Interpretative knowledge of prospective kindergarten and primary teachers in the context of subtraction

Background: Teaching and learning with understanding leads to the adoption of “what” and “how” each individual knows as starting points, requiring from teachers a specialised knowledge, called Interpretative Knowledge (IK), which supports constructive feedback and pedagogical actions aimed at developing the students’ mathematical knowledge and skills. Objectives: this paper aims to trace and discuss the problematic areas of the IK presented by prospective kindergarten and primary teachers’ (PTs) when attributing meaning to students’ productions within the scope of subtraction. Design: the focus is on the IK revealed by PTs when analysing and giving meaning to students’ written productions on a task involving subtraction between natural numbers. Setting and participants: twenty-six PTs attending the only course focusing on teaching and learning mathematics they have in their curriculum participated in the research. Data collection and analysis: the data collected and analysed, from the qualitative and interpretative perspective of content, come from the written productions of the PTs on a task for teacher education, together with the audio and video recordings of the group discussions. Results: the results show a “linear” interpretation of the students’ productions, associated with a single way of understanding subtraction, limiting the PTs’ development of constructive feedback and pedagogical interventions, so their practice is not based simply on “teaching how to do.” Conclusions: the limited interpretation and, consequently, the limited development of constructive feedback stood out, showing the need for teacher education to focus on tasks specifically conceptualised for developing the specificities of (prospective) teachers’ knowledge that would enable them to give meaning to students’ production and assume the associated mathematical reasoning as a starting point for practice