Project-Based Learning

Montessori IS the original project-based learning. 

It's a bit bigger than that, but the idea is that the project-based learning people got the idea from Montessori, directly or indirectly, and repackaged it in a way more palatable to non-Montessori adults.

Google search for  "project based learning and Montessori" for more information :)

My personal opinion is that "project-based learning" is the non-Montessori phrase for a portion of "cosmic education". ;)

The concept of project-based learning applies most especially for elementary children. If the children in the environment are NOT creating projects, presentations, additional materials, doing more research, writing out questions and answering them, consider making some modifications to make your environment MORE Montessori. What is missing?

What tools do the children need to do their research and present their findings that are not yet present in your environment?

Do they have the art-related tools?

Do they have a few books and videos or similar to inspire their creativity, their imagination, their wonder - but not so many as to be exhaustive?

Are you able to get to the library on a routine basis?

Do you have opportunities and the structure for Goings Out? (in the homeschool, this is simply the time to get out and visit related places of interest).

Most importantly, how are the words and nuances the adult puts into place? If the adult is encouraging thoughtful insight, and providing the right balance of guidance and honesty (the adults do NOT have all the answers - and shouldn't), interest-exploration will happen.

ONE project sample: 
Project-Based Learning Elementary Montessori education
takes many children down the path of historical (and healthier!) food-making
such as yogurt and real sour-dough, among many others.
(inspiration: fundamental needs of man; 2 timelines of humans)
The above shown photo is from a collection of photos that took one Montessori child down a path of historical food exploration; what can still be made now, what has changed too much; what do we still do now that uses different tools or different methods... these are the over-arching questions posed in the beginning stages of what become a TWO-YEAR project. It included sour-dough (we can't make it the same way because our wheat has been changed! let alone HOW the wheat is harvested, etc. which leads into celiac disease and why so many people can't eat what for millennia was a STAPLE in the human diet.); yogurt; meat storage; fruits and vegetables distribution around the world, storage; genetic modifications; food colorings and other additives (such as the poisonous high fructose corn syrup); food varieties that can be grown in the living room through the winter; composting; gardening; herbs; spices....

The study had been rabbit trails; but each step of the way reached a logical conclusion, some of which were used for jumping points into new, related projects, that sometimes wound back around to previous ones that then needed some updating.