How Are New Turkish Textbooks Presenting

Geometric Concepts?

An Analysis of the Turkish New Elementary Mathematics Curriculum and

Textbooks in Terms of the Presentation of Geometric Concepts

By Veli Toptas

February 2010

Elisabeth Heurtefeu

Author and Publisher

Author: Veli Toptas

Department of Primary School Teaching

Faculty of Education

Kirikkale University, Turkey

Publisher in the U.K:

International Journal for Mathematic Teaching and Learning

online at: http://www.cimt.plymouth.ac.uk/journal/default.htm

Purpose and Background of the Research

Purpose:

Examine how geometric concepts are presented in the textbooks

Methodology:

Case study & comparative data analysis method, compare target points in the curriculum to curricular documents and cases in the textbooks

Context:

Major curriculum reform in Turkey due to international studies results (TIMSS in 1999 and PISA in 2003) showed that the Turkish Educational System did not produce quality math and science education at the elementary level. The results of students were particularly weak in geometry.

Predisposition for Geometry

Children naturally examine the direction of objects in space, their positions and orientations and perspectives, related forms and sixes of the shapes and objects and the relation of a change of an object to the change on the dimensions (Adam & Powel, 1995)

Learning geometry has 2 main functions

- Improving human’s spatial abilities: Spatial relations Spatial visualization – such as converting 2D forms into

3D objects Mental orientation = capacity to rotate an object seen

from a different angle, find your way based on visual representation tools such as maps or stars (example Polynesians sailing navigation method)

- Enabling students learn further Geometry, mathematics, and other subjects (examples:

architecture, engineering)

Abilities Developed with Geometry

SPATIAL THINKING- Can form an appropriate ground for the development of

mathematical thinking

- Can be improved by playing with 2 and 3 D objects and their pictures, measuring them, forming various structures and drawing their pictures

- Learning the meanings of abstract geometric concepts is directly related to the development and thinking level of students (note EH See Van Hiele Levels)

Content of Textbooks

IN THEORY

Textbooks content should help students with the formation of the concepts and conceptual relations. Therefore, it is necessary to determine the appropriateness of the presentation of the geometric concepts in the curricular documents, textbooks and workbooks.

- Give opportunities to students for modeling their own conceptual worlds

- Use and analyze the properties of 2 and 3 D objects - Use and analyze different representative systems

Summary of Article Findings

Textbooks and workbooks show inconsistencies and absence of rigor when it comes to presenting geometric figures. Most textbooks ignore the representation with different sizes and orientations.

The curriculum underlines the necessity to deal with the orientation and size difference systematically in the presentation of the geometric concepts. However, this is disregarded in the cnent of textbooks and workbooks.

In Conclusion

1) Starting in 1st grade, orientation and size differences should be taught systematically as well as including tools and materials from the real environment. Students can select and use properties and features of 2 and 3 D objects, and convert them (NCTM, 2000). This means not the repetition of the same activity over and over, but the use of different representations and presentations.

In Conclusion

2) During the process of generalization (abstraction) of a mathematical concept, while the relevant variable is fixed, the concept is formed by changing the irrelevant variables systematically.

For example, when teaching the concept of parallelogram, the properties “4 vertices and being parallel” are maintained but many sizes and orientations can be shown while maintaining the relevant properties. This will help learning concepts in a permanent and meaningful way.

To Find out More Details on the textbooks, see next slides

Content of Textbooks

GEOMETRIC FIGURES

- 1st grade: presentation of geometric objects (cube, prism, cylinder, cone and

sphere) given by sample activities with size taken into account as a variable but not orientation

- 2nd grade: 2 D figures are given to see surfaces of 3D geometric figures. Orientation and size not mentioned

- 3rd grade: Different sizes, angles and orientations are given for 2 and 3 D geometric objects (cube, square, triangle, rectangle, and circle)

- Learning the meanings of abstract geometric concepts is directly related to the development and thinking level of students

Content of Textbooks

GEOMETRIC FIGURES

- 4th grade: Sizes and orientations are taken into account

to explain properties related to angles. No information related to sizes and orientation when dealing with 3D geometric objects

- 5th grade: Some samples from the living in-school and out-school environment. However, figures are given horizontally in the plane to explain properties of the cube, rectangular prism, square prism and triangular prism. No variation in size and orientation.

Content of Workbooks (published by the Ministry of Education)

- Size difference is taken into account in the 1st

through 5th grade workbooks. - Orientation difference is not given for cube,

cylinder, sphere, cone and circle in 2nd grade and for rectangle and square in 3rd grade, it is taken into account in 4th and 5th grade.

Content of Workbooks (published by a private publisher)

- Size and orientation differences are not always taken into account in

1st through 5th grade books. Open / closed figures are not mentioned at all. There is a comprehensive diversity in the tools and materials and sample models used.

- For 3rd grade, size and orientation differences are related to intersecting, vertical, horizontal, inclined and parallel lines and the types of angles. But triangular, rectangular and square prisms are not presented.

- For 4th and 5th grade, orientation and size differences in cube, disc and pyramids are not given.