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Maths is already quite an abstract subject, so to spend time discussing the quality of a student's or even a research-level mathematician's handwriting seems rather tedious. I proceed nonetheless.

When I was in school, among my peers I didn't necessarily notice (although maybe I didn't gather enough statistics on) any (positive or negative) correlation between those who have good handwriting and those who have good understanding of a subject or do well in homework or exams.

Obviously there is a trade-off between writing quickly, which allows one to carry out their own thought process quickly in regards to their working memory, and writing neatly, which makes their handwriting more legible for themselves and for others, i.e. communicating their thoughts when looking back upon their workings out.

I have always written as fast as possible because I need my working memory to get through it's thoughts as quickly as possible: this surely maximises my understanding. But my handwriting has suffered as a consequence.

One of the girls I currently tutor writes ridiculously neatly, and she doesn't write very slowly, but I think she would benefit from writing faster when getting her thoughts down, then re-writing her scribblings up neatly later.

I also feel that, now that I have gotten into a bad habit of my handwriting not being neat, that I need to re-learn how to write neatly again, and then once I have done this, speed will naturally come later.

My questions are:

Would it benefit me to practise making my handwriting neater and then once I have gotten into this new "good habit" I can start increasing my writing speed? Should my student who writes slowly but neatly sacrifice her neatness for scribbling but with speed, but then she can re-write her answer up later on? Should I encourage other students to write in this manner? Or should I encourage students to focus on neat handwriting and speed will come naturally later? Or does it not matter what I suggest to students because they are going to write how they write regardless of my suggestion anyway?

I am not sure if this is important or not, but I have always found that writing as quickly as possible, as close to the pace of your working memory as possible (my working memory is much faster than my writing speed anyway), to be the best way to improve mathematical understanding, and I imagine this is supported by statistical evidence: if you get your thoughts down on paper much slower than the speed at which you are trying to flesh out your thoughts, then this will surely hinder your understanding, right? I have always gone through this process as in the first sentence of this paragraph, and then re-written my answer up neatly if necessary or if I feel it would benefit me. But is this the right or best or a good way of doing things? Or is it personal preference / trial and error?


This is probably more of a convoluted ramble than a legit question, but I just want to see what others think. Maybe it's also a bad question because it is opinion-based, but who knows: maybe there have been statistically significant findings to some of my questions.

Moreover, you could argue that this question is not necessarily related to maths as it could be applied to other subjects as well. If others agree with this, what is the more appropriate stackexchange to ask this question on?

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    $\begingroup$ Rewriting takes significant time and effort, which is frequently better used elsewhere. The only times I would consider recopying A. when memorizing, B. when summarizing, restating, etc. or C. the original is unusable for whatever reason, but in most cases C is avoidable. $\endgroup$
    – nickalh
    Mar 17 at 9:42
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    $\begingroup$ @nickalh: I wonder whether there might be a misunderstanding: I do not think the Adam suggests to "recopy" a solution. Rather, when a problem is not completely mechanical, it is usually in vain to try solving it at first try. The main part of the work is then to figure out which approach or idea works, and in this case it's much more efficient if one does the "figuring out" by just scribbling down things instead of speding a lot of time on neatly writing down things the majority of which one won't be able to use in the end anyway. $\endgroup$ Mar 17 at 11:05
  • $\begingroup$ @JochenGlueck Adam specifically says "...then re-writing her scribblings up neatly later..." and "...she can re-write her answer...". Although when rewriting, one can certainly clarify, expand on, correct details, this sounds pretty similar to recopying to me. $\endgroup$
    – nickalh
    Mar 18 at 10:46
  • $\begingroup$ One common issue I see with students, especially high school students and earlier grades is mistakes due to poor handwriting or disorganization on the paper. Of course many times we modify part of an equation and simply recopy the rest to the next line. Miscopying a line is a common mistake and poor handwriting absolutely contributes to this. $\endgroup$
    – nickalh
    Mar 18 at 10:50
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    $\begingroup$ Writing as quickly as possible may work for OP, but I find detail, precision, and accuracy more important than doing a memory dump. $\endgroup$
    – nickalh
    Mar 18 at 11:06

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I think your question already contains the appropriate advice on what to do, but this might not become completely clear since the frameing of the question puts the focus elsewhere. I'd say the main point is not to either write neatly or to scribble - it's rather to adapt the writing style as appropriate to the situation.

When I teach at the blackboard in front of a class, I'll take care to have a very well-structured presentation and to write in a legible way (unfortunately I'm not particularly good at the latter, but still). When I discuss something with a colleague at a blackboard or on a sheet of paper, what I write will naturally be much less structured since we don't know the result of our discussion in advance - but it's still important to ensure that the other person can at least read what I write down. When I do math on my own (either on the blackboard or on a sheet of paper) I'll just scribble there whatever comes to my mind without caring much for structure or legibility. If, at the end, it turned out that my thoughts have lead anywhere, I'll rewrite the insights clearly and neatly and leave out all the clutter that turned out not to be useful.

