I absolutely remember being taught that the reason we could add something to both sides, subtract something from both sides, divide or multiply… was because it preserved the equality. I think 7th grade. And when I helped my kids on the relevant math (they did not inherit my “intuitive obviousness” gene) I would repeat this over and over.
Of course we all want to blame the teacher or the course when we haven’t learned something in the past, but I have seen too many people not learn things that I was repeating and emphasizing and explaining in as many ways as I could imagine or read, and still they didn’t get it. I think we have all head the experience of having someone we were explaining something to finally get it and exclaim something like “why didn’t you just tell me that in the first place.”
I absolutely remember being taught that the reason we could add something to both sides, subtract something from both sides, divide or multiply… was because it preserved the equality. I think 7th grade. And when I helped my kids on the relevant math (they did not inherit my “intuitive obviousness” gene) I would repeat this over and over.
Of course we all want to blame the teacher or the course when we haven’t learned something in the past, but I have seen too many people not learn things that I was repeating and emphasizing and explaining in as many ways as I could imagine or read, and still they didn’t get it. I think we have all head the experience of having someone we were explaining something to finally get it and exclaim something like “why didn’t you just tell me that in the first place.”