**5. Conclusion**

Problem-solving plays an important role in mathematics and in school curricula. However, studies show that its teaching is complex. The aim of all our work is to gain a better understanding of the interplay between teachers' practices and students' learning around problem-solving in mathematics. More specifically, we are looking at how teachers can help students better appropriate a problem, without overdoing it for them.

Chanudet's dissertation has shed light on the practices of secondary school teachers when teaching mathematical problem-solving. We will take up this work again with a study of some primary school teachers. Favier's dissertation has given us a better understanding of how students work when solving problems through trials and adjustments. We intend to extend his work to other types of problems.

Our collaborative project with secondary school mathematics teachers (with plans to collaborate with primary school teachers at a later date) aims to gain a better understanding of what students do in the classroom when they solve a problem, and what can be done to support and encourage their work.

We are using the design and implementation of sessions and the analysis of their progress to devise an in-service training system designed to equip teachers.

Our work is based on a collaborative research approach, which we believe is conducive to a better appropriation of the results obtained. Various theoretical frameworks from the didactics of mathematics are mobilized to construct the research devices and analyze the data collected.

*Improving the Teaching of Mathematical Problem Solving – A Collaborative Research Based… DOI: http://dx.doi.org/10.5772/intechopen.113258*
