Supporting the emergence of mathematical knowledge through problem posing

Problem posing represents a valuable strategy to create a bridge between mathematics classroom activities and everyday-life experiences. Despite the value of problem posing activities as opportunities for measuring students’ mathematical learning outcomes, more research is needed in investigating if and how problem posing could support the introduction of new mathematical knowledge promoting the development of mathematical concepts .  The aim of this paper is to start investigating how problem posing can extend students’ mathematical knowledge. After having introduced the notion of emergent problem posing, some results from a teaching experiment conducted in a primary school class are reported. The design of the teaching experiment was explicated through the development of the three components of a Hypothetical Learning Trajectory: learning goal ; hypothetical learning process ; learning activities . Results from the study indicate that semi-structured problem posing activities that start from a suitable artifact could support the emergence of new mathematical knowledge, supporting students’ in re-inventing mathematical strategies to solve problems posed by themselves.  However, further research is necessary, especially in: supporting the notion of emergent problem posing with more teaching experiments; investigating the role of different artifacts in supporting the process of emergent problem-posing; evaluating which characteristics an artifact should have in order to support the process of emergent problem posing; examining possible relations between students’ abilities and emergent problem posing performances.