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My students frequently mix up my $t$'s with my $+$'s and my $y$'s with my $4$'s.

What is a good handwriting font for distinguishing these and other easily confused symbols?

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    $\begingroup$ Sometimes spacing helps, but my students would almost always mix $z$ and $2$, until I stroke my $z$'s with a middle bar, like ƶ or Ƶ. Very useful question! $\endgroup$ – dtldarek Mar 14 '14 at 1:08
  • $\begingroup$ I think it would be good to collect the advice from the answers in a small table, for convenience (in a letter-how to make it recognizable format). $\endgroup$ – dtldarek Mar 14 '14 at 2:36
  • $\begingroup$ This is an excellent question. I once had a professor who said he'd worked hard to completely change his handwriting to make it more legible on the board. I had another professor whose k, r, t, x, and kappa were all indistinguishable to me. $\endgroup$ – Mark Meckes Mar 14 '14 at 14:26
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    $\begingroup$ Anyone coming here and looking to provide an additional answer: I would still love to see an answer that shows a good strategy for differentiating between 5 and s. Making sure the right angle at the top of the 5 is very pronounced is not enough, and this specific issue is not addressed in the (excellent) answers from Jim and Joel. $\endgroup$ – Chris Cunningham Mar 26 '14 at 15:06
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    $\begingroup$ I think it's probably worth linking this question to an old one on MathOverflow that deals with a similar problem mathoverflow.net/q/5853/45 $\endgroup$ – Loop Space Mar 27 '14 at 8:26

16 Answers 16

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I changed my handwriting font years ago for precisely this purpose, and I have continued to tweak my letterforms over the years, using the algorithm of changing the form of whichever letters seem to generate the most confusion. Here is my current font: enter image description here

A few notes about these letters:

  1. Capital letters aren't listed, but my experience is that they're all fairly straightforward. Just make sure to use print letters instead of cursive.

  2. It's crucial to have versions of a, b, d, p, and q that can be written using a single stroke. If you draw your circles and stems separately, they will constantly get disconnected, which vastly decreases legibility.

  3. I often omit the bottom "tail" on the f when writing it in the middle of a word, but I always include it when it's part of an equation. Similar statements hold for the top curve on the i. I will also draw a 1 as a simple vertical line if I think it's clear from context.

  4. The l (ell) is my newest letter, and I'm not really sure about it yet. I tried using a cursive $\ell$ for a while, but it never looked good inside of words, and it still wasn't very legible as a variable. At present, I am often omitting the top and bottom curves when the l is part of a word.

  5. In general, I've had bad experiences with vertical loops. I've tried loops on $\ell$'s, g's, j's, d's, and q's, and all of them seemed to make the letters less recognizable. (This is probably because such loops hardly ever appear in computer or typewritten fonts.)

  6. The tail curve on the t is crucial to avoid confusion with a + sign.

  7. The initial curves for the v and w are quite helpful for legibility. I also think v's and w's are more legible with relatively sharp angles, as opposed to a curvy cursive approach.

  8. The initial curve on the x is absolutely essential. This will be one of your most used letters, and it really helps to get it right. Curves on any of the other three stems don't seem to improve legibility, and make the letter annoying to write.

  9. I also think this curvy version of a y is easier to read than a two-sticks version. Among other advantages, it can be drawn in a single stroke, which avoids disconnection problems.

  10. The line across the z helps avoid confusion with the number 2, and the line across the 7 helps avoid confusion with a variety of symbols.

  11. I don't seem to be able to draw a curvy-bottom 9 that looks good. I wish I could.

  12. This version of a 2 is much clearer than any version with a loop on the bottom.

  13. I tried drawing a final loop on my o's for a while (like a cursive o), and it didn't work out.

Edit: By request, here are my capital letters. Unlike my lowercase letters, my capitals are really quite standard, and I don't have much to say about them. I've also included by Greek letters.

enter image description here

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    $\begingroup$ That list is great. I especially like the second point; it seems obvious in retrospect but until just now it never occured to me while I have considerable problems with this. I changed away from writing in my usual handriting style to 'printed' letters on the blackboard, and this was always an issue since then. $\endgroup$ – quid Mar 14 '14 at 23:45
  • $\begingroup$ @quid Thanks. I was taught to draw circles and stems separately in elementary school, and the result for me was about two decades of terrible handwriting. $\endgroup$ – Jim Belk Mar 14 '14 at 23:53
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    $\begingroup$ @Andrew: I've seen one-stroke x's. The results are not good. $\endgroup$ – Mark Meckes Mar 22 '14 at 12:42
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    $\begingroup$ Isn't that confusing when people will think of the empty set? $\endgroup$ – Markus Klein Mar 26 '14 at 14:44
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    $\begingroup$ @avakar Not only does it make x's clearly distinguishable from some sort of multiplication symbol, but it also just makes an x look a bit more like typical x's in math books. Almost all math books use some sort of italic serif font for variables, and in such a font the stems on an x are almost always curved on the ends. For a handwritten font, just having a curve on the upper left end seems to suffice for conveying this same visual impression. $\endgroup$ – Jim Belk Dec 17 '15 at 0:50
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enter image description here

