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I am curious, is anyone aware of a study which determines the advantage of typed vs. handwritten material in mathematics?

Of course, ideally, we would compare the best of both worlds. Say a beautifully $\LaTeX$ed document vs. the notes of someone whose handwriting is impeccable.

In my personal work, I probably create neither, but I aspire to both in various venues. At various times I hear positive things for one format over the other. I really doubt there is a quantitative case to make one way or the other. Am I wrong? Is there someone who has made the case that neat handwritten notes are inferior to cold sterile typed lecture notes? I beg the wisdom of the internet.

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    $\begingroup$ Who are you thinking would create the notes? My understanding is that the big advantage of hand-written notes is that the students go through the process of hand-writing them (and, iirc, research says the process of hand-writing the notes even beats the process of typing them). $\endgroup$
    – Jessica B
    Commented Feb 14, 2015 at 21:35
  • $\begingroup$ I second Jessica. Do you mean your handwritten notes to present to the class or having your students copying them by hand. The first might not have a good answer while the second I think making them copy is beneficial. $\endgroup$
    – Chris C
    Commented Feb 14, 2015 at 21:56
  • $\begingroup$ Roger Penrose (famous physicist) does his presentations using hand-written and hand-drawn notes. It gives more flexibility of layout and a unique style to his presentations. I think it works for him, but I wouldn't do it for myself. $\endgroup$
    – Richard
    Commented Feb 14, 2015 at 23:02
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    $\begingroup$ Not an answer, but related enough for a comment: I tend to handwrite solutions to tests, partly because I want students to see them as what they could have produced them themselves, as what a perfect but real answer would look like. Typed solutions feel too impersonal, too foreign to them. $\endgroup$
    – Benoît Kloeckner
    Commented Feb 15, 2015 at 20:23
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    $\begingroup$ @BenoîtKloeckner agreed, I also write solutions (to tests and homework usually) by hand. But, my reason is less noble. I just don't have time to do otherwise :) $\endgroup$
    – James S. Cook
    Commented Feb 15, 2015 at 20:37

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I have no study to cite at this stage, but I can offer some of my experience of working with thousands of students in my Maths Learning Centre.

Organisation

In my experience, students dislike things that are difficult to follow and difficult to find information in by themselves. They like things with clear layout and organisation, with important information highlighted and summarised, and where different parts of the text (proofs, examples, worked examples) are clearly delineated. These are not just likes and dislikes either, but I have seen a change in the structure of the notes encourage more independent learning between two semesters of the same course.

In terms of being able to achieve this organisation, the good things can be achieved in both handwritten and typed materials, and badly-organised things can exist in both. Personally I have found that you have to work harder with handwritten materials to be organised, especially if you are making them up on the fly. LaTeX has a natural structure of chapter-section-subsection-etc which helps you to be more organised as you type.

Already-written maths notation

In the specific case of worked examples of problem-solving, my experience is that maths that is already written down does not make any sense. The eye naturally slips over equations and symbols, often not pausing to even recognise the names of the symbols. Moreover, if you are projecting maths onto a screen in your lecture, the students will never have enough time to read it and understand what is going on, no matter how slow you think you're taking it. Already-written symbols are just too difficult to parse at any speed.

Leading by example

Finally, I believe that the goal of a worked example is to show what students are supposed to do themselves, and so worked examples should look as close as possible to what you expect the students to do. It is easier to imagine doing the maths yourself if it is handwritten. Moreover, you are more able to imagine how long it takes them to do it and the difficulties they face if you are doing yourself what you have asked them to do!

You could apply this argument to the information text as well. If you want them to learn the skill of reading maths (such as proofs etc), then you probably want to present those parts in the format they are likely to see in textbooks, journal articles etc -- that is, it might be better to have this part typed. [A caveat is that since maths that is already written down doesn't make sense, if I were presenting a proof in class, I would handwrite it even though it was typed in the notes. Alternatively, I would take the typed version and mark it up with highlighting and extra working just like I would if I was reading a real journal article myself.]

Summary

In light of my experience, I would recommend typing most of the materials you give to students, but handwriting anything that is supposed to show them how to do something for themselves.

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  • $\begingroup$ interesting philosophy of delivery, it would seem the next generation of LaTeX might be dynamic where the reader sees the equations worked out one at a time. I think the technology already allows this with some sort of Beamer derivative... I noticed the PDf reader already supports a read-aloud function, but, the math equations are not parsed very well just yet. I do LaTeX notes for most of the reasons you say here, the hyperlinks with hyperref package are really nice. But, their is still some inexplicable charm to the handwritten form... thanks for this post. $\endgroup$
    – James S. Cook
    Commented Feb 23, 2015 at 6:36
  • $\begingroup$ I'm more than eight years late to the party - but I can't refrain from explicitly agreeing that "maths that is already written down does not make any sense" really absolutely hits the nail. $\endgroup$
    – Jochen Glueck
    Commented Aug 14, 2023 at 21:49
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I'll stick my neck out:

There is no obvious advantage of handwritten lecture notes (written by the lecturer) over typed ones (typed by the lecturer), given infinite time, ability and willingness to create the notes.

Note: this is not intended to be a research-based answer, and I'm not even certain I'd agree with it if I spent a long time thinking. It is essentially intended to act as a poll of general opinion, given that nothing more concrete has come forward in a week. If this is felt to be inappropriate, I'm happy to delete it.

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