oldmanhawkins
Footballguy
I can only speak to how it can work in a math class. In mathematics, reasoning and justification will always be more valuable than getting the answer right or getting it quick. So, stronger students are challenged because they must justify their work to others. Sometimes that requires finding another way to solve it or explain it and that can be a challenge. It doesn’t always fall on the teacher to do this. If it did, the teacher would be the only one in the class actually doing math. The others would just be following procedures, which is a low level cognitive task even if you are doing it correctly. I encounter students all the time that think they are too smart for others in the group because they want to move fast and get it done. Truth is that those students don’t understand the math as deeply as they need to and just don’t like having to explain their thinking.
As an example, imagine you were in 5th graded and needed to do 1 divided by 2/3. You remembered the procedure and wrote the answer and tried to move on but your group didn’t get it. You had no idea how to explain it to them other than to say “that’s what you do, flip the second fraction and multiply.” No one understood and didn’t feel certain you were right. After all, nothing you said had any substance to it. The teacher might come by and suggest that you draw a picture. Maybe they model an easy problem like 20 / 4 and ask how many fours fit into a rectangle with an area of twenty. So you do and draw a circle that represents the one and shade two thirds. You can see now and hopefully communicate to the group that it would take 1 and 1/2 of the shaded 2/3 to fill the original circle. The end result of all of that is everyone doing math. You were forced to prove that you were right. The teacher had to provide a simpler example. The others in the group needed to question your logic.