$\times\ \ +\ \ 4\quad 2\quad \omega\quad 9\quad a\quad 1\quad i\\ x\quad t\quad y\quad z\quad w\quad g\quad q\quad l\quad j$

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    $\begingroup$ Some years ago, when I was a student, I was doing a calculation, and a z became a 2. Needless to say, the result was wrong. Since then I crossed my z's as seen here. Same for a curl on the bottom of a t. $\endgroup$ – Gerald Edgar Mar 14 '14 at 13:22
  • $\begingroup$ Like @JimBelk, I also put a horizontal line across my $7$ to distinguish it from $1$. $\endgroup$ – Joel Reyes Noche Mar 15 '14 at 1:10
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    $\begingroup$ I am impressed that you distinguish $\omega$ and $w$. $\endgroup$ – user173 Mar 25 '14 at 2:16
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    $\begingroup$ My only issue is with your 4. When written quickly, that style tends to resemble a 9. I prefer the open topped one and giving y a loop at the bottom off the tail. $\endgroup$ – David G Mar 27 '14 at 3:15
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    $\begingroup$ A friend of mine in undergrad used his bad handwriting to his advantage. He once found that he had to change a partial derivative symbol into a 2 in order to get the correct answer, which he did deliberately over the course of a few lines. (Or so he said; he never explained what happend to the other partial derivative symbol.) $\endgroup$ – Toby Bartels Mar 27 '14 at 16:41
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alphabet alphabet with stroke order

Here are what my alphabet and numbers have ended up looking like. For the sake of clarity, I've included a stroke order chart, where the first stroke is red, the second green, the third blue, and the fourth cyan.

I try to make distinctions between every character, but I agree with those above who have noted that "o" is, in general, a terrible name for a variable. I tend to only use the "O" with a flourish where I have to make a distinction between "o" and "O".

I use the double-story "g" to distinguish from "y", and "S" with a serif to distinguish from "5". I use serifs to distinguish between uppercase and lowercase ("c" and "C", "s" and "S", "k" and "K", "v" and "V", "w" and "W", "p" and "P"), but where I don't have to make that distinction, "c" and "s" get serifs to distinguish from "(" and "5", respectively.

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    $\begingroup$ I also sometimes put serifs on $Z$ to differentiate it from $z$ or $2$. $\endgroup$ – Joel Reyes Noche Mar 27 '14 at 2:30
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I would like to add a point that I've not seen explicitly mentioned in the other answers. That is that context can often be your aid in clarifying your lettering. As a trivial example, no one is going to misread they as +hey. So the "special alphabet" is primarily for mathematics in your lectures. (That said, you should cultivate a clear hand writing for normal text but it doesn't need to be as extreme as for the mathematical part.)

Similarly, if you never write $\times$ then the students will soon realise that x means $x$ and not $\times$. And I doubt that someone will mistake $x_k$ or $\vec{x}$ for $\times_k$ or $\vec{\times}$.

On the other hand, scale is often hard to see on a board so X and x are not easy to distinguish. It can be awkward to avoid using these together (consider the common desire to have $x \in X$) and distinguishing them visually can be difficult, but then context can help.

Here are some practical tips:

  1. Go in to a large lecture hall, write some random equations on the board, and then go to the back and try to read what you wrote. Then modify your handwriting until you think it is clear. This won't be perfect (since you know what you wrote), but it'll at least be a lot better than not doing it.

  2. Say what you write as you write it, and make sure that before you write anything on the board then the students are at the same point as you so that they are paying attention to what you say as you write it.

  3. Cultivate writing "the wrong way". It's a bit trickier for those not blessed with sinister tendencies, but if you can learn to write so that you do not stand in front of what you just wrote then it will be much easier for the students to see what you write as you write and say it. This doesn't mean writing with your left hand, it is possible to do this with the right hand but the body position takes a bit of getting used to. This has the added bonus of making you more turned towards the students as you write.

