Trakia Journal of Sciences, Vol.1, 2003

Series Social Sciences, No 1, pp 44-46

Copyright © 2003 Trakia University

Available on line at: http://www.uni-sz.bg

ISSN 1312-1723

Original Contribution

INTERDISCIPLINARY INTEGRATION BETWEEN TEACHING ALGEBRA AND GEOMETRY ON THE BASIS OF THE NOTION FUNCTION IN 8TH FORM

Galia Kozhuharova*

Department of Information and Qualification of Teachers, Trakia University, Stara Zagora

ABSTRACT

This paper unveils some potential for interdisciplinary integration of school subject content in algebra and geometry on the basis of the notion function in the teaching of mathematics in 8th form. The interdisciplinary integration is performed between algebra and geometry – and more specifically with the geometrical representations and graphics of functions, geometrical representations as images and extreme geometrical problems.

Key words: Education, Mathematics, Function

G. KOZHUHAROVA

INTRODUCTION

One of the basic tendencies in the modern development of science is the integration of scientific knowledge. That is why it is a main attribute of innovation in education. Mathematics is among the integrative sciences and the corresponding school subjects, since the knowledge it gives has a significant influence on the different aspects of human activity, and to the different school subjects in particular. In these trends there is much to rethink with a view to building such a structure of the school subject, which could project its integrative potential in a straightforward manner[.].

A basis of the interdisciplinary integration are notions, categories, laws and theories, which are characterized by a higher level of common ground and they are a sort of a “knot”, in which the synthesis is performed by way of necessity. The general scientific notions, categories, laws, etc. play the role of the integrative knots. Function is such a notion.

The aim of the current study is to give some results and conclusions of the experiment, a part of one totality research about application of functional approach in mathematical teaching in 8th grade in school.

METHODS

In our experiment work we research some potential for interdisciplinary integration of school subject content in algebra and geometry on the basis of the notion function in the teaching of mathematics in 8th form. The interdisciplinary integration is performed between algebra and geometry – and more specifically with the geometrical representations and graphics of functions, geometrical representations as images and extreme geometrical problems.

Except possibilities, obligatory classes have got, it has implemented free choose classes schooling of mathematics in 8th grade, containing four basic themes.

In Theme 1 “Functions and images” contemporary grasping for term “function” is summarized, exactly function as a image. Especially place is given of measurement like a images, We show them in appliance of functions in nature-scientific objects in school, and in realizing of interdisciplinary and inner integration interactions.

It is realized inner disciplinary links with learning in 8th grade geometrical images – translation, rotation, axes and center symmetry after summarizing of term “function” as a image.

In Theme 2 “Application of geometrical transformations in building of drawing of functions” We show to pupils change (transformation) of drawings of functions depending them properties - even or odd, from availability of sign of absolute value, conditions for “stretch” or “fold”, for translation along coordination axes.

In Theme 3 “Extreme geometrical problems” we offer systems of problems for minimum and maximum, there solutions use geometrical transformations. We make with this preliminary preparation for solving of extreme problems with elementary methods and show vary good application of geometrical transformations.

In Theme 4 “Graphical solving of equations and unequations. Parametrical equations and unequations” We realize inner disciplinary summary on the base of terms “drawing of the function”, “equation” and “unequation”. We use here observed transformations of a drawing of some functions for solving of parametrical equations and unequations.

Establish and forming experiment was implemented and tree technological variants was used.

Ist variant. Applying of preliminary created model for function applying approach in schools with abilities for addition learning of mathematics (NMS – St. Zagora and Gabrovo, IS – St. Zagora).

IInd variant. Applying of model in classes without addition learning of mathematics.

IIIrd variant. Traditional methods learning without especially created model for function applying approach.

RESULTS

Receiving results have to give answer of the question of learning of term “function” about following criterions:

1. Stage of learning of term “function”.

2. Interdisciplinary learning of term “function”.

3. Solid of getting learning.

To ensure validity and reliability of results during forming experiment was implemented we use diagnostic procedure for establish level of learning of term “function”.

To process of receiving results of the experiment we apply one factor dispersion analyses by “method of learning” for the tree technological variants.

We observe the general sets G1, G2 и G3 of pupils, they was learned by Ist, IIed, and IIIrd technological variant. We choose 24 pupils from each of them and do the applied test.

We choose probability of error , and we formulate null hypothesis:

Но: Are the general sets G1, G2 and G3 identical, or

Н1: Are not the general sets G1, G2 and G3 identical, with chosen probability of error

If Но, is confirmed we well able to say these methods are identical of statistical point of view, if Но, isn’t confirmed – they are different with probability of error .

At first we well proof G1, G2 and G3 are normal distributed. We do that with criterion of Pierson. Computing results are given in table below.

Table 1. Computing results.

I
technology
variant / II
technology variant / III
technology variant
calculated / 6,77 / 1,50 / 1,98
calculated / 7,82 / 5,99 / 5,99

We can see for all general sets G1, G2 и G3, therefore they are normal distributed.

Degree of freedom f is calculated in every different case depending of the data. Value of are taken from statistical tables for distribution.

Results of these calculations shows G1, G2 and G3 are normal distributed general sets with average and dispersion .

Table 2. Summarized table of averages point depending of technology variants and chosen criterions.

tech.
variant
criterions / I–st tech. variant / II-nd tech. variant / III-rd tech. variant
1 – level of learning / 35,28 / 31,72 / 29,64
2 –inter
disciplinary learning / 25,39 / 27,38 / 19,53
3 – solid of learning / 23,71 / 21,19 / 17,21

Figure 1. Drawing of averages of point depending of technology variants and chosen criterions.

Table 3. Summarized table of dispersions depending of technology variants and chosen criterions.

tech. variant
criterions / I–st tech. variant / II-nd tech. variant / III-rd tech. variant
1 – level of learning / 69,29 / 76,80 / 82,01
2 – inter disciplinary learning / 70,53 / 69,34 / 73,15
3 – solid of learning / 78,57 / 83,48 / 86,83

Figure 2. Drawing of dispersions depending of technology variants and chosen criteria.

The analysis of receiving results for different groups shows high achievement in pupils of 1st and 2nd technical variants of all three criteria.

CONCLUSIONS

1. Offered system of lessons for Free Chosen Schooling are suitable and accessible for pupils of 8 grade when learn “Functions and drawing of functions”. Its purposive and system use gives positive changes in knowledge pupils possibility.

2. The active methods we use contribute essential change in level of knowledge and its lasting. Pupils abilities for action in planning situations and take decisions are improved as a result of active inclusion in learning process.

3. Pupils orientation abilities in process of decision of practical problems of different field of study are improved too.

Trakia Journal of Sciences, Vol.1, 2003, Series Social Sciences, No 1

G. KOZHUHAROVA

Trakia Journal of Sciences, Vol.1, No 2, 2003

[.]*Correspondence to: Galia Kozhuharova, Dep. of Information and Qualification of Teachers, Trakia University, Stara Zagora