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I am UK-based but I guess this issue currently affects all maths educators and has probably been addressed by those how have been delivering courses through online channels for the past few years.

Say I wish to set a maths assignment for students in the age-range 16-18. In the UK these students would be taking A-Level which in the US I guess is SAT or college-entrance standard.

Say the question is a binomial expansion or an integration by parts where in a hand-written answer you would expect to see some lines of working.

Currently I am distributing question papers as pdfs attached to emails or via links to cloud storage. This is what I did pre-lockdown. For these questions the only approach I have found to be reasonable for students is they hand write their solutions and photograph or scan their answers then email them to me. So I receive either pdfs or image files (jpg or png) with their solutions.

All of the above is as before. The problem is the marking and feedback. I have to use "mark up" tools (is that the correct term?) built into packages such as Foxit Reader (pdf), Adobe Acrobat DC (pdf) , Adobe Photoshop (jpg/image), or Gimp (jpg/image) so I can "electronically" write on their solutions. This is (very) time-consuming.

However, the alternatives of converting questions to multiple choice format is both time-consuming and not suitable for these "algebraic working" style questions.

So what online tools do people use to set, mark and feedback this type of A-Level / pre-college question that speeds up the setting and marking process when performed remotely?

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    $\begingroup$ I've added the (online-instruction) tag. Feel free to remove it or add other tags as appropriate. $\endgroup$ – J W Jun 1 at 16:00
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    $\begingroup$ I added (secondary-education) tag due to the ages mentioned in the question. $\endgroup$ – Nick C Jun 1 at 16:02
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    $\begingroup$ Is it more time consuming than grading real handwritten answers on paper? $\endgroup$ – Rusty Core Jun 1 at 17:15
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    $\begingroup$ What exactly is the issue with printing them out annotating and rescanning? Is the quality too low? Obviously it's not a very eco friendly option, but it seems the easiest. Also everyone over 10 is old enough to learn LaTeX.;) $\endgroup$ – DRF Jun 2 at 13:35
  • $\begingroup$ Thanks for the additional tags. $\endgroup$ – Clive Long Jun 12 at 19:20
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My technique is pretty low-tech. I distribute solutions to the homework after it's due, so students can mostly tell what they did right or wrong by looking at the solutions. Then I reply to each student's email with any additional comments that they need in order to get feedback that they can't get just by reading the solutions. E.g.,

#37 -- What went wrong here was that in part b, you tried to use your two equations to eliminate both x and y, but the equations weren't independent.

This actually seems to go faster than writing comments on a paper in red pen. For one thing, many students make similar mistakes, so I can just cut and paste.

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  • $\begingroup$ Although there are other good suggestions, this approach seems the fastest but still individualised, which were my main aims. $\endgroup$ – Clive Long Jun 12 at 19:19
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If you have access to a device capable of touch input (like a tablet), then I would highly recommend using a stylus to annotate the pdf document. It should take almost the same time as if you were marking assignments on paper.

Foxit PDF and Gimp have in-built support for touch input. OneNote is also good for mobile and tablet devices.

If you don't have access to a stylus, and cannot get one due to the lockdown then you can easily make a DIY one: Instructables WikiHow

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I am recommending MyOpenMath (MOM) for this. It is a free, open source, online course management system for mathematics and other quantitative fields.

[Note: There are other systems out there, such as WeBWorK, which have similar functionality. I am recommending MOM for its quick set-up for those transitioning to systems like this.]

MyOpenMath supports "file upload" for student submissions (if you want to have students hand-write and then take pictures of their work). However, I recommend using a 100% typed format -- both for their work and your comments. And right before everything went online this term, a "show work" feature was added to MOM.

Say you want to see a student explain how to find $\int x \sin(x)dx$. If you enable show work, your question might look like this:

enter image description here

Note: Your students will have to type their work. See the math template tools in the problem for writing math content. A good first assignment is one that teaches them how to type mathematics.

In your grade book, you will be able to type your feedback to individual students, using the same math template tools they had for their work. [Copy/paste can be a huge time saver for commenting on common mistakes or using a feedback template.]

Other benefits of this kind of system:

  • You get to see exactly how long a student took to answer the problem.
  • You can author your own problems. Problems can be algorithmic if you want students to potentially have different versions of a problem.
  • Free to students.
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    $\begingroup$ Apparently MyOpenMath uses a slightly simplified form of LaTeX markup for writing equations, which gives it another advantage: students can learn this markup (and possibly for the first time about the idea of markup in general) during their math courses as well. Markup of various sorts is used widely across the web (Wikipedia, many discussion forums), in programming (for documentation, in source code comments, etc.), and in this age I think the ability to clearly state mathematical equations without restoring to graphical/drawing input is a useful skill. $\endgroup$ – cjs Jun 3 at 1:56
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We use Gradescope, https://www.gradescope.com/ Basically, you upload the scans to Gradescope, and as you make comments on one student's paper, you can assign point values to those comments and re-use the comments on every other student's paper. If you decide at some point that you want to change the point value, you can just do it, and all of the students' grades will be updated accordingly. We've found we can give much better feedback using this system.

This video gives an idea of the basic functionality: https://www.youtube.com/watch?v=F2e9AK7pNFY

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    $\begingroup$ My daughter is a TA for a computer science course that uses Gradescope, and she likes it. It seems like a heavyweight solution that is optimized for large classes that have a bunch of TAs. And it's not free. $\endgroup$ – Ben Crowell Jun 1 at 17:42
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An iPad with an Apple pencil- I can hand write comments and corrections on the .pdf and then upload it back to the LMS so that the student can see the feedback.

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This may be a case where falling back to more primitive technology makes things easier.

  1. Print out (on paper) each of the pages the student uploaded.
  2. Mark and comment on the paper copies as you normally would.
  3. Re-scan the page or pages from each student as a separate document, and mail that document back to the student.

This may not work well if you have a small home printer or similar that doesn't have a sheet feeder for the scanner, where you probably have to do further post-scan editing on the computer to recombine the pages into a separate document for each student.

Standard office printer/copier/scanners usually (when well configured) allow you to place one or more pages in the input feeder and press a button to create a single document from all the pages, stored for later retrieval over the network. This is key; you want to be able quickly to scan in a few dozen separate documents, getting exactly one for each student, since then you processing after that is simply to select each document and mail it back to the student.

That said, if you don't have a scanner and network system that itself provides good workflow, you may be able to develop fast post-scan computer-side workflow as a substitute:

  • If the your scanner can provide individual images, you may be able to just dump these all into a folder and attach them directly to messages back to the student. This does run the risk that you miss an image when returning multi-page documents.
  • If your scanner consolidates many images into a PDF, there are tools for rapidly separating pages out of a PDF into individual PDFs.
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