1. I’ll tell you what the right formula/process/etc is — as a hint on the problem.
2. If you still don’t get it, I’ll walk through the right steps with you.
I’ve never found it particularly useful to dig into what you have wrong or try to guide you into self-correcting unless the problem is minor (eg, you clearly understand and just need a nudge), you ask, or I’m dealing with someone that has a professional interest and will invest the effort debugging.
I can’t imagine how badly I’d hate it if StackOverflow tried to guide me on some Socratic journey every time, rather than just tell me the correct syntax for the magic invocation of pandas that solves my problem.
True that focusing on what they're doing isn't the best course unless they're making repeatable errors.
Teaching the "tricks" can help people who already have a mindset for relationships, but often people who struggle with math don't have this, and it takes practicing fundamental methods so they can apply them.
I also found a primer in symbolic logic greatly improved student comfort and familiarity with most other materials. Knowing the formal language and rules of logic and relationships is key to being able to express and interpret mathematics.
They do. The realization that something can be applied in other contexts is what takes them from feeling overwhelmed that each step is something discrete and isolated to memorize to being excited about making it make sense.
This also happens after teaching them how to use their calculators. When they begin to be able to visualize what the approximate bounds are by understanding eg- an expression and what it applies to, it's the difference from someone who only reads word by word and someone who reads with respect to the content of the arc or chapter.
So much of math is contingent on parallels to other subjects, and I've always felt not enough was done to relate to students the similarities between the formal rules.
Ie- when teaching linguistic notation for grammar and syntax, you can have students reduce sentences to expressions (a la Backus–Naur form) and then "solve" for them using, eg- a semantic net. This is often much more comfortable to the numerically adverse, since the logic of language is often understood more intuitively. It can also be taught at any level using simple substitution, parts of speech, etc with the added benefit as a primer for its applications to machine learning.
Right? I understand why its advised so glibly - it sounds nice and when it works its powerful but..
I had one mentor that was ruthless in forcing me to explain myself and almost pedantic in his insistence on correct vocabulary at all times (programming), but I was also able to interrogate the hell out of him and had practical strategies for identifying and rooting out my own misunderstanding - it was incredibly rewarding but frequently exhausting, half the time we'd wrap up and I'd feel like my voice had grown horse from shouting.
It wouldn't have worked if we didn't trust each other, or if ever I had grown discouraged by my own ignorance, or if he hadn't worked on a compiler team and been able to describe in detail and on command the function of any part of a computer system.
And I suspect most success stories using that method are somewhat like this; deeply personal, probably shouldn't be your expectation or plan A.
But I tend to do two steps:
1. I’ll tell you what the right formula/process/etc is — as a hint on the problem.
2. If you still don’t get it, I’ll walk through the right steps with you.
I’ve never found it particularly useful to dig into what you have wrong or try to guide you into self-correcting unless the problem is minor (eg, you clearly understand and just need a nudge), you ask, or I’m dealing with someone that has a professional interest and will invest the effort debugging.
I can’t imagine how badly I’d hate it if StackOverflow tried to guide me on some Socratic journey every time, rather than just tell me the correct syntax for the magic invocation of pandas that solves my problem.
I’d probably just quit.