International Journal for Technology in Mathematics Education, Volume 13, No 2 Experiments with Aplusix in Four Countries By Jean Francois Nicaud 1 , Marilena Bittar 2 , Hamid Chaachoua 1 , Parimala Inamdar 3 and Laura Maffei 4 1 Université Joseph Fourier and IUFM, Grenoble, France Nicaud@imag.fr Chaachoua@imag.fr 2 Universidad Federal de Mato Grosso do Sul, Campo Grande, Brazil, marilena@nin.ufms.br 3 Center for Research in Cognitive Systems, NIIT, Mumbai, India, ParimalaI@NIIT.com 4 University of Siena, Italy, laura.maffei@libero.it Received: 4 th October 2005 Revised: 12 th February 2006 The Aplusix system has been designed for helping students to learn algebra. Its capacity to tell the students whether their calculations are correct or not, to provide families of exercises of a chosen level, and to give scores after tests allows this system to be used in the regular functioning of the class. Its capacity to record the students’ actions and to replay the students’ work is a valuable feature for the researcher in mathematics education. In this paper, we describe four experiments conducted in four different countries with different goals: remediation piloted by researchers in Italy; remediation integrated in the regular functioning of classes in Brazil, collaborative learning in India, and learning and use during the entire school year in France. 1 INTRODUCTION Aplusix (Nicaud, Bouhineau and Chaachoua., 2004; a demo version can be downloaded in English, French, Spanish and Portuguese from http://aplusix.imag.fr) is a computer program that helps students in learning algebra, in the field of numerical calculations, expansions, factorisations, equations, inequalities, and systems of equations, mainly for grades 7 to 10 (ages 12 to 16). Usually, Aplusix is installed on the server of the school and used by the students in the computer laboratory. An administration program allows teachers to create and manage classes and students’ accounts. Aplusix contains 400 exercises grouped in families and structured in a map of exercises. They have random coefficients. Teachers also have the option of constructing their own lists of exercises through a special editor. The software records all the students’ actions and allows the teacher to observe the students’ work globally (through statistics) or in detail (with a replay system). Aplusix is available in French, English, Portuguese, Italian, Spanish and Vietnamese and is being translated into other languages, in particular German, Japanese and Arabic. It has been marketed in France since 2005 and will be marketed in other countries in 2006. One key feature of Aplusix is its advanced editor that displays and edits algebraic expressions in two dimensions. The editing facilities (input, delete, select, cut, copy, past, drag and drop) use the structure of the expressions, e.g. it is not possible to select 3 + x from 3 2 + x . With this component, students can do the calculations they want without any difficulties, either typing a new expression or modifying a copy of the previous one. Aplusix contains several modes. In the training mode, two fundamental feedbacks are provided to the student: the correctness of the calculation (see Figure 1) and the correct end of the exercise. Figure 1 The training mode of Aplusix, also called exercises activity. The student makes his/her own calculations. When a step is correct, a black equivalence is drawn between the two boxes. When a step is incorrect, a red-crossed equivalence is drawn between the two boxes. In this figure, the student has moved a sub-expression (selection and drag & drop) producing a non-equivalent equation. He/She has to change the sign to obtain an equivalent equation.