A Trip to HungaryAuthor(s): Ann M. AtkinSource: Mathematics in School, Vol. 5, No. 2 (Mar., 1976), pp. 6-8Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30211533 .

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by Ann M. Atkin, student at Eaton Hall College, Retford

Photographs courtesy Hungarian Embassy London

Introduction In September 1974 i applied to the Educational Interchange Council for a place on one of their Study Visits to Eastern Europe which were to take place the following Easter. Just before Christmas I learned that I had been accepted for the trip to Hungary.

The idea of the visit was to look at the educational system of Hungary, as well as to take in some of its culture and customs. The itinerary, which was extremely exacting, included visits to schools, colleges and universities, as well as to special schools for the handicapped, careers advice centres, kindergartens, and the Ministry of Education.

During our three week visit we stayed in three main centres - Budapest, Debrecen, and Szeged. I was particularly interested in the Mathematics teaching of Hungary and decided to base my final report on this aspect of the trip - I was therefore constantly on the look out for anything Mathematical in the schools we visited, and most of my ques- tions (through our excellent interpreter) were Mathematically orientated. Since there were only twenty of us in the party we all had plenty of opportunity for individual interests to be explored.

Overall, I thought the trip had been very worthwhile, and I had learned a great deal about this country's educational sys- tem and ideology in a very short time.

The Complex Mathematics of Hungary As the only Mathematician in the group, I was particularly interested in this aspect of the trip. Had the Hungarians, like us, turned to the new Mathematics? If so, why had they? Were they satisfied with it? What aspects of it did they select?

Unfortunately, not all my questions could be answered. I had the problem that students of Mathematics could not speak English. A further problem was that students of English said they never liked Mathematics. A third was that most schools were more proud of their Music classes than their Mathemati- cal ones.

It was not until the second lap of our journey that I came into contact with a Maths lesson and a Maths teacher; this was in

Debrecen, in the East of Hungary, on 2 April when we visited The Training College for Teachers of the Junior Elementary School. The college had its own Demonstration School on the premises (as did all the colleges we saw) and everyone was very excited and keen to tell us about "The New Experiment In Mathematics" that was being tried out in this school, and we were taken downstairs from the college to the school, to see a Demonstration Lesson.

The Head of the Maths Department of the college sat with us as we watched the lesson, given by a smart young teacher in the standard white overall that we saw everywhere, with a class of six-year-old children, all in their standard blue overalls which is also universal throughout Hungary. He explained that:

"Our intention is to introduce the children to Mathematical Experience through concrete devices", and that this kind of mathematics "develops structured thinking".

The Lesson The blackboard preparation for this lesson was phenomenal, and the lesson began with the teacher turning to the first section of the board where selected children had to connect the answer to a sum with a position on a number line:

4+4

117 -- 41

12 - 10 ]

L, 4 -

6+5

o

In this exercise, odd answers were signified by a grey box, even ones by a white one. I asked whether the children worked the answer out first and then drew it on to the line, or whether they used the line to work out the sum. (e.g. 12-10 count on twelve, then count back ten) and was told that they had to work the sum out first.

The second section of the lesson went as follows:

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Left: View of the Danube in Budapest Above: The centre of Debrecen

On the blackboard were certain words signifying duration, e.g.

four hours one month

a season

a week

a day

a minute

Selected children had to come up to the board and insert an appropriate sign to show "less than" or "greater than" bet- ween any two of the elements. I thoughtthis was a marvellous idea, because I did not come into contact with these symbols until secondary school, and have always found them difficult to deal with.

The head of department explained that this was an exercise in relationships between elements of a set, and the next exer- cise was to connect the elements of this set with those of a second set:

Four o'clock Friday

April

Summer IZZ

1975 Four hours one month

a week a season

a minute a day

The next section of the lesson involved the use of cuisinaire rods. The teacher said, "Pick up a Three, now pick up another Three. Now another Three. Now pick up one rod that will cover these exactly." The head of department explained that "This is a preparation for multiplying."

The teacher went on to ask the children to pick up a ten and a two and make a "carpet" of twelve:

Il[ljl I 1 I 1 1 1 I 1 I 1 i I 1 I 1 1

10 2

6 6

When this was completed she asked several children what they had got, thereby building up the number bonds of twelve.

The next task involved the use of orange cocktail sticks. "I am going to say a number and you must put out two more sticks than that number." "Eight."

Further, "I am going to say a number and you must put out two fewer sticks than that number," "Six."

The head of department explained that "there are two ways of arriving at a number - by measuring or by counting".

