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One issue I have when I solve math problems is that I've found that I have two threads going on at once. There's my primary thinking thread where I'm writing the problem out and evaluating it, but there's also another thread going on where I'm "voicing" the numbers and symbols in my head. Like it's just background babble. The problem is I frequently voice the wrong number or symbol and it confuses me into writing the wrong thing down.
I make so many stupid mistakes this way. I can't make it stop. The more I stress about it, the more I concentrate really hard on the problem, the worse it gets.
It's a genuine defect in cognition, IMO.
I kind of thought everyone struggled with this. And that this is what they mean when they say they hate math, but I had a professor point out that he saw I suffered unusually from stupid mistakes like this. It's not common but it's also not rare. He thought the fact that I wrote so big on my scrap paper to try to avoid getting confused was a tell-tale sign.
This isn't holding back my career or anything, but I did start doing mathacademy.com recently for fun and find I'm struggling in this way again.
Anyone know what I'm talking about?
I have not encountered this in the wild before, but it seems plausible as a sort of dyslexia for math.
The bad news is you probably are just slightly wired "wrong." The good news is depending on your age and profession you can probably get by just fine with some combination of compensation and correction. Sort of like how you can have the yips and be unable to throw to first and still be a starting pitcher in the MLB. And with the right training Lester even somehow got over his yips. It seems like you sort of have math yips and write the wrong thing down.
I'm not sure this has been studied thoroughly at all so take this all with a hefty grain of salt, but I do have a couple of suggestions.
The first, is based on the anecdote "It’s as Simple as One, Two, Three…" in the Feynman book What Do You Care What Other People Think? The brief summary is you can count and do another thing at the same time by using "different ways of thinking." For example counting visually so you can use your vocalization to simultaneously talk to someone, or counting using sub-vocalization and visualizing numbers or objects to calculate something else. If you are having problems with accuracy using sub-vocalization test trying to do problems focusing on only using:
If one of those has appreciably better accuracy start from there, and slowly add back in the other methods.
Which leads to the second piece of advice, slow down. If there's no time pressure it's fine to spend the time to do all three until your mental models reach consensus. As they say, perfect practice makes perfect. It sounds like you are not in school anymore. Either way, slow down to a pace where you can work with 100% accuracy when practicing. Progressively push this pace, but speed should come naturally with familiarity. In a school situation it's a problem of trading off accuracy and speed on an exam to maximize expected score. Fortunately, this isn't really a common thing that comes up IRL. For computer programing for example, working at 1/2 the rate in lines of code per minute but introducing no bugs is 1000x better than working twice as fast but introducing inscrutable bugs.
¹ Assuming undergraduate level applied math where there is usually a physical analog. RIP if you you're tying to do n-dimensional analytic geometry or some shit.
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