STUDENT ’ ALGORITHMIC, FORMAL AND INTUITIVE KNOWLEDGE: THE CASE OF INEQUALITIES

This paper presents a study that aimed at investigating Italian and Israeli high school students ’ solutions to algebraic inequalities. The findings of this study are analysed with reference to Fischbein ’ notions of intuitive and algorithmic knowledge. Students ’ intuitive ideas and their algorithmic models when solving algebraic inequalities are identified and discussed. Our claim is that students intuitively used the solutions of equations as a prototype for solving inequalities. They developed an equation-algorithmic model for solving inequalities. Students were intuitively drawing analogies to either correct or incorrect solutions of related equations, either by excluding only zero values when dividing both sides of an inequality by a not-necessarily positive value, or when dividing by an expression without the exclusion of zero values as well. The latter tended to use the balance model when solving both equations and inequalities, explaining that it is always permitted to “do the same thing on both sides ” of either an equation or an inequality. Student ’ algorithmic, formal and intuitive knowledge: The case of inequalities In his analysis of students ’ mathematical performance, Fischbein (1993) related to the algorithmic, the formal and the intuitive components. Algorithmic knowledge is the ability t