Similarly, a student should adapt their writing style to the situation: when they do a problem on their own and the problem is not merely about practicing an algorithm, then they should be spontaneous and have no inhibitions to scribble something on a sheet of paper. When they discuss a problem with other students, they should still feel free to write down their thoughts in a spontaneous way on a sheet of paper (or blackboard or whiteboard), but what they write should of course be legible for the other students with whom they are discussing. And when they have found a solution and, e.g. want to submit it for grading, they should write it down again - this time in a well-structured and neatly written way.

To a lot of students this does not come easily. When I teach undergraduate students in their first year, I notice that many of them have a very strong inhibition to just scribble something on a sheet of paper. I guess that this is because many of them were taught math as a mechanical rather than a creative subject in school. They were made to believe that math were a collection of methods or algorithms, so when you "are given a problem" there were a clear path to the solution and solving the problem meant to follow this path in writing.

I'm under the impression that, while you're interpreting the situation that you experience as being about writing slowly and neatly vs. scribling quickly, it might in fact not be so much the speed itself that causes issues. Rather your student might feel very inhibited to just "give it a try" and write something down without any expectations that this will become a presentable solution at the first try.

So my advice is not to convince your students to "scribble instead of writing neatly", but rather to teach them that it is - for all those problems that do not merely practice a method or an algorithm - good and desirable not to write down the solution of a problem at first try, but to be spontaneous and creative, to try several approaches and ideas, and only to turn it into a neat presentable solution at the end of the process.

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    $\begingroup$ Yeah, this seems like a sensible and clear answer on first parse. $\endgroup$ Mar 17 at 12:42
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"Its me I'm the problem its me"


I don't know the correct term to describe someone who tells someone to do a worse job because the other person makes you feel inadequate (in the case writing). But it is not complimentary.

You need to relearn how to write.

How legible/illegible your handwriting is, is not impacted by how quickly you write. But by how much effort you have put into practicing writing neatly. Source: I know people with perfect... and I mean perfect handwriting who can write faster then thought. and I know people with barely legible chicken scratch writing who are really really slow at writing.

Speed at writing will come in time to this girl as she practices writing faster. But writing fast won't help her understand things better.


I am not sure if this is important or not, but I have always found that writing as quickly as possible, as close to the pace of your working memory as possible (my working memory is much faster than my writing speed anyway), to be the best way to improve mathematical understanding"

This is wrong. Research suggests the opposite. The longer something stays in your working memory, the better you understand things, and the better your rate of retention is.

Hastily scribbled barely legible notes therefore aren't as good as slowly written meticulous notes. Because slowly written legible notes force students to keep that information inside of their working memory for longer.

That being said there is research that suggests that deciphering hastily scribbled barely legible notes does help with retention. Because bad writing is harder to decode it takes much longer to decipher it. The extra time it takes to decipher the words makes them stick the working memory for a longer period of time. Which helps with retention. SO its not the fast writing that helps you with understanding... its the time wasted trying to interpret your Egyptian hieroglyphics that increase retention. But the same results can be achieved with a lower chance for error by taking things slow and slowly/carefully writing easy clear notes.

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An answer by way of a cautionary tale:

In my second year at university (studying mathematics), I too reasoned that it's not worth spending too long writing notes.  However, rather than work on my poor handwriting, I looked at shorthand.  Since neither of the systems I investigated seemed suitable, I had great fun inventing my own — and was pleasantly surprised that I could write it faster than longhand after only a week or so's practice.  So I switched to taking all my lecture notes in shorthand.

The folly of this became clear when revising for my end-of-year exams — I'd had far less practice reading my shorthand than writing it, and even after many weeks I couldn't approach even a fraction of my normal fluency!  Result: revising was hard work, I learned poorly, and did pretty badly in most of my end-of-year exams…

(The following year, I abandoned shorthand, and instead redesigned my handwriting from scratch*, optimising for legibility at all speeds.  So my third-year notes are very clear and easy-to-read, and I did rather better in my finals — though not enough to fully make up for the previous year.)

Hopefully this demonstrates the importance of being able to easily read what you write, even if it takes slightly longer!

(Being able to write clearly and legibly is a life skill with far wider benefits, of course.)


(* In case anyone's interested, after much experimentation I settled on printing instead of joined-up (cursive) writing — with practice, it's not significantly slower, and remains legible even at speeds where cursive degenerates to an unreadable scrawl.  I also reduced the size of ascenders and descenders and instead enlarged the central part of letters — they need hardly any separation — and used simple, easily-distinguished letter forms.  In fact, it turned out very like the Century Gothic font, though that wasn't intentional.  I've written pretty much the same way ever since, and have been complimented on it.)

