The aim of this paper is to examine whether the use of a hypothetical learning trajectory as a guide to notice students' mathematical thinking could improve pre-service teachers professional discourse and enhance pre-service teachers' noticing. Twentynine pre-service primary school teachers participated in a learning environment in which they had to interpret students' thinking about the fraction concept using a hypothetical learning trajectory as a guide. Results suggest that using a hypothetical learning trajectory as a guide helped pre-service teachers develop a more detailed discourse when interpreting students' mathematical thinking, enhancing their noticing skill. The enhancement of the skill of noticing, however, was linked to pre-service teachers' mathematical content knowledge. This research provides teacher educators with resources to help pre-service teachers produce a more detailed professional discourse to attend to the details of students' answers and their different mathematical levels of thinking in mathematics teacher education programs.

The objective of this research is to understand how a learning trajectory supports pre-service primary teachers in their noticing of students' mathematical understanding. A total of 95 pre-service primary school teachers used a learning trajectory related to the partwhole meaning of the fraction concept to interpret students' understanding and provide instructional decisions. The findings indicate that the learning trajectory provided preservice teachers with a specific language to describe students' understanding and helped them to notice students' mathematical understanding. Furthermore, the pre-service primary teachers who produced a more detailed discourse also proposed more suitable activities based on students' understanding. These findings suggest that the learning trajectory can act as a scaffold to notice students' mathematical understanding.

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Decidir cómo continuar la enseñanza se ha identificado como la destreza más difícil de entre las tres que configuran la competencia de mirar profesionalmente el pensamiento matemático del estudiante. En este estudio 95 estudiantes para maestro de Educación Primaria resolvieron una tarea en la que debían proponer un objetivo de aprendizaje y actividades para apoyar el desarrollo de la comprensión del significado de fracción como parte-todo usando como referencia una trayectoria hipotética de aprendizaje. Los resultados sugieren que la trayectoria hipotética de aprendizaje ayudó a los estudiantes para maestro a proponer actividades centradas en la comprensión de los estudiantes usando los elementos matemáticos que articulan la trayectoria hipotética de aprendizaje.