**ERIC Number:**EJ859751

**Record Type:**Journal

**Publication Date:**2009

**Pages:**4

**Abstractor:**ERIC

**Reference Count:**3

**ISBN:**N/A

**ISSN:**ISSN-0045-0685

Finding the Area of a Circle: Didactic Explanations in School Mathematics

Stacey, Kaye; Vincent, Jill

Australian Mathematics Teacher, v65 n3 p6-9 2009

Learning about the area formulas provides many opportunities for students even at the beginning of junior secondary school to experience mathematical deduction. For example, in easy cases, students can put two triangles together to make a rectangle, and so deduce that the area of a triangle is half the area of a corresponding rectangle. They can dissect a trapezium and rearrange the pieces to make rectangles, parallelograms or rectangles and triangles, and so find the area of a trapezium from the area of other known shapes. The area of a circle, however, provides a new challenge. The curved edge poses a difficult mathematical problem, with an interesting history. In this article, the authors present several different explanations of the formula for the area of a circle, which have logically different status. Some are "light" versions of a proper mathematical proof, but others are not. However, they believe that they all have a role as didactic explanations in junior secondary mathematics. Explanations in school mathematics must do far more than "prove." The explanations were found in a survey of nine current Australian Year 8 textbooks. They saw a rich and interesting range of possibilities. In the sections below, they show some of the varieties of demonstrations found in their survey. (Contains 5 figures.)

Descriptors: Mathematics Instruction, Learning Activities, Concept Formation, Mathematics Activities, Mathematical Logic, Geometric Concepts, Educational Opportunities, Secondary School Mathematics, Mathematical Formulas, Validity, Foreign Countries, Grade 8

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Grade 8; Secondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers - Location:**Australia