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I became a better reader when I stopped sub-vocalizing (hearing the words in my head). I still do that when I read math. I tried not to do that when I read an expression today. I felt less confident about it, but it did seem easier. That lead me to suspect there are ways to make notation convenient (currently, it's a hindrance for me).

What are the best practices for reading notation fluently?

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Not sure whether or not this applies to you but I find that many students have problems with maths because they don't fully realise that it all means something. Therefore they are trying to solve problems by memorising meaningless strings of symbols, and I think it's pretty clear that this is unlikely to be successful. My suggestion for these students is that they should vocalise what they are reading. To take an extreme and admittedly made-up example, if someone reads $$\{\,z\in{\Bbb C}\mid z=\overline z\,\}$$ as "squiggle-$z$-funny-sort-of-e-C-with-an-extra-line-on-it-vertical-line-$z$-three-horizontal-lines-with-another-$z$-under-one-of-them-final-squiggle" then their chances of success in mathematics are vanishingly small.

Hope this helps! BTW I have never actually used the term "vocalise" with my students, but it's a good one so I might steal it ;-)

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  • $\begingroup$ Hm. I found that 'Zed is an element of C such that zed equals zed (don't know what that overscore means)' requires me to find some visual analogue of it. So my thoughts usually proceed, 'z is just a variable, so z, element of C - ::draw a circle for C in my head, put z inside it::, such that ::draw a circle around C representing attendant circumstances - put a note to self in there that z=z overscore. Then work with the set C and whatever else and check to make sure they don't violate the attendant circumstances. I don't know if that's an effective way to do it. $\endgroup$ – Hal Mar 15 '14 at 0:04
  • $\begingroup$ I certainly didn't mean to suggest you don't use visual images - sorry if it came across that way - they are indeed very important. I suspect that most mathematicians think both visually and verbally, with the balance different for different people. BTW $\overline z$ is read as "$z$ conjugate" and it is indeed a good thing to visualise, see here if you want to know what it means. $\endgroup$ – David Mar 15 '14 at 0:07
  • $\begingroup$ You didn't suggest it. I just meant to say "Here's what I'm doing - what do you think?" $\endgroup$ – Hal Mar 15 '14 at 0:08
  • $\begingroup$ I think what you are doing is good, but I wouldn't totally neglect the other approach. It may not give you much but I feel fairly sure it will give you something. $\endgroup$ – David Mar 15 '14 at 0:10
  • $\begingroup$ There is something a bit similar to what you are describing in Richard Feynman's memoirs Surely You're Joking, Mr Feynman!, in the chapter entitled "A Different Box of Tools". I haven't checked but you can probably find it online. $\endgroup$ – David Mar 15 '14 at 0:14

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