Abstract: This research report presents an experience of the use of non-didactic situations according to the theoretical foundation of Guy Brousseau’s Didactic Situations and Vergnaud’s theory of conceptual fields, theoretical references that were used in the analysis of inquiry regarding conceptualization of the negative numbers, in a fourth year student of Basic Education in a school in Valparaíso-Chile. Using the Scratch environment as a resource, situations were created, with the intention that the student extends her conceptualization regarding these numbers and without prior knowledge of the formal aspects of these. As a result, it was evident that the student extended his conceptualization. It is a qualitative investigation, which used as instruments the interview and the recording of the student’s written productions to carry out the analysis, through this process it has been possible to recognize the conditions in which the numerical extension is reached for the case studied, which They are: recognition of the different levels of conceptualization of negative numbers, duality of the minus sign and acceptance of integer subtraction, and exploring the difficulties he had in learning concepts of negative numbers.

Resumen. En este informe de investigación se presenta una experiencia de uso de situaciones adidácticas conforme al fundamento teórico de las Situaciones Didácticas de Guy Brousseau y la teoría de los campos conceptuales de Vergnaud, referentes que se usaron en el análisis de la indagación respecto de la conceptualización de los números negativos, en una estudiante de cuarto año de Enseñanza Básica en una escuela de Valparaíso-Chile. Usando como recurso el entorno de Scratch, se crearon situaciones, con la intención de que la estudiante extendiera su conceptualización respecto de estos números y sin tener conocimientos previos de los aspectos formales de estos. Como resultado de ello, se evidenció que la estudiante extendió su conceptualización. Es una investigación cualitativa, en la que se utilizaron como instrumentos la entrevista y el registro de las producciones escritas de la estudiante para realizar el análisis, mediante este proceso ha sido posible reconocer las condiciones en las que se alcanza la extensión numérica para el caso estudiado, las cuales son: reconocimiento de los distintos niveles de conceptualización de los números negativos, dualidad del signo menos y aceptación de la sustracción de enteros, y explorar las dificultades que tuvo para aprender conceptos de números negativos.

BACKGROUND: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct AIM: This study was set up to apply Action-Process-Object-Schema theory to study primary teachers' understanding of addition and subtraction of fractions SETTING: The participants of this study comprised 60 undergraduate full-time students, studying to become teachers. The participants were enrolled in a foundational course in Mathematics because they had not passed Mathematics at Grade 12 level. This course was intended to help deepen their understanding of basic numeracy, allowing them to continue with further courses if they wanted to specialise in teaching primary mathematics METHODS: Data were collected using written responses of the pre-service students to two tasks that focused on operations with fractions. Ten students volunteered to be interviewed of which three are drawn upon in this article RESULTS: Many of the pre-service teachers coped well with addition and subtraction of common fractions with the same denominator. However, more than 52% struggled to carry out these operations on common fractions with different denominators, showing that their conceptions had not developed into object-level structures CONCLUSION: It is evident that the incorrect procedures have become embedded in the students mental schema. It is crucial that programmes for upgrading pre-service teachers should include opportunities for teachers to interrogate their personal understandings of the basic mathematics concepts