year 2-3 march 2003 – september 2003

IPMAReport from Ukraine

Year 2-3March 2003 – September 2003

Budapest, October 10-11, 2003

Common data

A total of 246 pupils studying in 9 schools from 12 classes in Cohort1 and 206 pupils studying

in 9 schools from 10 classes in Cohort2 participated in IPMA in Ukraine.


Cohort 1, Tests 0,2,3




0.00

10.00

20.00

30.0040.00

50.00

60.00

70.00

001P 002P 003P 004P 005P 006P 007P 008P 009P max

Schools

Sco

re

Test 0 Test 2 Test 3

0123456789

10

001Р 002Р 003Р 004Р 005Р 006Р 007Р 008Р 009Р

School

Sch

ools

leve

l

Test0 Test2 Test3



0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

Q1

Q3a

Q3c

Q3e

Q4a

Q5a

Q5c

Q6.

2

Q6.

4

Q7b Q8

Q9b

Q9d Q9f

Q10

b

Q10

d

Q11

b

Q12

Q14

Q16

Q18

Q20

a

Q21

a

Q21

c

Q22

b

Q22

d

Q23

b

Q25

Q27

Q28

b

Item

% c

orre

ct

Test1 Test2 Test3

Cohort 2, Tests 0,2


Cohort 2, Tests 0,2


0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

001P 002P 003P 004P 005P 006P 007P 008P 009P max

Schools

Sco

re

Test 0 Test 2

0123456789

10

001Р 002Р 003Р 004Р 005Р 006Р 007Р 008Р 009Р

Schools

Sch

ools

leve

l

Test0 Test2

Comparative Results for Cohort1 and Cohort2


IPMAMath Curricula in Ukraine


Math Curricula in Ukraine


Math curriculum is defined by the program and Ukrainian schools work by four types of Math programs:

! ¨ State program (more traditional);! ¨ Developing education (L.Peterson);! ¨ Developing education (E.Alexandrova);! ¨ Author programs (in particular, Steiner school).



Approximately only 5% of schools work by the L.Peterson program but they all achieve good math results.

Why only 5%? The answer is:

• Teacher competence, • Traditions, • The cost of the textbook

and the whole educational package (textbook, workbooks for students, teacher guide).



This curriculum for primary school was prepared at the base of psychological and pedagogical researches made in the fall of the

70th under the guide of the outstanding mathematician and math deduct

N.Y.Vilenkin. The Primary Math Course is a part of the join permanent math

course developed from the positions of developing education and humanisation.

Math Curricula in UkraineMain principles


1. Orientation on the developing creativity, soul potentiality of each personality, and her/his interest to the subject:

1.1. Abilities to analyse, compare, generalise, classify, think by analogy;1.2. Activities to create, find, compose, choose, draw, etc.



1. 2.Close connections with real life and practice:– 2.1. Mathematisation Step

(constructing math model of some fragment of reality);– 2.2. Math Model Exploration Step

(developing the theory, describing properties of the math model); – 2.3. Application Step

(applying the developed knowledge to real life).



3.Permanence between the primary and secondary school.



4.Developing the thinking style successive for computer usage. The computer age implies the necessity to rethink the importance of different abilities and skills. For example, plan the work and control for its realisation, ability to make a choice from the set of variants, estimate the quality of the solution, follow given rules and algorithms, ability to organise the search of needed information, etc. become of more and more importance. The proposed course is oriented on developing all this abilities and the future wide ICT implementation in school practice.

Math Curricula in UkraineThe Educational Process


The term Educational Process is better then the term training, which suppose the trainer position.

Educational process in developing education follows the ideas of L.Vygotsky, P.Halperin, L.Zankov, V.Davidov. works devoted to the specifics of student thinking.



1.The main method is activity approach in education: new concepts and relations between them are not proposed to students as final, ready knowledge.

2.Students should discover new knowledge through insight by them own in the process of individual explorations.

3.The teacher only direct this process and summarise the discovered facts, giving strict form to discovered algorithms, acquainting with stable terminology.

4.Students construct their own mathematics, so mathematical concepts has personal significance for them, interesting not as for the observer but as for creator.



Step 1. Problem posing:The teacher includes the problem question to thelist of problems for knowledge actualisation,provoking the problem posing by students.



