Problem Based Learning - this is an approach that challenges each student to learn through engagement through a real problem.
Cognitive Apprenticeship - A relationship in which a less experienced learner acquires knowledge and skills under the guidance of an expert. (Educational Psychology glossary)
I think one are that I could use cognitive apprenticeship is in the reading area. During the story, you ask questions, but not everyone is receiving the content. If the case of ELL learners, we have to take into consideration that they do not have command of the English language. After the story I would do a narrative pantomime, which would bring the story to life and the child would be a part of that story. Students can articulate their knowledge of the story and do a turn and talk with a partner. I would ask the children questions of "what does this story remind you of?" I will then be able to see the connections that the children have with the story. The students will then be able to reflect on the story and the connections that they made or different ones they have heard form others.
Some of the challenges that we may face is the language barrier. We will speak slowly and with a friendly tone.
I actually have done this with the class and it was a real hit. I was amazed at the connections and the knowledge they had prior to the story.
We all want our children to do well and if we think of things for them outside of the box and to always make connections, we will be steering them in the right direction.