Revisiting Elementary Arithmetic Through the Development of Iterative Sentences: Some Brief Reflections about the Ordering of the Corresponding Teaching Activities

Abstract

This experience has taken place at the School of Education of the Universidad Complutense de Madrid. The goals of the subjects considered are to show how the computer can help in the teaching-learning process in Primary and/or Secondary Education and to clarify and strengthen the mathematical concepts of our students. Mastering a specific computational language or package is not a goal. We’ll focus here on a very specific problem, discussed and precised together with the second author: implementing arithmetic operators as nontrivial examples of iterative sentences (not exactly using Peano's arithmetic, but a similar constructive approach). We’ll analyse along the article why we believe the best ordering for developing the corresponding algorithm and implementing the code for the operators: power (with positive integer exponent), multiplication (by a positive integer) and addition (of a positive integer), is the reverse ordering in which they are introduced in elementary mathematics or introduced in an axiomatic.