Step 2. Insight of new knowledge:The teacher proposes the system of questions and problems, which guide to personal insight of newknowledge. After that the teacher summarise thediscovered facts, giving strict form to discoveredalgorithms, acquainting students with stableterminology.



Step 3. Primary fixing of new knowledge:Making exercises with obligatory comments and sounding of new algorithms.



Step 4. Training individual work:Individual work at training exercises on application of studied properties, checking results in a class and correction of mistakes. It’s very important to create the filling of success for each student (I can do it!).



Step 5. Repetition problem solving: The teacher propose problems for permanent developing of the main content and methodical lines of the course, leading to automatic skills in solving exercises and problems of basic form. By contrary the non-standard, logical, fun problems permanently are included to repetition problem solving.

Math Curricula in UkraineThematic planning


IPMAWhat is the matter of IPMA test?


What is the matter of IPMA test?

1. We use IPMA test as a compass in our research explorations –where are the better or worse results.

2. We use IPMA test as a final criteria of good educational practice.


But why are we sure that IPMA test is really such a tool? Our colleague Prof. E.Smirnov made an attempt to understand, what is the matter of the test items. He

proposed a classification of primary Math skills and analysed the items of the IPMA test from the point of view of this classification. We can agree or disagree with Prof. E.Smirnov arguments but we

should to try to penetrate more deeply into this question.

Test analysis

There are the developed theoretical background for preparing Hi-Fi tests and analysis of the test quality. We have a valuable sample of data. It should be interesting to make such analysis and evaluate the statistic characteristics for thewhole battery of items as well as the characteristics of the separate items: validity, complexity, and discrimination.

There are a lot of special packages for test analysis, for example, Testan – freeware software.

We can do such a work in Ukraine, if it is interesting for the project (this analysis can be done on the world set of data or on the Ukraine subset).


The content of items

What is the aim of Math education?Prof. E.Smirnov classified the majority of items of the IPMA test as algorithmic items

(their total weight is 46 from 81!), e.g. items, which can be solved by routine, reproductive procedure.

Is solving of algorithmic problems the main aim of Math education?

All algorithmic problems can be solved automatically with any CAS – package (CAS means Computer Algebra System), for example with the package Derive, which is a component of graphic calculator TI-92.


The content of items

Maybe CAS – systems should be used in education more widely? This allows us to spend more text problems, real problems, open problems?

Can we answer on this question with current IPMA test? Yes, but we should allow students using of graph calculator during the test (at least allow it to part of our students and compare results).


Algorithmic and non-algorithmic problems

The problem 4 Prof. E.Smirnov did not classified as algorithmic. But it depends from the curricula! If the students dealt with sorting of linear array, if they acquainted with sorting algorithm – it is an algorithmic problem! From another side, the sorting algorithms are not now in standard library of functions, but we can define the user function that will realise any sorting algorithm.


The content of itemsWe give below the commands which are needed for “teaching Derive” to solve sorting

problem by simplest bubble method. From now on for sorting any array it is sufficient to call the function BUBBLE with parameter – array that is needed to be sort.


The scaffolding method

The matter of it is to insight the algorithm for solving some kind of problem and then program it in appropriate environment, the most suitable for this is the CAS-packages with implemented modules for functional programming, for example, Derive or TI. The most productive aspect of “the scaffolding method” is that the teaching strategy becomes the strategy of construction the “tree of knowledge” and all algorithmically solvable problems would be solved in automatic mode. As one of the consequences of SM: at the step of studying of the new materials all the students can solve any previous type of math problem.

ICT “scaffold” the level of skills in solving the basic problems.


Correctness of math problem

Items 7,11, 20 are not the correct math problems. Any finite sequence can be proceeded in infinite different ways. There is needed additional information in the correspondent items; for example, the desired sequence should be mentioned as the arithmetic or geometric progression.


Math skills and math competences

In many countries the interest to math competences continuously grows, in particular it is so in Russia and Ukraine.

The math competences include common math competences (understanding the place of math in human culture, relationships of math with real world, art, the matter of math method and so on), and special math competences (basic math concepts, skills in solving of different kind of problems and so on).


