PRESCHOOLERS LEARN PROPORTIONALITY AND INTEGRATION THROUGH ICON-COUNTING AND NEXT-TO ADDITION

Abstract

Preschool allows rethinking mathematics outside the tradition of ordinary school. Seeing schooling as adapting the child to the outside world containing many examples of Many, we can ask: How will mathematics look like if built as a natural science about physical fact Many? To deal with Many we count and add. The school counts in tens, but preschool allows counting in icons also. Once counted, totals can be added. To add on-top the units are made the same through recounting, also called proportionality. Adding next-to means adding areas, also called integration. So icon-counting and next-to addition offers golden learning opportunities in preschool that is lost in ordinary school allowing only ten-counting to take place. 

Keywords

• count,add,proportionality,integration,preschool

References

1. Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathe¬¬matics education. Dordrect: Klüwer. Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht: D. Reidel Publishing Company Glaser B. G. & Strauss A. L. (1967). The Discovery of Grounded Theory. New York: Aldine de Gruyter. Kline, M. (1972). Mathematical Thoughts from Ancient to Modern Times. New York: Oxford University Press. Lyotard, J. (1984). The postmodern Condition: A report on Knowledge. Manchester: Manchester University Press. Niss, M. A. ´(2003). Mathematical competencies and the learning of mathematics : the Danish KOM project. 3rd Mediterranean Conference on Mathematical Education - Athens, Hellas 3-4-5 January 2003. Editors A. Gagatsis; S. Papastavridis. Athen : Hellenic Mathematical Society, 2003. p. 116-124. Piaget, J. (1970). Science of Education of the Psychology of the Child. New York: Viking Compass. Tarp, A. (2004). Pastoral Power in Mathematics Education. An ICME Trilogy. http://dev.mathecademy.net/wp-content/uploads/2013/05/An-ICME-Trilogy-online.pdf. p.59-70. Tarp, A. (2015 expected). ManyMath - MyMath. Publisher to be decided. YouTube video (2013). http://youtu.be/qgCwVZnALXA Zybartas S. & Tarp A. (2005). One Digit Mathematics. Pedagogika (78/2005). Vilnius, Lithuania.