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I say this as a fellow sinner, probably worse than you, and man to man: Yes, you should work on your handwriting.

I wouldn't sweat it in the immediate world of say lecture note taking, if you are pressed for speed. (But I find that pre-studying the textbook makes the compulsive "write everything down" much less needed. And I disdain teachers who want to create classes that don't have strong supporting textbooks...as if they were medieval lecturers at the University of Paris.)

But...on drill problems, I think you should have a moderate effort at neatness--even just to "respect" the problem and your demonstration of an answer--but very light...mostly working on the problems themselves.

In particular in the modern world, it is important in academia and business to be able to write clearly at the white/black board. I have personally had issues in the Navy, when my CO looking into a reactor incident I was involved in (which is another story) asked why my handwriting in the log (a legal document!) was so bad. And he was not even fussing for beauty...we are talking med school undecipherable Sanskrit. (I told him I would take a strain in the future and do better.)

One other note...I have personally have (often) found myself unable to decipher my OWN handwriting from classes or in the corporate world (e.g. interview notes). I do try to work around this in the corporate world by direct typing (or buying transcripts). And I'm a pretty intermediate level typer...but I slam away and get most of it down as running notes (not worring about perfection, going and cleaning up later). [I probably wouldn't do it in a classroom as my clicking can be pretty loud and distracting.]

Leave the girl who writes neatly (or others like her) alone. Find something else to work on. Teaching is an optimization problem where you (and the pupil) have limited time. Don't nitpick low priority items when there are much juicier fruit to pick first.

There is also an element of different strokes for different folks. Don't try to use yourself too much as a model, to expect everyone to be like you. And for all you know, slowing the problem down and being very deliberate may be helpful to the girl. For example if she typically makes mistakes in the details of multi-step algebra.

Same applies for bad handwriting kids. Leave 'em be, work on the math. Just deal with it and don't get into it. Unless the work is truly undecipherable or if it starts to show a lack of respect for the problem/answer (as my messy nuclear logs did). In which case, tell the kid to take a strain (but don't make some big hairy thing of it, or design a handwriting remediation program.)

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    $\begingroup$ "I disdain teachers who want to create classes that don't have strong supporting textbooks" - I wholeheartedly agree. $\endgroup$
    – Rusty Core
    Mar 18 at 20:58
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I see two questions, both about a similar subject.

Let me start by your second question: should you advise a girl with a neat handwriting to reduce that quality in order to "be able needing to" write the same information twice (once fast scribble in class, and next neatly written at home)? I believe the answer is in the question: NO WAY! That girl has a competence which you don't have: neat handwriting. And you seem to seek for a reason to criticise this girl, just out of pure jealousy. You should be ashamed!
Leave that girl alone and if you see that slowing down a little might be helpful for her, then that's what you do!

Second: your own handwriting. I remember in my second year at primary school, I had calligraphy classes, and although my current handwriting is a mess, I do realise the importance of those classes. But let's face it: calligraphy classes are given on paper, not on a blackboard (which is the thing you're writing on now).
As you admit that your handwriting is bad, I would advise you to get a blackboard with the typical calligraphic lines and do some calligraphy practices yourself in your free time, in order to improve your handwriting skills on a blackboard.

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    $\begingroup$ Regarding your second paragraph, I doubt that OP refers to note taking in class and wants the student to scribble her notes in class and then to rewrite them neatly at home. From the question, I rather think that OP refers to problem solving (for instance on homework problems or during their tutoring sessions) - and in such cases I think OP has a point that writing everything down in a nice and well-organized way at the first try is not always the best way to go. (But I believe the real point is not about the handwriting itself, but about how spontaneous one is with writing things down.) $\endgroup$ Mar 18 at 8:41
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    $\begingroup$ I don't criticise her neat handwriting: I praise it! And I am jealous of it. That said, I think that maximising one's writing speed and getting one's thoughts down on paper as quickly as possible (as close to working memory as possible) will maximise one's understanding of the thing they are working on. [But maybe I am wrong about this?] So actually what I am trying to say is that, the most important thing in regards to all this is to get your writing speed to match your thinking speed as much as possible. Maybe this is what I should be encouraging? Or maybe this is all nonsense? $\endgroup$ Mar 18 at 19:18
  • $\begingroup$ What I forgot to mention in the OP is that my student is also very impressively good at maths for her age, and I don't want her to not achieve her full potential because she is spending more than necessary amount of time making her writing neat rather than writing faster, thereby matching her writing speed to her thinking speed. But to be honest, I don't know how "fast she thinks". So yeah... And Jochen Glueck is thinking more along the lines of the question I intended. However, based on the responses I have got so far, I think I need to clarify my question somewhat... $\endgroup$ Mar 18 at 19:21

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