Abtract
Teachers’ knowledge assumes a major role in students’ understanding on what
they do and why they do it. Particularly concerning subtraction, in order to allow
its discussion with and for understanding, teachers’ knowledge needs to include,
amongst others, different possible mathematical approaches as well as associated
reasoning – from the less until the more formal. This paper discusses and reflects
upon early years’ prospective teachers’ knowledge and reasoning in solving tasks
involving giving sense to students ways of solving a subtraction using an algorithmic
approach. The preliminary results show that these prospective teachers perceive
giving sense to students productions as something similar as giving a description
of different steps and procedures, revealing serious gaps in knowledge which does
not allow them to equate its (im)possibility. These difficulties are exteriorized through
serious terminological and mathematical language incoherencies and mistakes.

Keywords: teachers training, Mathematical Knowledge for Teaching, mathematical
reasoning, subtraction.