SOME FACTS AND TENDENCIES IN THE HUNGARIAN MATHEMATICS TEACHING

Tibor Szalontai

For many decades, Hungarian student teams have gained distinguished places in the mathematics olympiads. This fact shows the power of mathematics teaching in general somewhat, but mainly the power of ‘elite training’. Also, the number and significance of Hungarian mathematicians known all the word over indicate a good schooling in the background in general, but mainly the good training of outstanding ability students.

Certain mathematics teaching philosophy, the methodology and the best practice of lessons in Hungary recently attract a deeper international interest, especially in the United Kingdom. The experimental Mathematics Enhancement Programme [MEP] of Professor David Burghes (Centre for Innovation in Mathematics Teaching [CIMT], University of Exeter, U.K.) for secondary stages was built on the outcomes of the ‘Kassel-Exeter’ international comparative project, partly on the Hungarian methods and examples of lessons observed.[1,4,6,7] The primary extension of this MEP has been built on a Hungarian textbook series (chief editor is Sándor Hajdu) more directly.[9.10,11] From some other countries interests have just arrived on ‘Hungarian style’ lesson plans and videos.

From the past, it is surely enough to remind our kind readers of the work and reputation of György Pólya, Zoltán Dienes, Tamás Varga or Imre Lakatos. These facts indicate a good mathematics-didactical tradition and also permanent good innovations in this field in Hungary. But we should not think that Hungarian mathematics schooling has the same high standard in practice. Some main features of that attractive mathematics teaching - learning approach, which is rooted in more than a hundred year tradition and developed gradually through many strategic changings, are:

• Whole class interactive teaching - pupils kept together as far as possible (but with natural ways of differentiation) - effective lessons.
• Harmonic proportion of whole class activitiy and individual work (which is always followed by whole class discussion again: report - reasoning - arguing, debate - feedback - agreement - feedback - self-correction - praising, evaluation - teachers’ extra comments or extension) - spoken and written abilities - clear mathematical language - frequent mental calculation.
• Flexible and sensitive diagnostics by feedback questioning during both the whole class activities and the discussions after the individual work. (Who agrees/disagrees with X? How did you think? How could you guess it? What did you got idea from? What did you write? Why did you think this? Who wrote this/other plan? Who got this/other result? Is it correct/incorrect? Why?, etc.)
• Investigations. Development of (mathematical) thinking. Manipulative and demonstrational tools, models - but less ‘free playing’ as it was in the ‘new mathematics’ - realistic problems.
• Focus on psychology of learning - interiorization - differences between the genders in different age-cohorts - use of both sides of brain (moving or imaginal thinking of right hand side part and logic or conceptual thinking of left hand side part) - complex use of advantages of different learning theories (e.g. ‘associational‘, ‘stimulus-reflexional’, mediational’, ‘operational’, ‘sign-signed’, ‘formal-structural, ‘problem-oriented’, etc. theories)

On the international stage, Hungary’s position in attainment has decreased. While in the IAEP measurement in 1991 Hungary was one of the two best European countries with Switzerland among 20 countries, not much behind South-Korea and Taiwan, then in the IEA-TIMMS measurement in 1995, Hungary’s result of 13+ years old pupils was the 14th (although) among 41 countries as the 10th European country.[13,14] The 2nd place of Hungarian 14+ pupils, rather behind Singapore and near to Poland, in the Kassel-Exeter project (1996-99) cannot tell us too much since the comparison of only 8 countries was published.[4]

The Hungarian school matematics attainment has decreased in absolute value. The official monitory measurements since 1986 have showed the declination at each age of 10, 14, 16 and 18 years olds. While the result of 10 years olds increased between 1986 and 1991 then it decreased back by 1995 and falled under by 1997. While the result of 16 years olds increased between 1986 and 1993, but it falled under by 1995 and falled again by 1997. The result of 14 years olds and 18 years olds gradully have fallen since 1986.[3,8,12]

A tipical example from 1995: More than 2 third of the 16 years olds could not solve a simple percentage problem.

In the 1997 monitory testing (published recently) they applied 4 subtests: ‘logical thinking’ [L]; ‘quantities’ [Q]; ‘plane - space’ [S] and ‘number - arithmetics’[N].

The 10 years olds found N and Q quiestions as the easiest, S as more difficult and L as the most difficult.

At 12 years olds, S was the easiest and L was the most problematic again.

At 14 years olds, S was the easiest and Q was the most difficult.

At 16 years olds, Q was the easiest and N the most difficult.

At 18 years olds, S was the easiest and L was the most problematic.

The range of mains of the 4 subsets was from 35% to 52% at 10 but by 14 this range became more narrow from 53% to 61%. In the main time, the deviation was similar in the total score of the three first age-cohorts and also in the subsets. At 16 the range raised again but the deviation was lower than at the youngers (despite the very different abilities and school types). At 18 the total deviation was the lowest (but then only about the 70% of the population learn mathematics, in ‘gimnaziums’ and ‘technical secondaires’ with maturation exam at the end).

