This helps the students more. Instead of purely lecturing to a class, interaction between different levels of peers helps engage the students and learn from one another. Compared to Piaget's stages, one student moves faster and farther ahead than other students. 
This is Guided Participation! Lisa knows the material very well, and is helping Lucas, who does not know the material well. Lucas will grow more efficiently by working with Lisa, who is more skilled in this topic. 
I picked this topic up rapidly, just as I do other topics, such as people, and language.
It's hard for some students to read and comprehend everything without breaks. Instead of learning this way, catering to their needs and helping them dissect the information can ultimately lead to the student having a better understanding of a text.
Since you have a harder time understanding the book when you read it all in one go, let's read just the first chapter and then discuss what it was about! This is called Scaffolding. I'm helping assist you based on your needs.
With this, teachers can now have a better understanding of their students needs and what they can accomplish. . Not everyone can do the same mental problems at the same age, as Piaget believed. Some are behind in this aspect and need assistance.
Ma'am, I can do problems 1-4 without any assistance, but I really need help on the multiplication in questions 5-7. This is my Zone of Proximal Development. This is what I can do alone and with assistance.
I don't understand this material... I know that if I add 5+5 I get 10, but how is 5^2 any different?This is my inner speech. They are my thoughts
My mommy had always told me that Santa could create chimney's, even if you don't have one in your house! That's what my grandma told her when she was a kid! That's my household culture, so this is what I believe. 
But my mom said that he comes in through the front door when you don't have a chimney! That's what she was told as a kid. This is our household culture and what I believe in. 
Comparing what they're learning from their culture and social influences, they can learn things about each other and be aware of how others live and think. Piaget had not accounted for knowledge coming from social and cultural experiences, only what the child learned individually. 
My parents showed me football/lacrosse as a kid, and now I love it! This is intersubjectivity. I was influenced by my parents as a kid.
By allowing children to think out loud to themselves without criticism, they are able to organize their next behaviors more efficiently and come to the right conclusion more often. In the past, they might not have been able to do this, and was more inclined to follow a more strict way of figuring out the answer. This is similar to different theories that children created in Piaget's stages, however they were thought to learn more by observation, not by figuring it out different individualistic ways, like talking the problem out loud. 
This is my private speech. It's not intended for anyone else to criticize or hear, but it helps me to focus on my task at hand by speaking out loud to myself. It helps organize my behavior and plans. 
Okay, so, I'll take these rings off of the holder, then compare each size to one another to see which is bigger. Then I can figure out which should go on first; whichever is the bigger ring. 
Wow! My mind works like these computers! I'm able to store my working memory like a RAM, and my Long-Term memory like a Hard Drive!
Yeah! Like a CPU, my central executive directs all of my activity and monitors it as well!