【And why do we need to draw on the paper instead of visualizing images only in the head.】
The reason why they should draw pictures to solve math and problem solving problems is primarily to reduce the energy consumption.
That makes thinking easier for children. It is very hard to keep the visual images especially for younger children (even if for adults) for a long time only in the head. That’s why, they have difficulty to operate them (think).
If we teach them the correct way to understand and think, children will enjoy working out difficult problems on their own. You will be amazed to see how flexible they think and how original and unique they are.
it is fun!