Some extremly negative examples:

The most difficult question for 10 years olds, which only 5% of them were able to solve, was: A frog is jumping 20 cm each time upwards but then slipping back 10 cm each time. After how many jumps will the frog take the 2m distance upwards? And only the 12% of the 12 years olds solved it. Also at 10, in a ‘closed end’ problem, only the 20% (level of blind hit) solved it where the equality of lengths of four ‘terracced broken lines’ (only from vertical and horizontal sections) had to be found. Only 47% of them solved a question which was based on notice of the incorrect exchanging of 56 days into 7 weeks.

Only 27% of 12 years olds could answer correctly this ‘closed end’ problem: If two people start at the same time from A and B towards each other with different speed, then at the meeting point, which of them will be farther off from A? It points to our big problem in appreciative reading ability of the children. At 14 this question was solved by 38%, at 16 by 29% (!) and at 18 by 45%.[12]

By the new law on education and its National Curriculum of 1997, the number of mathematics lessons were drastically cut. Especially in the first 5 years of schooling, the 5 mathematics lessons per week were reduced to 4 lessons per week, although with 1 extra lesson possibility in the first four years for dealing with poor or outstanding pupils in mathematics or Hungarian.[5] In practice, in Year 1 and 2, about half of the pupils are estimated to learn mathematics in this extra lesson (or in one week they practise mathematics and in the other week Hungarian).

The new government decided to revise the National Curriculum and plan to insert a ‘Frame curriculum’ between the NC and the schools’ local curriculums. This plan cuts the mathematics lessons toward and more strictly. In the first 8 years, the numbers of mathematics lessons would be the follows:

Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8

4 4 4 3 4 3 3 3

and actually those possible extra lessons also disappear. In the main time, the numbers of Hungarian lessons in the first 4 years would remain 8, 8, 7, 7 per week. We have not heard about similar lesson numbers in other countries. Slighter reducing in mathematics is also planned in the secondary schools, but they have more possibilities in setting groups for extra lessons.

Thus, of course, the content of teaching-learning materia of the mathematics school subject has to be reduced also. A few publisher houses reacted on the previous changing with revision of their textbooks in advance and now, one of them is rewriting its textbook series year by year in accordance to the planned changings. Its authors plan to arrange the content for alternative number of lessons (e.g. for 3 +1 lessons in Y4) with hope in miracle of returning to the former numbers. Anyway, since 1990, when the textbook publishing and market were deliberated, very various standard of mathematics textbooks have appeared in Hungary, mainly for the most sensitive primary years and one’s dangerous effect could be calculated in that declaining attainment at 10 years olds.

It is also a tendency, that less and less students want to be mathematics teachers, mainly for age-cohort of 10-14 years olds pupils, while more and more of them have poorer mathematical abilities and sence or ambition of this vocation. In the main time, universities, which train teachers for the 14-18 age-cohort, began to entice students from teacher training colleges, which train teachers for that 10-14 age-cohort, although, because of their traditions, colleges give more advanced and reacher methodological training in mathematics practically.

Summarising these facts and tendencies, we can say that Hungary must face up difficult problems in mathematics teaching in the near future, while several countries could adopt its best traditions, in addition its older and recent good innovations yet. It might be happen that some countries import the best Hungarian system and methodology, while Hungary will lag behind.

[1] (Burghes, D.N.:) Hungary is the answer to our maths problem

The Sunday Times, 12 November 1995

[2] Szalontai, T.: Changing educational framework in the teaching of mathematics in Hungary

Teaching Mathematics and its Applications (Dec 1995) v. 14(4) p. 149-155

Oxford University Press, London

[3] Report on the education of Hungary 1995 OKI, 1996, Budapest (in Hungarian) http://www.oki.hu

[4] Burghes, D.N.: Kassel Project -- Year 3 progress report http://www.exeter.ac.uk/cimt/kassel/

[5] National Curriculum (=Nemzeti Alaptanterv) OKI, 1997, Budapest (in Hungarian)

[6] Why we lag behind in maths News Focus, Maths extra, TES March 15 1996

[7] British maths fails to add up News Focus, Maths extra, TES

[8] Kindrusz, P.: The Monitory ‘97 measurement in our county

[9] Mental maths pushes out calculators Times, 30 July1999

[10] Mathematics Enhancement Programme, Primary Demonstration Project R; 1a; 1b; 2

[11] Practice Book Y1a;Y1b; Y2a; Y2b

Mathematics Enhancement Programme, Primary Demonstration Project,

Műszaki Könyvkiadó / CIMT University of Exeter, 1998/1999, Exeter, U.K.

[12] Vári, P (et al): Monitory ‘97 / Changing in the knowledge of the pupils

in: Measurement - Evaluation - Examination 6. OKI, 1999, Budapest (in Hungarian)

[13] http://ustimss.msu.edu/cdata.htm (on TIMSS international measurement)

[14] http://forum.swarthmore.edu/social/timss/ (on TIMSS international measurement)