This family of situations especially addresses the following items:
flexible access to a diversity of representations of functional objects,
and connections between these;
dynamic access to families of functional objects depending on one
or several parameters (through the use of sliders).
Aims for trainers
Providing trainers with a class of situations where algebraic resolutions of functional equations can be relied to graphical intersections of curves and to numerical tables with varied levels of complexity;
Showing how technology can be useful for connecting algebraic and functional frames or algebraic, numeric and graphical registers in the context of resolution of equations;
Showing how these different perspectives can be approached and worked out with teachers, using such a class of situations;
Comparing the respective affordances of different technological tools, and helping trainers to choose those they would give priority in a training program according to the context;
Showing the interest for a trainer of thinking in terms of class of situations whose particular exemplars are characterized by specific values of identified didactic variables, and of approaching these situations with different technological tools, for allowing flexibility in the design and adaptation to different targeted audiences, and also for supporting the consolidation of trainees’ professional knowledge.
Aims for trainees
Showing that resolutions of algebraic or functional equations present a strong didactic potential for connecting numerical, graphical and algebraic representations, form grade 8-9 (resolutions of first degree equations, systems of two first degree equations) to grade 14 (resolutions of complex functional equations with parameters). A teacher can easily vary the types of equations or functions involved, for adapting the tasks proposed to students to their mathematical knowledge and competencies, and if desired, differentiating the tasks given to different groups of students;
Showing that resolutions of algebraic or functional equations can be adapted with several software, each of them leading to the development or mobilization of core ideas or properties attached to functional objects in secondary schools: numerical tables, graphical curves and algebraic formulas.
Aims for student (pupils)
Offering students an educational experience for resolutions of algebraic or functional equations in both numerical, graphical and algebraic contexts and connecting the three contexts, with technology efficiently supports mathematical activity;
Developing jointly their mathematical and technological competencies, through the work on equations from a diversity of perspectives, with the support of technology;
Offering students the possibility of resolving complex type of functional equations with or without parameters, discussing the existence of solutions helped by technology manipulations.