Geoboards
Geoboards, usually made of wood, exist in different sizes and shapes. 25-point geoboards are have 30-cm sides a 5 x 5 network of equal size squares (6-cm sides) is marked out. In the centre of each square is a brass nail. On some geoboards, like the ones in the photographs below, the squares are not strongly marked. Elastic bands can be stretched over the nails so that segments, lines, angles, polygons, etc., are created.
Multiple situations in pure and applied geometry can be created and analysed. For example, in applied geometry a unit of length is the distance between two nails that are adjacent on a line parallel to the edge of the geoboard, and the unit of area is the square constructed from the unit of length.
By manipulating the elastic bands, the students can carry out their own research, observe the results of their actions and to make hypotheses.
"For teaching to be in agreement with the true activity of the geometer and all the time at the level of the pupils, it is ... enough to use perception and action in the proper direction...
...
The method consists in first allowing time for exploring the various Geoboards,...
... and then in establishing a graded exploitation of the situations involved, with the production of statements that express the findings."
Caleb Gattegno, Geoboard Geometry, 1971, pp 3-6
More information
Articles about teaching mathematics on this site:
A cautionary tale about rabbits and moles and choices - C J Breen
Humanising Mathematical Education - C J Breen
A Lesson on Fractions - Suzanne Lachaise
Mental Imagery in Mathematics - Maurice Laurent
Forcing Awareness of Mathematics: Self, Mind, and Content in Dialogue - Arthur B. Powell
Books by Caleb Gattegno available as web books:
The Science of Education Part 2B: The Awareness of Mathematization
The Common Sense of Teaching Mathematics
A Teachers Introduction to Arithmetic
Arithmetic - A Teachers Introduction to Cuisenaire-Gattegno Methods
Arithmestics Makes Arithmetic Child's Play
Gattegno Mathematics Textbook 1: Qualitative Arithmetic - The Study of Numbers up to 20
Gattegno Mathematics Textbook 2: Study of Numbers up to 1,000 - The Four Operations
Gattegno Mathematics Textbook 3: Applied Arithmetic
Gattegno Mathematics Textbook 4: Fractions, Decimals, Percentages
Gattegno Mathematics Textbook 5: Study of Numbers
Mathematics with Numbers in Colour Book VI: Applied Mathematics
Mathematics with Numbers in Colour Book VII: Algebra and Geometry