Take a look at the LEGO serious play method. The following book forms a good introduction: LEGO Serious play open source Take a look at the sections discussing facilitation - Do adults need a different approach or role in facilitation? Which concepts are relevant?
In the LEGO serious play (LSP) the role of facilitator is to make sure the workshops functions well and does what it needs to, and that participants can speak freely. Two things facilitators are told to keep in mind for this process: LSP is about having constructive reflection and the LEGO part of LSP should be fully engaged with. Based on the open-source book the LSP method seems to be modelled for adults so they would not need a different approach in facilitation in LSP.
In general, I do think adults and children have slightly different ways of needing facilitation. Facilitation is about helping people with their learning journey. Children are very used to being helped with this. They spent most of their time in schools where there is a teacher to guide them and ask questions. Adults spent a lot less time learning in this way. They follow courses and might also attend lectures, but most adults do not spend most of their days being facilitated in their learning goals. Because of this difference I can imagine adults might be less open to facilitation than children. An example I can think of is when I took part of a symposium about Teaching Assistants (TAs). During the symposium we were tasked to form a group and discuss some situations. During the session the organizers/teachers did not walk between groups, as might be common in schools, but instead waited for us to finish and then we discussed the results with the entire group in a discussion.
Another difference might be openness to get physical. I think that when given the option to play with Legos most children will go wild to represent their ideas. That the manual explicitly stated that the facilitator should motivate people to use the Legos makes me think that adults might be different in regards to playing with Legos.

• Read Invent to Learn chapter 5. Summarise the key principles mentioned by Papert and also the key principles by Montessori. Where do Papert and Montessori meet up? What is a fundamental difference in their approach? How well do their mantra's and thoughts on teaching translate to tinkering for 'children of different ages'?
Papert has a list of eight big ideas that tell about his key principles. The ideas are already pretty short but when summarised even more the key ideas is that the best way to learn is to do something that is challenging but fun. Montessori is very focused on the physical way of learning and on letting children explore. Therefore both Papert and Montessori are focused on physicality in their learning methods. They are also both interested in self directed learning, letting a child decide what they are interested in. A difference in their approach is about the tasks taught. Montessori uses activities like cleaning in her cleaning methods. She also calls “play the work of the child”. Papert as less of a focus on ‘’real world’’ tasks except for self time-management. The large focus on doing to learn in Papert’s mantra fits well with the idea of Tinkering. However, two points of his eight big ideas go against the rules of tinkering as described in the lecture. The first one is the big focus on digital technology, something this course is trying to move away from. I wonder of this difference in focus is partly because of the time Papert’s list is from. In current days we do nearly all our learning before a screen. I assume this was different in 1999 and thus motivating students to explore computers make more sense. The second ‘rule break’ is that Papert says we learn best when we make something we really want. This does not fit with the idea tinkering should not have a goal.
Apart from those ‘rule breaks’ Papert’s big ideas do focus on exploration and learning to learn which fits well with Tinkering.

• read Invent To Learn chapter 9. What are useful pointers for the space (location) and setting, what is the message? Do you need a designlab/fablab?
Simply summarising the tips the book give will not get us new information so let’s first answer the second question: Do you need a designlab. I would say no, Tinkering can be done anywhere. There are ways to facilitate tinkering that might make it more successful or easier, but those things are not necessary. I personally enjoy crocheting on the train. Trains build for the function of transport. Yet, I can still tinker while being on them. If I can tinker in such a space than you do not need a designlab to tinker.
The reason we still have a designlab is because it does make tinkering easier and offers more possibilities. Some of the great parts of the designlab, which also match with the message of the book on tinkering spaces are that it is open for all, there is much freedom in what you can do, and you can very easily work together if you want. The Dreamteam is also very nice in that they will likely not stop you from working things out on your own but that they are there if you need them.
• Now get back to your own practice as a designer/engineer:where in a process do you use tinkering?
There is again the problem of the combination of the goal focus of education and the lack of goal in tinkering. Nearly all of my designing is done for university meaning I have a goal or an assignment. The last time I can remember doing something tinkering-ish was when I needed a button for my coat. Yes I had a goal but I had no idea of the possibilities for how to make it so I went to the designlab and looked around to see what was possible and decided laser cutting would work. I then went looking for inspiration and had fun trying out some laser cutting options
• how can you translate a design problem or research problem into a tinkering playground?
To make it a playground you need to be able to understand the problem first because to teach something you need to understand it. (Something I experienced often when explaining homework to friends.) Then a good step is to think what you want people to learn. Last but not least adding a physical component is important
• what can you use to get unstuck?
My go to action for getting unstuck is explaining my problem to a friend. When I explain something, I have to think about my problem in detail so that they understand it. By doing that I can often understand what is wrong. An example is when I had a problem with designing my sugar bottle. The bottle has stickers on it and I was stuck on how to remove it so I asked my housemate. While explaining the problem I realised it would be fine to keep on the stickers so the problem was fixed.
I use this same technique when I’m helping friends with mathematics. One of my friends is currently doing mathematics that I understand about 50% off. However, when they gets stuck on a question I can still help by making her explain what they did so far and then explain the technique that is needed for the question. Often by explaining it they gets unstuck.
• how do you get in the flow?
The absolute easiest way for me to get in the flow is to make a jigsaw puzzle. Something about them just works perfectly for me, and I can easily concentrate on them for hours. In designing it is more difficult. What does help to start working is set a timer for myself. By having a timer that is ‘timewatch’ I don’t need to use brainpower for that and can more easily get in the flow. So by taking the timewatch part of the work, I don't need to multitask and that makes the challenge of designing fit well in the channel of flow.