The choice of appropriate educational materials, visual or physical, for teaching mathematics to children on the autism spectrum, is an important topic in the context of inclusive education. In this article we first focus on some theoretical issues concerning the manipulative material, on the teaching of proportional quantities in the Greek high school and the difficulties it presents, as well as on the Asperger syndrome. We present the design, the implementation and the basic results of a teaching intervention conducted in a 14-year-old student with Asperger syndrome studying in the 8^th grade of a high school in Greece on the use of manipulative materials for solving authentic real-world and word mathematical problems. The research showed that the student understood the differences between the real analogy and the illusion of linearity inherent in the problems he was given to solve using manipulatives. The paper concludes with suggestions, perspectives and limitations for teaching proportion problems and the tackle of the illusion of proportionality using manipulatives.

The choice of the appropriate instructional method for teaching Euclidean Geometry to children with Special Learning Difficulties is an important topic. In this paper we study some theoretical issues related to the teaching of geometric concepts to students with Special Learning Difficulties, focusing on the teaching material. We present the design, implementation and results of a qualitative research conducted with six 9th grade students in a Special Vocational High School in Greece, on the use of the website “Byrne’s Euclid” in the teaching of propositions of Euclidean Geometry. The research showed that the children understood the key points of the proof of the proposition we presented and they assimilated basic geometric concepts and processes using colors and figures. The paper concludes with a discussion upon suggestions, perspectives and limitations for teaching that utilizes Byrne’s Euclid.