IPMA and other international comparative projects

The common Math competences are closely connected with views on Math, Math teaching and learning, and Math believes. The common math competence can’t be evaluated by any test, but it is an important component of math culture. The common math competence can be evaluated by the responses on the special type of questionnaire. In the middle of 2000th there were an interesting project concerning the Math believes – MAVI. The matter of this project was the analysis of questionnaire responses of the 7th grade students. The analysis of the responses gives a lot of interesting information.

Materials in comparison of views of the students in Ukraine and Finland in a framework of MAVI project are given in appendix to this report.

It should be interesting to study relations between MAVI – responses and attainments in IPMA project.


National materials in Math education and IPMA

Materials collected in a framework of IPMA project are really a treasure as for researchers as well as for practical educators. It should be interesting to prepare special issues with math curricula in different countries, description of math teacher teaching, collections of video clips of good practice, description of appliances, computer programs.


Gymnasium “Ochag”

The secondary school of the I-III level “Gymnasium OCHAG” was founded in 1992. It is a private school – its leader (the director and founder in one person) –Eugene Medresh. Gymnasium is one of the first private gymnasiums not only in Kharkiv but also in Ukraine as well as in former USSR. At this moment 225 students graduated from the “Gymnasium OCHAG”, 25 of which graduated with honour (silver and golden medals). All the graduates of the “Gymnasium OCHAG” proceed their education in the best universities of Kharkiv, Ukraine and abroad. Among the students of the “Gymnasium OCHAG” there are a lot of winners in Ukrainian and international competitions, Olympiads, participants of different humanitarian programs.


Gymnasium “Ochag”

The science and methodical work in “Gymnasium OCHAG” varies in forms: pedagogical workgroups, conferences, seminars, group reflections, etc. A lot of teachers have publications in different scientific and methodical issues. The primary teacher Kurganov S.Y. has more than 200 publications. He published a book “Student and a teacher in educational dialog” wined the first prise in the competition in Russia on the best publication in pedagogy in 2000 year. He is one of the authors of a new educational approach “The Dialog of Cultures”.


IPMATeacher Style in Ukraine


Teacher Style in Ukraine


“The role of a teacher nowadays was dramatically changed: from the sage at the stage to the guide by the side”.

Excerpt from the UNESCO report “Math Education in 21 century”, lost by the coordinator from Ukraine

This paradigm more and more penetrates to the wideeducational practice in Ukraine. The video clip of a lesson in school“Gymnasium “Ochag”” is a real demonstration of such teacher style of future.



Developing education, constructive approach, creative thinking, critical thinking, … What lays in the base of any of these and other educational

innovations? We think that the base is the emancipation of a student. The 20th century was not only the century of terrible wars, not only the

century of ICT, the most valuable characteristic of the 20th century is as the century of emancipation.



Emancipations of women, race emancipation, emancipation of childhood, emancipation of history, emancipation of cultures,

emancipation of life – the steps of this great emancipation process. What does it mean “emancipation”?

In this context it means not only equity of rights, but also much more –understanding and acceptance that

all in this World is self sufficient, complex, unique and remarkable.



“Each Child has rights for:¨ Be himself / herself;

Today;Death.“

Yanush Korchak, famous Poland pedagogue

It is so difficult to understand these, much more difficult to follow these in real life.



“Each child is talented. The teacher mission is making all the best for developing student’s talents.”

Vasiliy Sukhomlinsky, famous Ukrainian pedagogue

It was so remarkable when in the discussion at the meeting on the IPMA project the idea was sounded that

principles of the developing education can be used only with talented child.

At the moment the audience reacted that there are no non-talented child at all – this is a nonsense.



Of course there are a lot of obstacles on the way of such humanistic pedagogy in Ukraine:

¨ 1.The remainders of the communist totalitarity;¨ 2.Class size

(it is so difficult to follow collaborative pedagogy, principles of the person oriented, developing education when there are 35 students in the class);

¨ 3.Great amount of class work: 24 hours per week;¨ 4.Low salary level:

50$ US per month as a consequence teacher works 36 and more hours per week;



¨ 5.Low level of Informatization, which implies the restricted access to world experience and contacts;

¨ 6.Low level of Informatization, which implies low level of technical support for teacher work;

¨ 7.Low level of Informatization, which implies obstacles for implementing and wide usage of packages supporting educational explorations as a base of developing education (CAS and DG, for example).

year 2-3 march 2003 – september 2003

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