Again - correct but misguided in the general sense.
> It is the same reason the word for 'dog' in English is taught as being spelled D-O-G. There is no why behind it.
I agree with you completely, but I think you're guilty of speaking the wrong language in response to the question (and it would behoove you to consider it from the perspective of someone outside the field).
The question "Why" in maths almost always gets asked by someone new to the field, and they are not asking from a mathematical perspective - They are not asking you for a formal/provable "why", they're asking you what is the utility of learning this thing.
So lets go back to D-O-G. The utility is clear - I have this hairy, 4 legged animal that keeps licking me that I'd like to discuss with you. We can agree that D-O-G (or perro, or 개) refers to it.
But with math, SO MANY PEOPLE (especially those established in the field) jump right into the "Here are the rules of this system of math" without ever taking the time to talk about why someone might give a flying fuck.
It would be like me going and making up my own language and forcing you to learn it. No one else speaks it, it's got no books/literature/history, there are no works of art that reference it - it's literally the language this random person made up that serves ZERO purpose except for talking to that person.
No wonder so many kids don't like math!
Instead you need to explicitly start with the utility of math - ideally in ways that are entertaining and fun. Once a person has an application for some of the rules, they become SO MUCH MORE INTERESTING! Suddenly I care about why this rule might impact that rule over there, or why A and Z are related, or what sin/cos/tan mean.
Basically - sell me on the value proposition of your fucked up whacky language - That's what "why" is asking. Once you know those rules do something useful, it becomes a much more engaging field of study.
You are correct, but this explanation is cultural and sociological, not logical.
We must motivate math, absolutely. And to do so in my opinion starts with socratic questioning. You must convince the student that such an inquiry is even worthwhile.
One thing I'll point out is that we're not just seeing this in math. We see it in every field. More and more kids every year are insisting ( and their teachers are agreeing) that we can do away with inquiries into the English language and the humanities as well. There is a small, but continuing, effort to remove the knowledge of English masters like shakespeare and classic philosophers and treatises from the curriculum.
As a whole, American schooling fails to motivate learning of any kind. Math was the first victim, but the other subjects are also failing.
Sure, but we're in a thread talking about why some folks are choosing to send kids to "Russian" style maths teachers.
The whole discussion is from the perspective of the cultural and sociological.
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As an aside, I generally agree with you about american schooling. I think it's less a concerted effort, and more a sad reality of the fact that modern schools have essentially become federally funded child care in the US.
Indeed... As my mother was told by her principal in her inner city school for poor minority kids... "We're just here to watch them until they go to prison".
> It is the same reason the word for 'dog' in English is taught as being spelled D-O-G. There is no why behind it.
I agree with you completely, but I think you're guilty of speaking the wrong language in response to the question (and it would behoove you to consider it from the perspective of someone outside the field).
The question "Why" in maths almost always gets asked by someone new to the field, and they are not asking from a mathematical perspective - They are not asking you for a formal/provable "why", they're asking you what is the utility of learning this thing.
So lets go back to D-O-G. The utility is clear - I have this hairy, 4 legged animal that keeps licking me that I'd like to discuss with you. We can agree that D-O-G (or perro, or 개) refers to it.
But with math, SO MANY PEOPLE (especially those established in the field) jump right into the "Here are the rules of this system of math" without ever taking the time to talk about why someone might give a flying fuck.
It would be like me going and making up my own language and forcing you to learn it. No one else speaks it, it's got no books/literature/history, there are no works of art that reference it - it's literally the language this random person made up that serves ZERO purpose except for talking to that person.
No wonder so many kids don't like math!
Instead you need to explicitly start with the utility of math - ideally in ways that are entertaining and fun. Once a person has an application for some of the rules, they become SO MUCH MORE INTERESTING! Suddenly I care about why this rule might impact that rule over there, or why A and Z are related, or what sin/cos/tan mean.
Basically - sell me on the value proposition of your fucked up whacky language - That's what "why" is asking. Once you know those rules do something useful, it becomes a much more engaging field of study.