OMG - processing the last few days and where to next?

It is very nice having 5 days breathing space to catch up on study and time to get my head around what I want to do for my Literature review/teaching as inquiry assignments.  A light bulb moment in maths last week - using whole class, real world problem solving has got me thinking, why aren't we / I using PBL (Problem Based Learning) model more often across the curriculum? 

Is it possible to use collaborative activities in mixed and multi levelled classrooms where children are grouped, not academically, to work together to solve problems, and support each other to learn new skills and build on existing and explore new knowledge?

For me it's obvious if we are working towards incorporating 21st century skills, focusing on collaborative learning opportunities for the future using digital tools, apps and web sites etc, then why is there often still not student engagement? 

Does this take time?
Have some students been allowed to remain silent, passive, and not been encouraged to contribute?
Why have they not been interested or engaged in the topic?
Have we provided a safe environment to encourage them to take risks to move out of existing comfort zones and speak up?
Do we as teachers allow enough time for sharing and reflection?
Are we still confined / constrained by the timetable and content?

Some questions I am starting to formulate in my head are:

• Does PBL provide authentic learning opportunities for student engagement?
• Why is PBL not fully implemented / integrated across the curriculum in educational settings?
• How are teachers engaging in PBL opportunities for their students?
• Does or could the Agile based learning model fit into PBL?

I need to narrow down and focus my questions before I start my Literature review. My initial library search shows that there is a lot of research already done with PBL. I teach at year 7 & 8 level in a full primary so I would clearly like to relate it back to the primary setting.   Where to next?