Dr. Labzovsky Sh.
Sapir Academic College,
Nahushtan Y.
Thinking and Learning Programs Development, L.T.D.

On Mathematics Teaching Purposes in elementary and secondary school

Here in the Table below we present the test and poll of children education in mathematics. These results are taken from the Ministry of Education research conducted in 1996 (the current results are expected in the middle of the year 2001).

 

The 4th grade

The 5th grade

Conclusions

 

J

N

J

N

Motivation

Positive attitude to mathematics

80%

70%

61%

70%

Decrease of motivation

Average

mark

Average mark

74%

53%

60%

42%

1.Decrease in the evaluation level of index J-school students

2.Difference between formal subjects marks and non-formal subjects ones

3. Elementary math’s knowledge doesn't influence the non-formal topics comprehension.

Formal subjects mark

79%

59%

69%

45%

Non-formal subjects mark

60%

43%

45%

36%

Use of TV and computer system

 

31%

23%

-

-

 

Reference: 1)The research was conducted in Israeli schools. Index “J” refers to schools with prevailing Jewish students, while index “N” – to non Jewish schools.

2) the number of teaching mathematics hours in J-index school is considerably higher than in N- index school.

Let us consider two amazing facts. First of all, the motivation decreases in J-index schools, but not in N-index schools. Secondly, elementary math’s knowledge does not influence non-formal topics comprehension, and the level of logic thinking in J-index school is exceptionally low< practically it does not differ from that in N-index schools. These two facts take place under condition in reference (2).

The first fact means that students feel bored at the lessons. From the second fact it follows that the system of teaching mathematics ruins harms the logic thinking. The essence of this problem is observed in the teaching process of any mathematical subject including teaching of applied mathematics at the University. Students require ready-made formulas and feel themselves uncomfortable when a creative process must be applied, e.g. problem formulation.

What is the matter? Maybe the teachers are not of high qualification, or the system of teaching itself is not suitable. All these aspects of mathematics teaching under consideration require a considerable reorganization. In our report we discuss one of the main aspects, namely, the purpose of mathematics education in the elementary school.

It is of special interest that the mathematics textbooks available in Israeli and Russian school differ mostly by the level of complexity of exercises, but not by their ideology. Besides, methodic literature does not formulate evidently expressed teaching purposes, although they can be understood from educational programs and textbooks taught and consist of

  1. Stable commands of manipulations with the number and simple operations with
  2. geometric figures;

  3. Elements of formal thinking (problem formulation and problem solutions defined by means of verbal description;

3. Elements of practical application of the gained knowledge.

All these purposes, arranged in the order of their importance do not coincide with the teaching purposes of other school subjects. In Biology, for example, the main purpose of teaching at the early stage is to stir the student’s interest in the subject (by means of amazing stories about nature and latest achievements in biology).

Other purposes of teaching biology together with the one mentioned above are:

  1. To transfer the knowledge in the subject which is characteristic for every educated personality to the student.
  2. To describe the essence of biology as a profession for a student to decide

whether to choose biology for deeper study in high school and maybe later at the

academic level.

Not rejecting the existing purposes in teaching mathematics, we, however consider as more natural the approach to mathematics purposes used in teaching biology.

Nowadays we have all the preconditions to organize the mathematics school curriculum according to new purposes of teaching. These preconditions are as follows:

  1. The level of up-bringing and teaching in Israeli kindergartens is much higher
  2. nowadays, than it was a couple of years ago when the existing mathematics

    textbooks appeared;

  3. The fact that a calculator is available in each Israeli family, makes it possible to
  4. simplify some complicated and routine topics such as multiplication and addition

    of fractions etc., which seem difficult for students to learn.

  5. The fact that a computer is available in each Israeli educational center and in

many Israeli families helps deepen and improve some teaching ideas.

Let us emphasize that the availability of computer programs such as “Mathematic”, “MATLAB”, “LINDO” can not but change the mathematics curriculum, which keeps less and less place for teaching routine elements, i.e. integration, solutions of differential equation, evaluation of extremums, etc. As a result, the modern school curriculum has to be prepared for such changes.

At present we go on are developing a school curriculum and a corresponding textbook with the computer program appropriate for the purposes mentioned above. It is based on the transfer of all the cultural mathematical values (historical facts, the most advanced mathematical achievements etc.) to the student to underline the necessity of logic thinking, while the most necessary routine elements are presented gradually and in the from entertaining the student. The contents of the curriculum and textbook includes general knowledge of the most important mathematical fields, such as infinitesimal mathematics, topology, optimization etc. to make a student understand the essence of mathematics and to choose it consciously for further deep study. We consider our program as the transition period program that is why it includes the all-necessary elements of the existing program.

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