“Geometry” Is A Verb:Making Elementary School

Geometry Come Alive

Tad WatanabeKennesaw State Universitytwatanab@kennesaw.edu

http://science.kennesaw.edu/~twatanab/Geometry.pdf

Geometry: NCTM Focal Points• Geometry: Composing and decomposing

geometric shapes (Grade 1)

• Geometry: Describing and analyzingproperties of two-dimensional shapes (Grade 3)

• Describing three-dimensional shapes and analyzing their properties, including volume and surface area. (Grade 5)

Geometry in Japanese Curriculum

Geometry in Japanese CurriculumThe main objectives of this domain (geometric figures) are to help children:– Understand the basic idea of geometric figures

and space,– Foster a rich sense of the geometric figures,– Utilize the concepts and properties of geometric

figures– Learn to think logically– Foster mathematical way of thinking– Understand the merit of mathematical

manipulation

Geometry Instruction

… since being interested in and exploring figures, logical relationships, and how to manipulate them are basic to creating new things and also related to enriching human character, it is necessary to consider enriching children’s sense of beauty and developing their affective sides.

Teaching Guide, p. 32

Geometry InstructionActivities related to geometric figures:• Discriminating geometric figures• Composing (drawing a figure of)

geometric figures• Investigating the properties of

geometric figures• Focusing on the relations among

geometric figuresTaching Guide, p. 32

Geometry InstructionWhen having children do activities such as concrete manipulation, teachers need to keep in mind that it is important for children not only to have fun but to have specific goals for the activity, to do the activity in a manner which is suitable to accomplish the end, to write down what became clear, and to confirm it.

Teaching Guide, p. 33

Geometry Topics in Gr. 1-6• Grade 2

– Triangles & Quadrilaterals– Rectangles & Squares– Right triangles– Shape of a box

• Grade 3– Isosceles & Equilateral triangles– Circles & Spheres

Geometry Topics in Gr. 1-6• Grade 4

– Trapezoid, Parallelogram, & Rhombus– Rectangular prism & cube

• Grade 5– Regular polygons

• Grade 6– Prisms, cylinders, pyramids and cones.

Grade 1

Grade 1

Grade 1

Grade 1

Grade 2

Grade 2 Right angles

Grade 2 Rectangles

Grade 2Squares

Grade 3

Grade 3 Circle

Grade 3 Learning & practicing how to use compass

Grade 3 More Circles

Grade 3 Compass as a Tool

Grade 3 More on Compass

Grade 3 Classifying Triangles

Grade 3Definitions are derived from children’s problem solving

Grade 3 Understanding through drawing geometric figures

Grade 3 Understanding through drawing geometric figures

Grade 3 Understanding through drawing geometric figures

Grade 4 Quadrilaterals

Grade 4 Perpendicular

Grade 4 How to draw perpendicular lines

Mathematics Frameworks

Grade 4 Unit 4

Grade 4 How to draw perpendicular lines using set squares

Grade 4 Parallel lines

Grade 4 Parallel lines

Grade 4 Exploring parallel lines

Grade 4 Drawing parallel lines using set squares

Grade 4 Drawing parallel lines using set squares

Grade 4 Drawing parallel lines using set squares

Grade 4 Drawing parallel lines using set squares

What was the definition of rectangles?

What can we say about the sides of rectangles (and squares)?

They are parallel.

Grade 4 Trapezoids, parallelograms, rhombuses

Grade 4 Trapezoids

Grade 4 Parallelograms

Grade 4Rhombuses

Grade 4Exploring rhombuses

Grade 4Exploring rhombuses

Grade 4Exploring quadrilaterals

Grade 5 Congruent Figures

Grade 5Exploring Congruent Figures

Grade 5 Drawing Congruent Triangles

Elementary School Geometry

• It must go much beyond simply recognizing and naming geometric figures.

• It must be based on students’ activities -folding papers, working with blocks, drawing/constructing, etc.

• Teachers must have a clear goal for each activity.

Japanese Curriculum Materials• Tokyo Shoseki Textbooks• Teaching Guide for the 1989 Japanese

Course of Study (Elementary and Lower Secondary)

• Excerpts from Japanese Curriculum Materials (Whole Numbers, Rational Numbers, Geom & Meas, Algebra)

• Available from Global Education Resources

http://www.globaledresources.com/