Students’ mathematics learning require that they work in an autonomous way in challenging tasks. Such autonomous work may be carried out either in pairs, in small groups, or individually. Students should carry out an activity in which they have to make sense about the aim of the task, design a strategy to achieve it, and carry out this strategy. Students need to be highly involved to make progress in solving the task, so it is necessary that they feel challenged by the task, they understand it, and they identify or design the tools to solve it. If students work in pairs or groups in challenging tasks, they may share and discuss ideas, overcome difficulties and blockages. If they work individually they will have an opportunity to explore the situation according to their own preferences. This will most likely to yield different solving methods, which, brought together and properly discussed, are of great value to support students’ learning.
As the students’ work autonomously, the teacher needs to monitor their work. It is necessary to know if everyone understood the task and if they are working on the task. It is necessary to know who is making progress and who needs to be pushed more. In addition, the teacher needs support students’ struggle so that a deep mathematics learning takes place. Such support needs to be differentiated, according to the particular needs of each student or group of students. In order to move on in solving the task, the students may need different questions from the teacher, different prompts, to experience the possibility of working with different representations and materials and to interact with their colleagues in different ways. In this kind of work, providing challenge to the students and differentiating the attention and support to their activity are two key issues that require the teacher’s attention.
So, during the autonomous work of students the teacher needs to make decisions regarding different issues, such as

• How to collect information from students?
• To which students give priority in monitoring and supporting?
• Is it necessary to provide enablers or extenders to the students?
• What questions to ask to which students?
• Which student solutions select for the whole class discussion and in what order?

The cases of practice that we present in this module address different aspects of the activity of the teacher as the students work on the challenging tasks in an autonomous way, receiving differentiated attention and support from the teacher. There are 3 cases of practice for the (pre-)primary level (pre-primary and grades 1-6) and other 3 cases of practice for secondary level (grades 7-12).