, heptagon becomes Siebeneck or seven corners. At the end of a section on polygons, the pupils were able to come up with the internal angle sum of a 22-sided polygon (by having understood the pattern) and a child with just over a year of German produced the answer: 'Ein Zweiundzwanzigeck hat dreitausendsechshundert Grad'. She could not have produced that answer in English using accurate terminology. Nor can I, but it's getting close to a Kreis (or circle) and I'm first and foremost a linguist.

There was also a second sense in which 'Angle' was an excellent choice compared to many other mathematics topics. It was possible to introduce the language we used by illustration, because it is a practical and visual topic, and to introduce it organically, building up from compass use to describing a circumcircle and from the angle sum of a triangle to the angle sum of any polygon. There was indeed, an unanticipated bonus in this process. When thinking about having the pupils follow me 'lockstep' through the very basics of drawing a circle with a compass it occurred to me that the very words to describe the sharpness or bluntness of our pencils (spitz and stumpf- and pupils would already know der Spitzer (pencil sharpener) from their German lessons) were going to be recycled later when talking about angles. Ein spitzer Winkel and ein stumpfer Wzinkel are, respectively, an acute and an obtuse angle. Pupils also already knew from their German lessons the delightful word Winkelmesser: angle measurer, or protractor. How much easier must mathematics be for German children than for English children having to cope with this constant 'language interference'? And similarly how much easier must science be for them where a placenta is Mutterkuchen (mother cake) or lactic acid is Milchsaure?

To help myself be able to teach the series of lessons I started by observing a mathematics teacher colleague work through the content (in English) with a parallel class. As it is often a very solitary occupation it is always fascinating to observe other teachers teach. Here I had the even rarer opportunity of observing a colleague in a different discipline. Clearly there are many necessary qualities that all teachers must share to achieve their ends. The requirements to engage with the class, to give clear exposition and to allow for regular feedback are some of those. There seemed to me, however, to be some interesting differences between us that said much about language teachers' needs to control classes arising from their concern that what we say in class is both medium and content at the same time: everything we say, we feel, is deserving of the pupil's fullest attention. My mathematics colleague allowed a degree of background chatter (some of which was very pertinent and productive) that I would have been quite uneasy about.

Once I had my lesson observation notes, notes from a chat with the Head of Mathematics to clarify the difference between a circumcircle and an inscribed circle, and a German language mathematics textbook, I set about preparing my lessons. This took me hours, not because of

4 Mathematics in School, September 2003 The MA web site www.m-a.org.uk

This content downloaded from 147.8.31.43 on Sun, 6 Oct 2013 13:50:02 PMAll use subject to JSTOR Terms and Conditions

any technical difficulty on either side but because of the need to develop two aspects of knowledge and understanding in tandem. My lesson objectives are broken down into very small stages all with a mathematical strand and a linguistic strand, e.g. 'constructing an equilateral triangle using compass and arcs - revision of Winkel, Bogen, Grad, gleich, introduction of Dreieck and Seite'.

Colleagues in the Graduate School of Research and Education at Southampton University filmed throughout the lessons. A collection of small tape recorders was placed on many tables to catch pupil utterances. The Headteacher came to observe one lesson and many other interested colleagues observed all lessons. One problem I didn't have was poor pupil control. Indeed, the attention being paid to the class because it was so 'special' made it a little difficult to know to what extent it became such a successful project due to the inherent 'specialness' of the immersion experiment. I like to think it would all have worked just as well if I had had the class in that normal teacher way: isolation with the class. Their responses were tremendously heartening, from both a mathematical and a linguistic perspective. Children still find it hard to hide their enthusiasm at that age and their smiles at their successful answers under that degree of challenge were unmistakable.

The degree of pupil involvement gave me the luxury of allowing a far greater response time than either a mathematics or a languages teacher would typically give. With the combined demands of the mathematical calculation and the linguistic response a lengthier response time was also a necessity. These moments were wonderful and often led to sublime outcomes. On one occasion I asked 'Was ist das?' hoping for the answer der Umfang as I pointed to the circumference of the circle on my OHT. Some hands went up confidently, cogs churned and then a girl's hand slowly went up. 'Ja, Rio, was ist das?' Rio replied: 'Das ist 21,09cm!' I am fairly sure the pupils covered as much mathematics in the time as they would have done had it been delivered in English. I am more sure that they learned more German in that time than they do in a typical series of four German lessons. One secret of the success lies in the fact that the pupils know mathematics is far more important than their ability to describe their pets in a foreign language. Another is that it is amazing what challenges children can respond well to, especially when they have a feeling it's all 'special'.

Keywords: Geometry; German; Cross-curricular work.

Author

Andrew Fleming, The Mountbatten School and Language College, Whitenap Lane, Romsey SO51 5SY.

"My maths textbook

really helps me do better"

............................... i:iiiiiiiiiiaa~iiiiii~~~iiiiiii z!!!!!!!!!!!!!!!! ...............aa:::aiiiiii,

( iii~~iiiiiiiii!!a,aa

,a i iiia ii iiii,a'iil aa~a!'I

ii~ iia : aaa ' . ...... ... . .... . . . . . . . . . . ............. '''' !i '

80% of KS3 students say that coursebooks really help them understand

maths better. They know that books help them raise their own standards.

Yet research from Keele University also shows that less than half have maths textbooks to use in class and at home.

Do your students have all the books they need?

Are you spending enough on coursebooks?

Booktrust Benchmarks are there to guide you.

The independent charity Booktrust has drawn up guidelines on how much you should aim to spend on textbooks. These figures (broken down by subject at both primary and secondary level) are included in the full Booktrust Report 'Recommended Spending on Books in Schools', which you can read and download from the Books Raise Standards website. Don't short change your pupils - check it out today.

f ) 11111~~~~(1~1 ~ '1 ~(I II ~ It

Ilrllll~i~r~l ~tl~~lll~~li~ll~rll il~T~I~~;1~1~(11 I;llrlll

Mathematics in School, September 2003 The MA web site www.m-a.org.uk 5

This content downloaded from 147.8.31.43 on Sun, 6 Oct 2013 13:50:02 PMAll use subject to JSTOR Terms and Conditions