“Geometry” Is A Verb: Making Elementary School Geometry...
Transcript of “Geometry” Is A Verb: Making Elementary School Geometry...
“Geometry” Is A Verb:Making Elementary School
Geometry Come Alive
Tad WatanabeKennesaw State [email protected]
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/