Hacker News Reader

This is a minor point, but I found understanding the "discourse" behind a field super helpful. In abstract algebra my professor spent a lot of time why we study certain structures (groups, commutative rings, modules, fields) more than others. One time he was making this super frustrated remark that our book (Dummit&Foote) calls ring a non-unitary ring whereas in class he'll call ring as a ring with unity (i.e. a ring that has 1). He was frustrated because for him this was not an interesting distinction and "to have interesting results you need to introduce a 1 anyway". I think this sort of emotional and human responses emphasizes what is important to understand in that field and what is not. Some people saw algebra as a laundry list of structures with axioms, whereas it's just another way of solving problems and structure is the approach, so finding useful structures for the problem in hand is more important than studying all those structures, as if memorizing the periodic table.

Private maths tutor here — what I find most gratifying about tutoring is revealing to my students how much they already know.

Often they'll know that they know the answer, but they don't realise that they also know why it's the answer!

How much are your services? I'm an out-of-school adult that never really grasped math but hate that I don't know more about it to this day. Just wondering what kind of range I'd be looking in to just get some explanations or something. I don't currently have any specific questions though.

~150 AUD/hr for in-home

That's a fair bit above the regular rate though, you can get a decent tutor for less.

Have you tried Khan Academy? It lacks all the person interaction and customization of a private tutor but they have (IMHO) really good explanations and quite good problems to solve for all math through high school.

Love their resources, but having somebody to guide you to the resources that match your deficit is the real magic imo.

I'm a private tutor so obviously I agree it's the best ;-) thanks

However, I wanted to pick up a couple of your examples - "parent touching math for the first time in 20 years" can also often be a great way for students to learn!

Adults are usually able to figure their way around a subject and this is a great learning point for kids - that you don't have to know everything, if you know how to find out about it.

Any parent has got through undergraduate education in any subject (and many who haven't) - who have learned how to learn - can find out what they need to know by looking it up and finding resources that help their comprehension. Being stressed about it is a different situation, and of course I agree with you there.

I also do sometimes say "This is stupid shit you have to know for the course" - because many courses contain bad content - but I will follow it up with "if we have time, it will be more practical to think about..." That also isn't a bad thing necessarily.

It's important for students' development to critically analyse why they are doing a particular course - if they're doing it to pass, then they should first pass.

I think this transference of attitude is a really insightful model for teaching. One of the other methods I've seen used (especially for math) is treating problems like a game. There is a joy in solving even difficult problems, that you can teach gradually with the right feedback... and learn.

When I was 16/17 I did private maths tutoring for some of my classmates. As a tutor I enjoyed the conversations we had about 'why'. These people were missing a lot of context about why they were even doing anything, so the steps were all mechanical and it was hard for them to do anything beyond what they'd memorised. Conversations about the material, outside what's strictly required to solve a problem, really work wonders.

As for teaching outside the comfort zone, I actually think that's a great opportunity. It puts you in the same place as your student so you can model the meta-cognitive skills of learning, curiosity, etc. You can even demonstrate how to 'fail' at something with grace - and give the student the opportunity to be better than their teacher at something!

> Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn.

I really disagree with your choice of words here, specifically, “just-in-time”. This makes it seem like the tutor is teaching things to the student right before they need it for an exam, which is an unfortunate effect I’ve seen happen because in the long run it doesn’t really teach anything. But where a private tutor really does excel is having a better understanding of how to tailor the curriculum to the student (this includes both simplifying or making it more challenging, depending on the student and the topic).

> This makes it seem like the tutor is teaching things to the student right before they need it for an exam

On the contrary, I found it really precise. JIT processes in manufacturing are about providing the correct inputs at the time they're needed. If your desire is mastery over the material, a teacher who can predict or extemporize tutorials on the subject as you need them is invaluable.

Ah no, my intended meaning of “just-in-time” was definitely not in the sense of just-in-time-for-the-exam. In fact I think there is very little use for last-minute cramming... at most you can survive the test, but definitely not build fluency or understanding.

I was using “just-in-time” in the sense of just-in-time-for-the-lesson, e.g., if the tutor wants to teach concept X which requires knowledge of prerequisite concepts α1, α2, and α3, then the tutor can provide a quick review of these concepts before explaining X. Tutors can do this "custom filling in of gaps," whereas in a groups setting the teacher might be forced to say "you should know this already."

Great post. FWIW in discussing this topic I've heard and now adopted the term "(in)numerate" vs "STEM-(il)literate" -- though the latter might be intended to be broader in scope?

I don't think it's very helpful to make such a distinction between people who "get it", and those who don't. It's a spectrum. Unless of course when it's relating to a disorder, like dyslexia for example.

As Zeebrommer mentioned, I'd steer clear of this thinking. Carol Dweck's entire research has been on "fixed" and "growth" mindsets, and their impact on people's performance. Instructors that believe someone is or is not an "X person" have a negative impact on students. That is, if I believe in the idea that there are STEM-illiterate and STEM-literature people, why should I both helping someone who is STEM-illiterate?

Instead, adopting a growth mindset, that while one may not know something now, with time and effort they can gain understanding is much more powerful. As I've argued in other threads, this may include doing things that are frustrating or otherwise "not fun" to establish grit/perseverance.

Think of it this way, when you were a baby, you were "spoon"-illiterate. If you parents decided you're just "not a spoon person", you would be raised not knowing how to use a tool everyone else thinks is easy. If you grew up never using a spoon, and it became a requirement for future career advancement - you might become frustrated because you were taught you "were not a spoon person" instead of "I need to learn how to spoon!"

I think you've misunderstood me or conflated my comment with someone else's; mine said nothing about fixed vs growth mindset. The term "innumerate" -- just like "illiterate" -- indicates the current state of a person's abilities, not some fixed or inherent trait. The remedy is education.

My apologies, this my interpretation of your comment. Thanks for the clarification

aside: Sisk et al (To What Extent and Under Which Circumstances Are Growth Mind-Sets Important to Academic Achievement? Two Meta-Analyses DOI 10.1177/0956797617739704) looked at >450,000 students and found little or no effect size for this approach.

standard primary literature caveats etc and where it is/is not applicable but this does put 'growth mindset' on the back foot.

Interesting find, I had no idea! I'll read through it, I'm curious if it discusses Dweck's "helpness" terminology as well.