Everyone loves a little mystery in life and most people like to think hard. I have noticed my lessons go best when the learning target is stated at the end. When I teach with an inquiry lens, and let the kids discover the math and science, engagement goes up, learning increases, and all students push through to learn at greater depths.
When I start the lesson with, "Today I will teach you how to add fractions," I notice that half my class tunes out and the other half already knows how to do it.
In order to have students engage in productive struggle, we as teachers and parents, need to present our students with problems that they truly don't know how to answer. They need to play with the numbers and explore concepts without someone telling them how to do it. Students need to try and fail and be okay with that because later on in life, they will encounter problems that they need to solve, and they need to have the logical reasoning skills to tackle them head on.
Today, one of my students was trying to add fractions for the first time. He has not been taught how to do such and I was watching as he logically thought his way through. T. drew two models of fractions and then was trying to figure out how to cut them into the same sized pieces so he could add them. T. told me that he had learned about equivalent fractions on i-ready and he was trying to use this concept to add.
I did not tell him any of this. I watched as he crossed out numbers, sketched brownies on this graph paper, erased and tried again. At the end, he was close, but mis-named the numerators because his sketches were not accurate enough.
At that point, we talked about ways to draw accurate diagrams for equivalent fractions and he eagerly solved the problem. The teaching point was at the end and he was satisfied to have tried something hard and found a way to come up with an answer.
