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This is pretty common advice that I am starting to disagree with. In my experience (in person math and chemistry tutoring and answering programming questions on

This is pretty common advice that I am starting to disagree with. In my experience (in person math and chemistry tutoring and answering programming questions on public discords) this technique really only works well with some one who is on the verge of understanding and has perhaps made a simple error or already has mastery over the techniques and concepts at play and are learning one entirely new thing. In those cases this technique is great! You can guide them to that moment of epiphany, and it is very rewarding and efficient. Much more commonly it feels like pulling teeth. I think this is because most kinds of misunderstandings and confusions are hard to identify from the inside. For example, when some one learns a new thing that is in contradiction with something else (that they perhaps misremembered, never fully understood, or misunderstood a nuance in a way that was internally consistent) the resulting inconsistency can be very difficult to identify and verbalize. If you can help them identify and resolve it on their own then great- my experience is that when that works it is exhausting and time consuming and that taking a more active role in identifying the conflict is much more productive. In programming it commonly takes people years to learn enough background context that this method becomes effective. I think it is better to be quick with examples and explanations, there is just too much to know to make this sort of highly examined introspection efficient or effective. Other times its simply because the student isn't intrinsically motivated to learn the material and this style of teaching involves a lot of emotional labor in order to be effective. Turns out people shut down a little when you ask them to explain their thought process and they feel they should not tell you frankly they care not one wit for Pythagoras or your damned flag pole .

zmgsabst 3y ago
As a math tutor, I’m with you. 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.
- washadjeffmad 3y ago
  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.
  - burnished 3y ago
    Do you find that people who get that practice become more receptive to tricks?
    - washadjeffmad 3y ago
      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.
- burnished 3y ago
  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.

zmgsabst 3y ago

As a math tutor, I’m with you. 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.

washadjeffmad 3y ago
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.
- burnished 3y ago
  Do you find that people who get that practice become more receptive to tricks?
  - washadjeffmad 3y ago
    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.
burnished 3y ago
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.