CHAPTER 4: MATHEMATICAL KNOWLEDGE AND PROGRESS IN THE MATHEMATICAL LEARNING OF CHILDREN WITH SPECIAL NEEDS IN THEIR FIRST YEAR OF SCHOOL

The paper is a summary of an empirical study which showed that the ”mathe 2000” approach is feasible also for children with special needs. A research project conducted by the Institute for Special Education at the University of Freiburg, Switzerland, has evaluated the mathematical knowledge of children with special needs at the start of their school education. One definition of ”special needs” is children with learning disabilities. In Switzerland, these children are assigned to special classes where, as a criterion, an intelligence quotient between 75 and 90 is employed. Alternatively, so-called ”introductory classes ” are common in Switzerland. This kind of class is meant for children with partial delay in their development and, in some cases, when the maturity level required for entering the first class is questionable. Here, the subject matter of the first class is extended over two years. The children then enter either the second year of the mainstream class, or a special class for children with learning disabilities. Current approaches to initial mathematical teaching are strongly marked by an understanding of the concept of numbers developed by Piaget. It recommends introducing numbers step-by-step after a lengthy pre-numerical practice (several months, up to one year). Classification, seriation and number-conservation are considered as prerequisites for understanding numbers. However, the ”mathe 2000” approach (Wittmann; Müller, 2000) offers the sphere of numbers between one and twenty simultaneously. Exercises, which precede concrete calculation, are completely lacking. In addition, the emphasis lies on working with images of quantities with a given structure. The reasons for this are as follows: There are many studies showing that the numerical knowledge of first-grade children in mainstream classes is much higher than traditional schoolbooks assume. Lengthy pre-numerical practice, based on the concept of number by Piaget, is ignored because such an approach to mathematical learning is under question. For example, many studies show that number-conservation is not a prerequisite for the development o