Children can develop fairly sophisticated ideas about spatial visualization and spatial patterns during the primary grades. Many people think that skills so essential to success in a number of careers - carpentry, architecture, statistics, mechanics, engineering, map making, surveying, and design - are simply inherited. We have learned that children can develop and improve these skills when given the opportunity to do so.

Patterns consist of repeated elements. One of the most common spatial patterns that we experience and use are shapes. For example, a simple shape like a square contains repeated elements - a side and a right angle, repeated 4 times. Children's reasoning about shape generally follows a predictable sequence. Awareness of this typical sequence helps adults understand how a child's growth is progressing and what to expect next. However, the sequence is not lock-step; children often reason in all of these ways at the same time, but most of their reasoning will be at one of these levels.

It is very important for children to discover such properties and be able to talk about them. One of our goals is to help children develop rules about shapes, like "triangles have 3 sides and 3 corners (angles)". By developing these rules, children learn to make mathematical arguments and to apply their knowledge to shapes they have never seen before. Geometry is a form of reasoning that people have developed to describe and discuss space systematically. When children understand shapes as collections of properties (rules) they are on their way to higher level thinking and reasoning.

Another way for children to develop knowledge about shape is to think about shapes as paths - as a series of moves and turns.

*For example,
you can walk the path of a square by moving forward 10 paces, then turning right 1/4 of a turn, then moving forward 10 paces, turning right 1/4 of a turn, and so on. *

Remember that in one of the previous newsletters, you worked with your child to write directions for a path between two landmarks (e.g., your home and a friend's home). Your child will use a computer language, LOGO, that helps children develop ideas about shapes as paths.

Here's a small sample of LOGO's commands:

- F 5 - Moves the turtle FORWARD five turtle lengths.
- B 5 - Moves the turtle BACK five turtle lengths.
- TR 1 / 2 - Turns the turtle 1/2 of a whole turn to the right.
- TL 1 / 2 - Turns the turtle 1/2 of a whole turn to the left.
- FD 10 - Moves the turtle FORWARD 10 steps (a step is about 1/12 of the turtle's length)
- BK 10 - Moves the turtle BACK 10 steps.
- RT 180 - Turns the turtle 180 degrees to the right. This is the same as 1/2 of whole turn because each degree is 1/360 of a circle.
- LT 180 - Turns the turtle 180 degrees to the left.

After writing directions in the last newsletter, children have been using LOGO to make a model of their path on the computer. For example, if you walked 20 paces, turned right 1/4 and walked 10 paces, you might model this walk with LOGO as FD 20 TR 1/4 FD 10. If you have a computer at home, the Verona Schools have a site license for LogoWriter, a form of LOGO that combines word processing and turtle graphics. The site license will allow you to use LOGO at home. Please contact Betty Wottreng for details.