Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We offer a detailed critique of a research group who promote the movement of introducing algebra in primary school ("Early Algebra"). Method: In this collaborative research, we show how to promote advanced numerical-algebraic thinking through experimentation with certain activities (problem situations) in two groups of secondary students (grade 9), with 24 and 36 students, respectively. We use a specific methodology for collaborative learning, scientific debate and self-reflection (ACODESA methodology). Results: The pupils in this study constructed covariational reasoning as a prelude to the function concept. They also developed control elements that helped them in the process of solving problem situations. Discussion: Numerical reasoning is essential to giving meaning to the syntactic processes that, if manipulated or conceived of incorrectly, can lead to an error in a given situation. Advanced numerical-algebraic thinking helps us develop sensitivity to contradiction, enabling us to detect error. We believe that working with manipulative materials and producing functional representations that can evolve into institutional ones, and using collaborative learning with scientific debate and self-reflective reasoning (ACODESA methodology), can help pupils to more easily retain their mathematical concepts over time. (Contains 3 figures.)