Learning Rate

I have tended to treat learning skills as a purely hours of effort process.
Practice an hour a day, sometimes put in a couple of sessions, overreach occasionally.
10,000 hours of good directed practice to achieve expertise.

Sadly, I have found this to be a technique that has almost always lead me to failure of one sort or other.
In some cases, I lacked the physical or mental talents and in others because life simply interfered. Daily progressive mental and physical training is definitely better than not but it seems like I am missing a fundamental element to success.

In truth, I have no idea how to develop talent beyond an intermediate level. For those that do it seems to flower naturally and incredibly quickly and for those do not (me) it seems like an eternity of plodding to become much stronger than average but not clearly excellent.

I like to hope that there is a process improvement; something similar to periodization or the westside barbell of rational thinking that could dramatically sharpen my skills with memory, calculation, logical thinking but I have not found it.

So… If you have some clues on how to develop a plan for mental calculation I am all ears as my current path will give me reasonable narrow results over the next couple of years if life does not distract but is terribly unlikely to provide me with the level of success I would like.

It may simply be that I would need to invest an amount of time unavailable to me and be 30 years younger.
It may be that my processor speed is inadequate to the job. It is hard for me to be objective.

Often I find internal anxiety in the process of difficult thinking and am not sure if that is the result of simply being stupid or is the cause of being stupid. Either way, removing the anxiety of hard thinking would likely help the process.

Not sure what other data points I can throw at the wall as regular daily practice provides me with reasonable and progressive results but my rate of mental improvement seems limited by the number of sleeps available to me and I don’t really have enough of those left.

I need to find some more efficient ways of consuming mental calculation.

TL;DR… Looking for suggestions to improve the rate of learning in mental calculation; and mathematical thinking in general.

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Started rewatching art benjamin ttc course tonight. He has some good hints in there. He explains how they successfully teach young children the times tables. Have to listen carefully for the stuff he says between examples. Seems like that is where a lot of the gold on practice is.

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The truth is when you have achieved mastery in something you tend to ask yourself the question “Could I have done it faster?” The answer is almost certainly always “yes”.

There are people who grow faster than others or slower but ultimately that is different than picking a faster route, it doesn’t even matter. We are not really talking about much speed at all, even looking at reading rates the maximum difference is a multiple of 5 without employing a new method and that is not found. The actual upper difference is more a multiple of 2 and everyone can get to a multiple of 2 with sufficient practice without special techniques. It’s not really having a strong processor and a weak one at all the difference is negligible and in the end only a difference of practice without differing techniques.

When I was in my mathematics class the entire class with some people who were exceptional was spending a year to learn the material, me being in that class I naturally was gliding along with their pace there wasn’t much a benefit of going faster. The next year when the course had gotten the most difficult I spent the last 5 days of my summer (before the start of the course) to complete the entire year. The same year I would have spent and did spend doing it in class all over again even to lesser mastery than I had after those 5 days. The 5 days were around 10 hours a day, still with inefficient methods. Attempting the questions in the harder bracket then if unable to going to some elementary questions until I can do all of them, catered to my own pace with full focus. Never looking up the answers but delaying questions I was struggling with if they ended up being the only ones to the topic that I still couldn’t quite do.

You see the hours I put in don’t really matter. The only reason they don’t matter is because under normal settings a lot of these hours are wasted, not used in the most efficient way possible, require maintenance and are sub-optimal. Regardless of how many hours you are spending doing the same thing again you will eventually stop getting faster, yet you will also see someone who is faster than you. Within those golden 10000 hours you will come across a way to do what you have been doing faster with much more mastery. This is the same thing you could have however done before spending those hours. The reason something like this happens is because people in a field that is different than learning truly do not know how to learn faster. I don’t even think the research on learning faster is at any point where it provides sufficient use.

A lot of people believe you have no other choice than putting the hours in and doing the same thing. The only issue with this is, it does not have true basis. If you are doing something again and again and expect to become faster or more efficient. You are only going to get faster and more efficient by as much as you have been doing the last day. It’s not going to suddenly jump up and give you a miracle. It is however capable of just plateauing. You must really carry that awareness with you when you are doing something.

In truth though, moving beyond intermediate level is not actually that difficult, regardless of your ability if you do more than everyone else is doing you will end up being ‘professional’ or skilled sooner rather than later. You will however also plateau there.

While some people expect to spend years and I wouldn’t really call this a bad thing, it is usually the people with the greed and rush to do things faster that either do them faster or don’t do them at all.

I mean in this current world people are arguing about reading speed, everyone who has different ‘processors’ is within a multiple of 5 between each other or employs methods that when practiced also put them within multiples of 5 between each other and I am being rather considerate here saying 5 when it is close to 2.

Onto your question though,

This means regardless of you doing what you are doing you do not have enough time to get to where you want. So you have to do something more efficiently.

Take note of why you are improving by splitting the process up and then try to maximize the factors causing your improvement and minimize the chain of waste time between them; just re-compile more efficient algorithm.

Dissect and isolate the precise cause of anxiety then cut it or modify it and recompile. Remember exception handling, try and catch, etc. You may quickly find it is something like the perception of the load rather than the actual load itself, which gives you a simple solution of splitting it up in the day, or telling yourself it is only X more where X is ‘little’ , N times rather than telling yourself it is K which is large.

All I am really saying is that what you are describing are problems. Mathematicians solve problems too, this shouldn’t be limited to particular problems.

That was an extremely long post to be content free.
You might consider becoming a lawyer or going into sales.

I am looking for pragmatic techniques from those who have succeeded.
I can hand wave with the best of them but this is not that.

TBH, this forum is what keeps me thinking about and practicing new methods of mental calculation.
For - of course - I do a mental calculation once or twice a day. But it is not the life throws calculation after calculation at me.
So for me, this forum is what keeps me on my toes.

@RobertFontaine, you need to find a way to keep this alive in you. You already do daily practice and you seem to find the most amazing new videos about it. So I have no other advice for you than keep it up!

If you find that your progress is slow, what I would do is analise the progress. Find out what it is that stalls it. Easier said than done I know, but like I said, I don’t know what else to advice you.

As for pragmatic techniques, I train on the train, bus, metro.
I make trainings stuff that I can use on my smart phone.
So I sometimes make spreadsheets to give me challenges.
Or just randomly pull numbers and start playing with them.