AlNuSet

Alnuset (Algebra of Numerical SETs) is a system developed at the Educational Technology Institute (CNR Genova) by the participants in this operative unit as part of their work in the EC ReMath project. Alnuset is constituted by three integrated components: the Algebraic Line, the Algebraic Manipulator, and the Cartesian plan. Algebraic Line The algebraic line is based on a representation built by mathematicians over previous centuries, the numerical line. The algebraic line exploits quantitative properties and visual characteristics of the numerical line to pursue algebraic aims concerning the development of an algebra of quantities. The transformation of the numerical line into the algebraic line is made possible by the exploitation of technology allowing us to associate a letter to a mobile point on the line (i.e. to a point that can be dragged by the mouse) to reify the notion of an algebraic variable. This new operative and representative feature can be exploited to reify other algebraic objects, processes and relations: oto construct expressions involving algebraic variables and to represent them as points on the line. These points indicate the results of computation executed in sequence; oto drag mobile points corresponding to algebraic variables and to observe the movement of the points of the expressions involving them; oto search for polynomial roots with integer coefficients; oto explore and to identify the truth set of algebraic (in)equations and systems of (in)equations. Symbolic manipulator This environment has been designed to support an algebra of formal operations, performed in the current scholastic context and to integrate this with an algebra of quantities mediated by the use of the algebraic line. The manipulator makes available a structured set of basic rules that covers all the algebraic transformations foreseen in the current algebraic curriculum of lower and upper secondary school. These rules correspond to the basic properties of addition, multiplication and power operations, to equality and inequality properties between algebraic expressions, to basic operations among propositions and sets. Moreover, there are two specific rules that are also present in CAS systems which make it possible to determine respectively the result of a numerical expression and the result of a computation with polynomials. Finally three rules allow the user to import results obtained in the Algebraic line component. The system also allows students to create new transformational rules once these new rules have been proved using the basic commands available in the interface. Cartesian plan This environment is constituted by the algebraic line and by a cartesian plan. It is possible to select an expression represented on the algebraic line and to obtain its graph on the Cartesian plan, with respect to the value of a letter contained in the form of the expression and chosen as a variable by the user. The dragging of the point correspondent to the letter on the algebraic line determines (a) the movement of the point in correspondence with the expression on the line, and (b) the movement of the point in correspondence with the pair constituted by the letter and the expression values on the graph of the Cartesian plan.