The next part of the lesson involved sets, and the children were given cards with pictures on them and were asked to classify them in any way they liked and then explain how they had decided to classify them, e.g. These are all red. These are all large. This was followed by taking out cards with numbers on them and classifying them as odd or even.

Towards the end of the lesson the teacher returned to the blackboard work, and for a given result the children had to decide whether it was true or false, e.g.

12+4+3=19 7+3+4=12

If a child got an answer wrong another child could come out and insert the correct answer.

This was followed by more connecting games such as: 6xivv

X4I

14

and the lesson ended with examples of "Function Machines", i.e. "if you put 7 and 5 into the machine and get 12 out, what do you get out if you put in 9 and 6? What do you put in with 4 to get 7 out?" and so on.

S 12V 12\

Materials After the lesson, I talked to the head of department, through our interpreter, and he showed me the books he uses to get ideas. These included: Carson KO & Barret IM

"Thinking Through Mathematics" Nelson. "Down In Hickory Hollow" Nelson.

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He said they don't want to copy the Americans, but would rather produce their own material, and he showed me exam- ples of the worksheets they use in the second and third grades (7-8 years). He later presented me with a huge wad of these worksheets - all in Hungarian - which he said I could keep, and which I had to carry all over Hungary with me throughout the rest of the trip.

Szeged The next chance I had to see anything of a Mathematical nature, was on 10 April in Szeged in the South of Hungary, when we visited The Training College for Senior Elementary School Teachers there.

In the question and answer session which came first, I asked about this new "Complex Mathematics" which seemed to be taking over from the old methods. The man answering our questions was not a Mathematician, and so could not give a full account, but the points he made were:

At this college the head of the Mathematics department has been all over the world and is well qualified to teach "Theory and Methods" of Mathematics. (I talked to this man later.)

The brightest Maths students have two extra periods a week in the afternoons.

Hungary has a shortage of Maths teachers because most Maths graduates go into engineering.

With the Complex Mathematics, some students are now doing in the eighth grade, what had not been done before until University. Later, I talked to the Maths lecturer mentioned above (with

difficulty, because I had to share a translator with a group of music students talking to a Music lecturer), and he said that he expects Complex Mathematics to take over completely from Traditional Mathematics, as it "helps to develop logical think- ing". He told me that it is now introduced to all first and second grade children in the college school, but the syllabuses have not yet been worked out for the other grades.

Schemes of Work I asked to see a scheme of work, and he showed me an assignment done by one of the students. The scheme con- tained the following main topics: Set Theory - Venn Diagrams Fractions and Decimals Function Machines Concept of Greater than and Less than Line graphs - Straight Line and Hyperbola Symmetry

He then showed me some of the wo rksheets that the present twelve year olds at the school are doing: e.g.

It has 4 sides and four angles Its sides are equal It has only 3 right angles The sum of the angles is 3600 It can be divided into two triangles by one line Two of its sides are parallel

By a line we can cut off a pentagon

True for all True only quadrilaterals for some False

e.g. Put in the factors:

2 3 4 5 6 7 8 9 10 12 + + + + 20 + + + 24 + + + + + +

8

e.g. Is Smaller than: 0 -,a

6

Y

)2A

I(PA

(b-

0. 4 0

Here, the arrows not only go to the greater one, but it also has to be a multiple. e.g.

Square Not Square with hole without with hole without

large Red

small

large Not Red

small

This table is filled in using "Logic Blocks". e.g. Greater than, Less than, Equal

75 ZO

(9/00

e.g.

a b c *

4 5 3 60

9 4 2 72 1 1 1 4 2 8

1.5 1.5 1.5 ? 3 2 ? 4.5

10 8 ? 8

? 5 5 2.5

e.g.

Finding Factors: 60

2 30

2 15

/ \ 5 3

12

3 4

2 2

60=2.2.3.5 12=2.2.3

Conclusions My final opportunity to ask questions came on the last evening of our visit, in Budapest. A farewell buffet had been arranged for us, and various important people from the Ministry of Education were invited. I talked to a man who was some high-up in the education world, but was also a scientist, and during the course of the conversation I asked why this Com- plex Mathematics experiment had been started.

At first he said that many children did not like Mathematics and it was hoped that the new Maths would make them enjoy it more. I asked if it was succeeding in this and he said it was too early to tell because the experiment had only just started. I asked if the people involved in the experiment really knew why they were doing it or whether they did it to be "on the band wagon" and his reply was "there are far too many experi- ments going on in Mathematics - we don't know whether they will be good for the children."

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