Comment by vishnugupta | Hacker News Reader

Comment by vishnugupta | Hacker News Reader

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I'm teaching my 9yo son to take baby steps in algebra and I can totally relate to your comment. When he encountered a variable "X" for the first time he was completely flabbergasted. I tried several examples but it's just plain difficult for a human mind to go from numbers to an abstract concept of a "place holder". It's a big leap of faith to go from "a specific number" to "a place holder that you later fill up with". I asked him to divide "5 * A" by "5" and he was like "I don't know what A is how do I divide?".

A related challenge is to translate descriptions into mathematical equations. Things like "Bob ate 5 times as many berries as Sue". Funny thing is in his head he works out and comes up with the correct answer. But when I ask him to go through the process it's totally alien to him. The only way I think is to make him practice with as many such challenges as possible.

Now when I look back 30 years ago, I recall the struggle I went through to even understand the meaning of "X + 2 = 3" let alone do the magic of moving 2 to the right and change its sign.

When due to lockdown I was doing some homeschooling and giving some exercises to my 7yo, I was also anxious to introduce variables; the magic "x" that scares so many.

I ended up drawing squares or triangles instead. Maybe they scared me less, but he really seemed to grok it. When I asked and what's the value of "this", he'd just give the answer without knowing something about equivalent transformations and the stuff.

Made me wonder if math should maybe be taught more intuitively, not so much about the formal stuff, which in the end is pretty useless for our minds if we don't have any intuitive grasp of it.

I'm fairly certain that's what Common Core was trying to do... And parents around the US freaked out because it was different than how they learned math and states like Texas made it illegal...

Start with an empty box of instead of x. I have found that an empty box transfers to them the concept of placeholder that needs to be filled. it can transition to a x later

You can also compare to words like it, thing, she, he, and equations to definite descriptions.

"I don't know who she is."

"The culprit was wearing a red coat."

"The mystery number plus 3 is equal to 5."

"I'm thinking of a number, but I'm not going to tell you what it is. But I will tell you that if I multiply it by 3, and then subtract 5, I get 1."

I remember how frustrating it was to do this.

For me it helped to just be really explicit with it:

X + 2 = 3 X + 2 - 2 = 3 - 2 X + 0 = 1 X = 1

That basically unlocked it for me. I was older than 9 though :). For division I'd probably just say that you actually have (1/5)5A = (5/5)A = 1A, but that probably necessitates symbolic juggling to be something you already have as a skill.

Anyway, symbolic manipulation is interesting, even without letters.

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