VDW Ch 20: Geometric Thinking

Dr. Robert Raze, Jr.

EDE 4304

SPC

The Geometry “Big” Ideas…

What makes shapes alike or different can be thought of as properties, such as parallel or perpendicular sides, symmetrical or not, etc.

Shapes can be described in terms of their location in space (coordinate grid)

Shapes can be moved in a plane or in space. Shaped can be viewed from different perspectives,

and helps us to be able to mentally change the position and size of shapes.

Spatial Sense

Just as number sense implies a natural sense about numbers and their relationships, spatial sense is defined as an intuition about shapes and the relationships among them.

Spatial sense was once thought of as an innate ability; you either had it, or you didn’t. Not true!

NAEP has charted geometry progress since 1990, and students’ geometric reasoning at all levels has improved, due to more focus on geometric thinking in the curriculum.

Van Hiele levels of Geometric thought…

Dutch researchers whose work began in 1959, was first noted by Soviets, not until recently recognized in the US. But, the levels are now the driving force of US Geometry curriculum…

Consists of 5 levels, which describes the thinking processes, not how much knowledge should exist.

Van Hiele, con’t.

Level 0: Visualization Focus is on how shapes “look.” Can begin to

classify by shapes such as square, circle, etc. Level 1: Analysis

Focus is on the properties of shapes. Can think of a “class” of shapes.

Level 2: Informal Deduction Focus is on the relationships among properties.

“If-then statements…”

Van Hiele, con’t…

Level 3: Deduction Focus is on a system of assumptions and truths

that can be trusted in order to arrive at conclusions (traditional high school course)

Level 4: Rigor Comparisons and contrasts among systems

***In elementary, many students will be at Level 0, some at Level 1, and few will get to Level 2.

Sub-strands within Geometry Shapes and Properties

Activities: pgs. 406-410 Pattern Block manipulatives Tangrams and Puzzles Tesselations

Location Early grades: Early Position Game pgs. 424-425 Coordinate Grids (Paths)

Transformations Slides, Flips, and turns (Pentominoes!)

Visualization Shape Hunts Face Matching p. 430

Activities for Level 1

Shapes and Properties You must know all 2-dimensional shapes and

their general descriptions! See pg. 410, Table 20.1

Also, all 3-dimensional solids, pg. 412 Table 20.2 Activities can consist of Sorting and Classifying,

Constructing Shapes, Similar Figures and Proportions, etc.

Level 1, con’t… Location activities

Using coordinate grids to reflect across x- and y-axis Dilations with grid paper: coordinates mult. And divided to

make proportional figures Transformations

Symmetries Tessellations!!!

Visualization Viewpoints of structures activities ****Remember that elementary only goes up to Level 1,

and only in the upper grades. KEEP THIS CHAPTER available if you ever have to teach this kind of geometry!