Logical Arrangement of Topics in the High School Geometry Curriculum: An International Comparison
This paper compares the sequence of topics in geometry courses in the high school curriculum in Texas and Russia. Four textbooks used in Texas and Russia were selected for this comparison.
The order of topics of a course could be arranged in different ways depending on students’ learning objectives, preference of the instructor and other factors. The objective of this investigation is to compare the sequence of the topics in the course, determine how the sequences of topics correspond to the purpose of the Geometry course and its expectations, and understand why the topics of the course were arranged in such a way.
Some attention is devoted to the comparison of different definitions of the term “logical” and the usage of this term in this investigation. It turns out this term has a variety of meanings. Almost every author understands the term “logical” in different ways. So, the problem of any educational course is to define a set of certain logical rules which correspond to the purpose of the course.
The author recognizes two approaches in constructing a geometry course:
1) Topic approach – when sections of the book are being arranged in accordance with the complexity of objects/terms under consideration. Such an approach is most suitable for basic education with moderate complexity and expectations.
2) Proof approach – when sections of the book are arranged following proofs of theorems or properties of figures. These types of courses are better suited for more rigorous programs which require a higher-level of complexity and expectations. In Texas, they can be found in Pre- AP, AP and IB curriculum.