Having just given a lecture, I'd add one more practical point: ensure that the board is clean before you write on it. Stray squiggles left over from before you erased it can be confusing.

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This is my handwriting font for mathematics. (Excuse the shakey-ness, this was made using the stylus on my phablet.)

It isn't as minimalist as some of yours, but I have never had anyone tell me they had trouble reading my writing. I make it clear which letters are which by using size and giving attention to negative space.

I find that using big loops and serifs is really good for board work, where it can otherwise be difficult to distinguish capital letters. (Spencerian cursive is actually pretty good for board work too, just not for equations.)

The prototypical gesture here is the J, from left to right to down. That is the leftmost part of many capitals.

Keeping track of where the bottom line of the word is also important, for example the tail on the lower case t is just below thst bottom line, and it is crossed exactly on the middle letter line.

My biggest problem is that my vs look like nus.

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    $\begingroup$ That's a nice handwriting font! $\endgroup$ – Mark Fantini Dec 21 '14 at 19:45
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    $\begingroup$ It's a beautiful font, but I can see where students who are not used to it still might be confused. Especially g's with 8's, p's with ρ's, f's with j's, S's with ∫'s. Some students in the back row might even think the capital T is an i hat. $\endgroup$ – user3932000 Mar 25 '16 at 21:05
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I think you need to fix any problems you have by modifying a letter or two of the way you write. For example, I used to write my y's in two separate straight strokes, but they would get confused with my x's if I wasn't careful about where the stroke stops. To correct this, I started writing my y's more like the way you write a g, with a curly bottom. I also stroke my z's with a cross to keep them separate from my 2's.

To fix your t's, add a curl on the bottom.

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As others have suggested, adding a serif can make a big difference. I write my y's like g's, and I also stroke my z's through the middle. Lower-case l's are written cursive-style, with a loop, and I make sure to make the 'tail' of my q's big enough to ensure there's no confusion with 9's.

I also never use certain letters as variables (if I can help it) - especially o's.

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In response to Chris Cunningham's request, I think this sort of 5 is unlikely to be mistaken for an s:

5

The key is not just the right angle at the top left, but the sharp angle directly below it. The danger here is to make sure you don't come so close to closing up the bottom that it looks like a 6.

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    $\begingroup$ My 5tudents will thank you. $\endgroup$ – Chris Cunningham Apr 25 '14 at 4:40
  • $\begingroup$ I know this thread is really old, but I haven't seen my solution discussed. I don't alter the digit 5 to distinguish it from the letter s, because I write 5 so often in comparison. Rather, I just change the letter s (used in mathematics) by writing it with very pronounced serifs (top and bottom) in one stroke. This takes very little change in practice, and I stick to the plain old curvy s for normal, non-math writing. $\endgroup$ – Nick C Feb 9 '18 at 22:39
  • $\begingroup$ @NickC: Well, I don't alter my 5 either; this is just the way I write 5s. But it's a good point in general: modify symbols in inverse proportion to how often they're used. Hence (as discussed elsewhere on this page) change z instead of 2, and change t instead of +. $\endgroup$ – Mark Meckes Feb 10 '18 at 2:00
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We discussed this, or more specifically the subject of handwritten $x$, a while ago at The Aperiodical.

I still don’t understand why the two-curves $x$ never caught on in the US. Newton wrote $x$ the way modern Brits do, so it predates American independence. Curious!

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    $\begingroup$ The linked photo clearly shows that Newton usually wrote "x" by crossing two lines. There are only a few cases otherwise on a page with dozens of x's. $\endgroup$ – Nick Matteo Jan 15 '15 at 17:04
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Taking my cue from printed math (and particularly TeX), I use different fonts for text mode and math mode. The italic font (math mode) is cursive, while the roman font (text mode) is printed. This helps distinguish ‘a’ from ‘$a$’, for example. (And assuming that you and I are both using the default fonts on this site, then my handwriting looks pretty much like those two letters do on the screen.) When I started this, I had a somewhat too exaggerated cursive style, so the fonts look less different now than they used to, but I maintain a difference in all letters.

Also, after several false starts, I've settled on a little loop at the top of ‘0’ to distinguish it from ‘O’. (Much as TeX uses merely slanted letters for math-mode capitals, I don't distinguish text-mode and math-mode capitals at all, saving the fancy cursive stuff for calligraphic font, which I use only in extreme circumstances.)

