Abstract:

The use of spreadsheets in mathematics education has been widely investigated both at elementary level, as a tool for collecting and organising data (in tables) and their presentation (by charts), and at secondary school level, for the semiotic mediation of more complex concepts such as variables (cell references), functions with their domains and ranges. Spreadsheets are often introduced and studied also as tools to ease the algorithmic approach to problem solving.
Many and still on-going important researches show how the shift from arithmetic to algebra is one of the most delicate and relevant steps in the pupils’ mathematical education process.
The spreadsheet proves to be an appropriate support to such shift, but the responsibility of smoothening the transition from the “numerical evidence” (made clear by the typical interactivity of the tool) to the “algebraic proof” is actually left to the pupil’s intuition, though assisted by the teacher.
In this paper we present a tool which may ease this transition: a numeric-symbolic spreadsheet - N3S - which is able to perform computations with both numerical and symbolic data. In fact, N3S allows the user to fill the cells not only with numeric values (such as ‘5 €’) but also with parameters (such as ‘x’ or ‘UnitaryPrice’). In the latter case, N3S (symbolically) propagates the parameters to all dependent cells, performing, if necessary, all relevant substitutions and/or simplifications.
In order to switch between equivalent formulae, N3S also provides the user with a menu which allows to perform the most common symbolic manipulations of the expressions contained in the cells (‘simplify’, ‘expand’, ‘factorize’, …).
An additional N3S’s feature is the capability to produce charts either from tabular data (as it usually happens for spreadsheets), or by directly plotting the function represented by the symbolic content of a single cell.
The double (numeric and symbolic) nature of N3S also supports problem solving activities, allowing a better understanding of the functional dependence of the results from the initial data. In fact, pupils can get a better understanding both at quantitative level, by “playing” with the problem numerical data, and at qualitative level, by using symbolic parameters instead (thus revealing the functional dependence).
In the paper, some examples of problems solved with the aid of N3S show its main features and provide evidence of its didactical potentialities.
Although N3S is still a (working!) prototype and its piloting is still in progress, we plan to release its final version as an open source tool. We also like to remark that N3S proves the advantage of the open source approach to the production of educational software, because it has been developed by originally combining complex but already available open source software.

Keywords:

technology, mathematic education, spreadsheets in education, introduction to.