Are You Convinced?
To start with, teachers must be able to prove certain formulas or rules because some of these formulas are "undigestable" without proofs. In addition, some other rules need to be worked on with the students step by step, so they will completely get them and gain the ability to use them correctly.
Myself, when our professor gave us the "Building Four Stories Towers with Two Colors without Repeating," I thought of this: 0 1 2 3 4 3 2 1 0
0= no mixture of color, the original color
1= one color interapting the original color
2= two of the same color interapting the original
3= three of the same color interapting the original
4= the interapting color gets over the original color
Then, repeat the same thing from the beginning.
And here appears the idea of "Patterns." Some problems in math need the application of "Backward" thinking to be solved, and this is another strategy shown in mathematic textbooks for Problems Solving.
After watching the video, I became convinced that the best way to deliver a proof to young students is with the use of Hands-On-Learning strategy. It is a method that must be included in teachers' daily lesson plan as much as possible. When a child gets in touch with an activity, he/she will learn and understand at the same time much easier than only reading from the text book. Logically, the brain will process freely when it is not framed with rigid instructions. The children in the video were exchanging ideas in a very relaxed environment. More over, there is a big difference between the outcomes of individual work and team or group work, as part II of video II showed.
In the second part, I saw how the students were able to organize and discuss their solutions between each other in a clear platform. They were comparing their conclusions and justifying them. Each one of them was convinced that his way was the correct path to be followed and applyed as a solution to that activity.