First year student teachers dealing with non-routine questions in the context of the entrance examination to a degree in Primary Education

We understand Fundamental Mathematical Knowledge (FMK) as the initial mathematical background we expect students to have at the start of their education to become Primary School teachers. In this paper, we focus on the answers given by 241 first-year student teachers to two non-routine questions that were part of an entrance examination. Non-routine questions are those for which students do not have a straightforward algorithm available to reach the answer and/or the result obtained by using it needs to be interpreted within the problem's context. The results show that non-routine questions are a powerful tool to assess the solidity and stability of their initial mathematical knowledge but also a powerful tool to find out whether the students have appropriated the essential ways of thinking and working in mathematics. Our findings also suggest that the mathematical knowledge of first-year student teachers is far from the desired FMK.