Abstract:

In the kindergarten (3-5 years old), mathematics plays an important role because it is at that period that children begin to have a first contact with that science and start to know all the mathematical content that go being deepened throughout its journey academic.

In the Portuguese case, mathematics in kindergarten takes on a domain of its own content that is inserted in the area of "Expression and Communication" and that appears in the Curriculum Guidelines for the kindergarten of the Ministry of Education. Particularly, the most varied opportunities for classification and serialization around us are also fundamental for the child to construct the notion of number, as corresponding to a sequence (ordinal number) or a hierarchy (cardinal number). In this age group the number definition is not required, but its construction and comprehension, as well as the distinction between digit and number.

In the first years of basic education, mathematics plays a key role in clarifying what was less consolidated in kindergarten, so that the children create their own definitions of mathematical knowledge that will deepen throughout his life and applying in their day routine. In particular, the topic of numbers is also important in this age group (6-9 years old). The teaching of numbers has not always been as we know it today. In the past, this teaching was centered on algorithmic, routine, and formal calculus, where understanding about numbers was undervalued. In Portuguese case, the particular sub-topic of non-negative rational numbers is included in one of the three mathematical contents for the first year’s basic education “Numbers and Operations”.

Rational numbers begin to be worked out in the first two years of this level of basic education, with an intuitive approach from situations of equitable sharing and division of unity in equal parts, using models and fractional representation in the simplest cases. It is in the 3rd and 4th years of the basic education that the study of these numbers is going to be deepened, either by using problems that allow other meanings of the fractions to be worked on, or by introducing numbers represented in decimal form from situations of equitable sharing or measurement, refining the unit of measurement. The learning of rational numbers is peculiarly complicated, with considerable studies proving that pupils show many difficulties in learning these numbers, including fractions, decimals, and percentages.

In an attempt to make teaching and learning of this topic more accessible, both for teachers and students, we present in this communication some proposals of tasks that have arisen within the framework of the Supervised Teaching Practice of the first author that can be developed, both in the kindergarten as in Basic Education and constitute a proposal of intervention in these levels of education.
In addition to the mathematical approach, we aim to highlight also the importance of interdisciplinarity, particularly in the teaching and learning non-negative rational numbers in the basic education.

Keywords:

Mathematics, practical pedagogy, rational numbers, interdisciplinarity, teaching and learning.