Sure the bucket isn't doing math, but how else would you describe it? Integration is the word we have come to use to communicate the meaning of what is happening. In other words, math isn't just about understanding. It is about communication.
Sure we have intuition. But intuition can be wrong. Not all problems are as simple to explain as zero and empty buckets. Intuition is also worthless if you cannot communicate those ideas in an unambiguous fashion.
So if the OP really develops a method for communicating the concepts described by math in a much more efficient way - I am all for it! But I find that highly unlikely when even it is admitted in the article itself that he has no idea what this will look like.
Sure we have intuition. But intuition can be wrong. Not all problems are as simple to explain as zero and empty buckets. Intuition is also worthless if you cannot communicate those ideas in an unambiguous fashion.
So if the OP really develops a method for communicating the concepts described by math in a much more efficient way - I am all for it! But I find that highly unlikely when even it is admitted in the article itself that he has no idea what this will look like.