Computational Thinking is part of the new curriculum in many countries and this new
competence is often combined with Algebraic Thinking. Both types of thinking are part
of the core of Mathematics and Computer Science. Algebraic Thinking is linked to acquiring
the ability to represent and generalize patterns in any application area. Furthermore,
the ability to communicate a mathematical argument, using the necessary language and
symbolism, is a skill that is dependent on training in this type of thinking. Although
Algebraic Thinking can be developed at different levels, and it is also developed
at university levels, more and more countries see it as a basic mode of thought that
should be encouraged from early childhood education. Algebraic Thinking has also a
close relationship with Computational Thinking, and they are currently united in different
situations, such as the international PISA student evaluation tests. We argue in this
paper that this is a transversal competence that can be practiced in any subject and
at any age. Sometimes combined with the process of teaching Mathematics. It is essential,
in our opinion, to strengthen the inclusion of strategies that encourage students
to reflect deeply on the concepts, theories, and applications they are learning, giving
rise, among others, to number sense and abstraction. In this paper, we present the
implementation of these two types of thinking, algebraic and computational, in the
pre-university curriculum, particularly in Spain, within a European project. In this
project, we seek to create more appropriate learning approaches for those who are
often disadvantaged and help them to take advantage of Computational Thinking and
Algebraic Thinking and, therefore, STEM knowledge, helping to a stronger and more
equal society. We analyze its status and its relationship with the concepts taught
in the different courses, although focusing on the subject of Mathematics.