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    $\begingroup$ I like this idea in general, but regarding 0/O, a loop at the top makes me think more of the letter, not the numeral. $\endgroup$ – Mark Meckes Apr 18 '14 at 9:38
  • $\begingroup$ I can see that, but since that would be a cursive letter and the capitals are printed (see the parenthesis above) it doesn't really look much like an O. At least, I don't think it does! $\endgroup$ – Toby Bartels Apr 19 '14 at 22:34
  • $\begingroup$ But it's surprisingly hard to get a distinguished zero! Sometimes people use a slash, but we need that for the empty set. I tried a dot for a while (like some computer displays have), but it was too much work for too little result. So now I have the curl; quick and easy, and can be made more or less noticeable as required. Still not ideal, however, I agree. $\endgroup$ – Toby Bartels Apr 19 '14 at 23:31
  • $\begingroup$ To me, it looks like a script O, so if you think of all capitals as printed, I see your point. But how often do you need an O in math mode anyway? I would think it would come up rarely enough to qualify as the kind of "extreme circumstances" for which you save the calligraphic font. $\endgroup$ – Mark Meckes Apr 20 '14 at 8:10
  • $\begingroup$ It's rare, but if it's an ordinary "O" then I still don't want the fancy font. $\endgroup$ – Toby Bartels Apr 23 '14 at 11:54
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I write like this: enter image description here

And everybody can read what I'm writing. Especially, take look at letter x.

And here are my digits: enter image description here

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  • $\begingroup$ Ohhh, I love it. Looks right out of a Tim Burton movie. Cool Q, too. and j. and y. $\endgroup$ – Alexander Gruber Feb 8 '15 at 21:25
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How about using cursive handwriting as shown below:

enter image description here

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  • $\begingroup$ And is this good? $\endgroup$ – András Bátkai Apr 18 '14 at 7:00
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    $\begingroup$ @AndrásBátkai With this at least y and 4 look "different". The word good is subjective and yes this is good for me. $\endgroup$ – Aquarius_Girl Apr 18 '14 at 7:12
  • $\begingroup$ Sorry, if I sounded rude. I thought some explanation why you think is good belongs to the answer. $\endgroup$ – András Bátkai Apr 18 '14 at 7:13
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    $\begingroup$ @AndrásBátkai you didn't sound rude, you sounded as if you disagree with this being good. :) $\endgroup$ – Aquarius_Girl Apr 18 '14 at 7:14
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    $\begingroup$ I do this (see my answer), but I notice your "z" … students would complain that they couldn't recognize that as a "z", so eventually I had to heavily modify it. (Now it almost looks printed, but it still has a curl.) $\endgroup$ – Toby Bartels Apr 20 '14 at 0:15
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The key is neatness. I am a student, and I take for granted that my lecturers will use neat handwriting. I don't like it when a lecturer's handwriting is scrawled hastily and messily because it makes it difficult to read. I also don't like it when a lecturer neglects to write down something they have said, or something that is helpful with understanding what is being communicated (e.g. writing "Proof" before a proof to let the class know that the theorem has ended). Below I have given some pictures of the best handwriting that I have encountered.

Picture 1

Picture 1: this lecturer gives a tail on his v's and w's. The only problem with this handwriting is that the difference between a u and a v can be confusing.

The following two pictures show writing done by a lecturer who is exceptionally neat when he writes on the board. His style of teaching is to have a lot of discussion, and to only write down the mathematical symbols which he is talking about.

enter image description here enter image description here

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One thing I have run into is, when learning or tutoring probability, being able to distinguish the random variables with their density functions' support.

To that end, I typically put serifs on my capital letters only, and that helps me tell the difference. One big issue is telling the difference between $W$, $w$, and $\omega$. I typically put serifs on $W$, keep the angles crisp on the $w$, and exaggerate the round parts for the $\omega$.

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I don't understand how you can mix up a t and a +-sign:

  • the letter t contains a curl at the bottom and the bar does not pass left of the vertical line
  • the +-sign consists only of straight lines.enter image description here
  • the letter y starts with a curl and has a hole at the bottom
  • the digit 4 consists only of straight lines.
  • the letter z is written in the French way, the hole is quite long.
  • the digit 2 has a small but clear hole.
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enter image description here

I tend to loop my ζ so it doesn't look like a Z and I also put the lines on the z so it is not a 2.I also make my 1 like shown in the picture so it is not an I. I make my lowercase g fancy so it is not a 9. I put lines on my Θ so they are not θs. I also make my α short so they are not a ∝. I do not make my Phis like a plain old circle with a line. I tend to make a loop and then come down. My μs have a loop on the side.

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