### Joensuu and Mathematical Thinking

#### by G Malaty

Article

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Effective and Joyful Ways of Teaching Mathematics   (2010-03-11)

 by mathseducator

This Paper resented the factors behind the work the author has made to develop mathematics education in his country, Finland. The strategies of teaching he uses are effective in both aspects: Quality and Quantity. For instance, the approaches he uses to give the children to discover the decimal system and the role of zero as placeholder are of such type. It brings both: economy of time and deep understanding. From one hand the economy of time is an outcome of deep understanding, and from the other hand going from ones to ten and from tens to hundred in relatively short time brings deep understanding of decimal system.   These approaches makes the discovering of Ten and Hundred as new unites an easy task do not need more than 3 classes of 45 minutes, including exercises, where operating with tens and hundreds is of the same difficulty of operating with ones. His use of his own box for Unifix materials, combined with his use of his own type of dynamic visualization give the children the chance to easily discover Ten and Hundred as new unites in a short time after dealing with ones, from 1 to 9 and 0. This all is done in a way that brings to children joy of discovery and as well fun by doing in hands and register every work in time in a 9 squared figure. Here to notice, that for the discovery of Ten and Hundred he doesn't use a figure of 10 squares as commonly used, but he uses a figure of 9 squares. This from one hand form isomorphism between the figure and decimal system and from the other hand this gives children to discover the new unit through solving a problem caused by having only 9 squared figure and 10 of unifix blocks. This figure in addition has 5 squares in a row and 4 squares under the first 4 of the firs row from left. This from one hand gives metaphoric relation with the word nine’s origin and from the other hand shows to children that one only is missed to get a higher unit. This work can be a model for those searching for meaning for spiral education, discovery and constructivism. But it is also a good example of using visualization manipulatives as associations and metaphors. Not forgetting heuristic questions type and its role. (Genuine work).