### SCHEMATIC LEARNING OF THE ADDITION AND MULTIPLICATION TABLES | STICKS AS CONCRETE MANIPULATIVES

The Teaching, Mathematics
1998 unpublished
The numbers 1, 2,. .. , 20 are represented in the form of arrangements of horizontal and vertical lines and, when materialized, these lines are replaced by at, longitudinal, rectangular sticks each h a ving two sides dyed in two diierent colors. Sharp individuality of these arrangements is excellent for quick recognition of the numbers they represent. The way of arranging emphasizes the relation of the numbers 1, 2,. .. , 1 0 t o v e and ten and this \ten ngers" model is basic, both
more » ... and operationally, for our approach t o s c hematic learning of the arithmetic tables. In case of addition and subtraction, the chosen structures of the arrangements reeect clearly \crossings the ve and ten lines", serving ecently as illustrations (and explanations) of these methods. The suggested designs of pictured products m n are easily seen as m groups of n sticks and, in the same time, as groups of tens and ones. Wall maps of these designs might be used in the class, letting the pupil have t h e m t o f a l l b a c k on and so helping him/her form gradually a store of mental images related to the multiplication table. The use of space holders is also suggested to help the child compose the symbolic codes which immediately follow manipulative activities. Thus, a one-to-one correspondence between manipulative, reeective and symbolic operations is established, what also makes them connected in a child's mind. 1. Introduction. The addition table consists of all relations k + m = n, where k and m take values in the set f1 2. .. 9g and the multiplication table consists of all relations k m = n, where k and m take v alues in the set f2 3. .. 9g