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 preuniversity 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.