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:

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 1 st 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 - 1 st 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 - 2 nd grade: 2 D figures are given to see surfaces of 3D geometric figures. Orientation and size not mentioned - 3 rd 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 - 4 th 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 - 5 th 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 1 st through 5 th grade workbooks. - Orientation difference is not given for cube, cylinder, sphere, cone and circle in 2 nd grade and for rectangle and square in 3 rd grade, it is taken into account in 4 th and 5 th grade.

Content of Workbooks (published by a private publisher) - Size and orientation differences are not always taken into account in 1 st through 5 th 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 3 rd 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 4 th and 5 th grade, orientation and size differences in cube, disc and pyramids are not given.