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A study is presented on the strategies employed to solve additive change problems by three students with intellectual disabilities (two of them with autism spectrum disorder). The students followed a program involving modified schema-based instruction. The results show an improvement in the problem-solving skills of the three students, who achieved successful formal strategies associated with identifying the operation. We analyze the importance of adapting and/or emphasizing certain steps in the instruction process in order to tailor them to the difficulties of each student.

A b s t r a c tThis paper shows how to solve homogeneous polynomial systems that contain parameters. The Hilbert function is used to check that the specialization of a 'generic' GrSbner basis of the parametric homogeneous polynomial system (computed in a polynomial ring containing the parameters and the unknowns as variables) is a Gr6bner basis of the specialized homogeneous polynomial system. A preliminary implementation of these algorithms in PoSSoLib is also reported.

Whensymbolically solving inverse kinematic problems for robot classes, we deal with computations on ideals representing these robot's geometry.Therefore, such ideals must be considered over a base field K, where the parameters of the class (and also the possible relations among them) are represented.In this framework we shall prove that the ideal corresponding to the general 6R manipulator is rezd and prime over K. The practical interest of our result is that it confirms that the usual inverse kinematic equations of this robot class do not add redundant solutions and that this ideal cannot be "factorized", establishing therefore, KOVACS [7] conjecture. We prove also that this robot class has six degrees of freedom (i.e. the corresponding ideal is six-dimensional), even over the extended field K, which is the algebraic counterpart to the fact that the 6R manipulator is completely general Our proof uses, as intermediate step, some dimensionality analysis of the Elbow manipulator, which is a specialization of the 6R.

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