The making of mathematical connections in the classroom plays a dual role. While many studies highlight the importance of connections for the learning of mathematics, others inform of students’ difficulties associated with the making of connections. This study aims to characterise the mathematical connections that arise in habitual classroom practice, using an inductive approach, in the context of introducing integers with pupils aged 12–13. Results show that connections emerge as networks of links resulting from interactions between the teacher and the students. We present a definition of connection, a detailed characterisation of their internal structure as networks of links and a global characterisation which takes into account the role of the connection in the context in which it takes place. The complementarity of the two characterizations allows us to coordinate, from a classroom perspective, existing specific classification proposals for connections with a broader notion of connection used by relevant curricular guidelines. Factors that may determine the complexity of connections and may be related with students’ difficulties when dealing with connections in the classroom are also discussed.
El objetivo de este estudio es indagar sobre las conexiones matemáticas entre manifestaciones del área que establecen (o no) los maestros en formación al resolver tareas asociadas al cálculo del área de superficies planas. Los estudiantes para maestro, reunidos en parejas, respondieron un cuestionario que solicitaba: 1) medir el área de superficies planas utilizando dos o tres procedimientos diferentes, y 2) justificar cada resolución con base en los procedimientos utilizados. Los resultados obtenidos evidencian que la gran mayoría de estudiantes para maestro privilegian el uso de procedimientos numéricos y el uso de fórmulas, ignorando procedimientos geométricos e intuitivos que facilitarían la tarea de cuantificar el área. En este sentido, se advierte la dificultad de los estudiantes para maestro para establecer conexiones entre las manifestaciones del área.
In this research, we explored the potential of using a research-based teaching and learning sequence to promote pupils’ engagement in practices that are coherent with those of real world mathematical and scientific activity. This STEM (Science, Technology, Engineering and Mathematis) sequence was designed and implemented by pre-service teachers and science and mathematics education researchers with the aim of modeling the growth of a real population of rabbits. Results show explicit evidence of pupils’ engagement in relevant mathematical and scientific practices, as well as detailed descriptions of mathematical connections that emerged from those practices. We discuss how these practices and connections allowed the progressive construction of models, and the implications that this proposal may have for STEM task design and for the analysis of extra-mathematical connections.
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