Good to hear from you, Alexander. Thank you for this suitable  illustration. With your example I can clearly see the function of the Mediator. I am going to try the scene soon.

Diana,if we look at the questions from the point of view of the Thinking Task Framework, the first question we should ask is about the challenge we set for our children and how we get them to accept this challenge. In your example you are saying that the trucks were quarrelling about the stones they should take. But was it clear for Dana why they couldn't agree? What I'd probably do is to 'play' the quarrel. For example:Truck 1: Hey, little one, these are the stones for you.Truck 2 (trying to get the stones): Sorry, mate, I can't do it. Here another toy could appear (a thinking character if you introduced one?) and say that it's easy and he/she knows the solution.You could then ask Dana if she had any idea what that solution could be or something like that. 

Dear Renata and Alexander, thank you for you comments. This time we\'ve sorted stones. I showed her two cars (big and small) and asked her to help solve their quarrel, because they cannot divide these stones. I wanted to see whether Dana understands that  she could give big sstones to the big car and small stones to the small car. She couldn\'t cope. Again she divided the stones in halves, which I accepted at first, but then I encouraged her to group again. She was silent. Me too. She didn\'t have any ideas. So she divided at a random, I asked to justify her choice. SHe couldn\'t. Asked again (when I  say so, it means, that cars didn\'t accept her division, telling, that we do not understand why you divided like that) - no way. Then I decided to help. I switched her attention to the size of the cars and asked which stones would the big car like? Here she got the point and grouped the stones acoording to size. Then she felt tired and we stopped the activity. And here again my question - how would i switch her attention to the quality (features) of the element?

Diana, thanks for sharing. Renata might be right re helping too much but it also depends on what your objectives were. If you wanted to check your daughter's ability to group objects according to a given parameter, then your actions were justified. If you are more interested in seeing which features of objects your daughter can notice and whether she can group them accordingly, then you were probably too helpful. Both can be legitimate objectives - they are just different. Anyway, from the point of view of developing thinking skills, we should ensure that the challenge is there. 

Thank you for sharing this experience, Diana! I think that you are right, you were too helpful with your child:) I'd say the general thing to start with is to simply try to ask Dana to make two or three groups out of any objects which you are playing with at the moment and explain the choice (and to wrap the task into motivating activity, like the hero she likes asked to make two groups because...). And then if she doesn't cope, you provide a little bit of support or if the task is too easy you increase the number of objects/groups.