# Students' Messy Sheets: The Big Problem of Exams and Homeworks

Students' messy exam and homework sheets (which are messy because of a bad handwriting or an irregular logical argument in proofs) cause many serious problems. e.g.

• Reading their arguments takes too much time.
• Messy sheets could be confusing. Understanding the truth or falsity of a particular mathematical argument could be so hard if it is not written properly.
• It is a bad habit if they continue their bad math writing in future.

I assigned some extra grades for good writings but it seems insufficient.

Question. How can I overcome the messy sheets problem?

• Asking for LaTeX-ed solutions may fix bad handwriting but I don't know about the others. Practice combined with seeing plenty of well-written proofs helps with others. – Mark Fantini Mar 30 '14 at 7:48
• In my experience, bonus points rarely achieve anything. Slowly draining points does (i.e., add an ever increasing penalty for badly-written solutions). Unfortunately, depending on several factors, this might lead to strong protests. – Wrzlprmft Mar 30 '14 at 9:55
• I see the fact that student are not able to write a proof in a proper way as a very big and common problem. Often, TAs give full credit if the idea is somewhere hidden, even if it is really messed up. Even if this costs more time, you should never give someone full credit if you have the feeling that the do not learn how to write things. At least, take them away a little bit to show them that it is not perfect! – Markus Klein Mar 30 '14 at 19:11
• My worldview is that the instructor serves the students; therefore it is the instructor's responsibility to read and to fairly grade homeworks and exams no matter how bad the handwriting is or how messily the answer is written. – Daniel Moskovich Apr 1 '14 at 4:53
• One drastic way is to be really really hard with those who are messy. Math is also about communicating what one knows. A really bad grade changes people, I mean at least ot forces some students to think what was wrong and how to correct it. – Diego Robayo Feb 26 '15 at 3:18

First, make sure they know that:

• The purpose of exams is to test students' knowledge and understanding.
• The burden of proof is on their side, that is, blank/unreadable sheets work against them.
• The teachers might choose to decipher some of the messy work, but this choice is intrinsically unreliable, erratic and may produce unfair results.
• The teachers grade papers according to their whimsy and the fairness relies on trust in the faculty. The fact that some professor is your teacher is a display of institution's trust in that person. There has to be some amount of goodwill involved, and it is there (i.e. in the teachers).

There are several methods I have seen in practice, some better, some worse, decide what fits your style by yourself.

• Use "clarity points". For two correct proofs, the one which is easier to understand is simply better. Let the students know there are such points. Personally I had used $1\text{pt}$ on $[0\text{pt},10\text{pt}]$ scale, students didn't liked it, but it did make the solutions better. It also had some funny side effects, like more students preferring to return an empty sheet (100% clarity) than a bit of something (often 0% clarity), if they were uncertain about it.
• Let the students explain (e.g. assign $0$ points and make them come to your office). This is time consuming and tricky, because students might want to update their solution. However, according to my experience, it is frequently the most fair way.
• Time-limit your grading process. If you can't understand it, it is unclear; inference with huge mental leaps is invalid.
• Assign enough time, so they can rewrite their solutions (unclear solution is worth 0 points).
• Request a "clear solution rewrite" with no strokes, linearly ordered, etc. This is related to previous bullet, some students still won't do it, but many will, and it is justifiable to have much higher "unreadable" threshold (for example: Mr. Student, please look at this <huge stack of nice, clean solutions>, are you sure that your work is as easily readable as these?).
• Request solutions in LaTeX (e.g. for homework or take-home exams). Many students rebel against it, but in my experience (from both student and teacher perspectives) it is one of the best solutions available.
• Use answer sheets. Unsuitable for wide range of question types.
• (for computer-science exams) Require code indentation. The rules are clear enough that it's fairly objective to decide if the code is correctly indented or not. Helps a lot. Some require underlining keywords, but that's kind of extravagant.

I hope this helps $\ddot\smile$

• In exams I ask my students to strike out what they don't want to have graded. I tell them that if they make me work twice, I'll take off points twice. Not that I'd do it, but I don't want to have to cobble up a solution out of a collection of random pieces. An orderly (but incorrect) reasoning gets some points, a collection of correct (but unconnected) statements none (or very little). What is graded is the process, not the result. Correct result with incorrect derivation is wrong, gets no points. – vonbrand Mar 31 '14 at 3:45
• @vonbrand Another technique I've seen is to mark off points for incorrect answers due to incorrect derivation, but not for solutions to later sections/subquestions that are built off of the incorrect answers and are solved correctly given the answers as derived, even if the final result is not what you would get using the correct answers to the previous sections/subquestions. – JAB May 7 '14 at 16:13

Besides mastering the material in the course one thing that the students have to learn during studies is to communicate mathematics in written form. Almost nobody comes to university and is able to write clear proofs or mathematical arguments. You need to communicate that this is part of what they have to learn.

You may grade as harsh as you like if you are willing to engage into discussion about your grading. When I had messy sheets and graded harsh and these students came to office hours we usually had good conversation. More often than not the conversation goes roughly like:

Student: What I mean here is X.

Me: I see, but that is not the right argument at that place.

Student: But at this point.

Me: Right, a similar argument would help at this point. But yours is not totally correct.

Student: But this (slightly different) argument works.

Me: Correct!

Student: …

Me: At this point the conclusion is not clear to me.

Student: But it is clear from Y.

Me: If it's clear from Y, write that it is clear from Y. Conclusion: If something is clear, write it down clearly. Moreover, you wanted to write Z at place B and not X at place A. So please write that down in the first place next time!

Student: (Leaves with new insight but the same grading… In most cases happy.)

The sheets got a lot less messy next time…

The way I choose to combat this is to make my -> Homework Guidelines <- very clear from the start of the semester. I expect the students to follow the guidelines and have the disclaimer that "If your turned-in homework takes too much effort to read, it will not be graded!" Since I have instituted my guidelines, the homework assignments have been pristine.

I make sure that my students are accountable for the guidelines by asking them to read through that webpage (and the rest of my syllabus) and answer questions on a "Syllabus Quiz" for their first homework assignment. This makes sure we are all in sync to start off the semester.

Great question! I also have the same problem (don't we all?) in absolutely any class I teach. One additional idea that I've recently came to is the following. Our students don't distinguish between solving a problem and writing your solution. Solving can naturally be messy, because you need to think and figure out how to do solve the problem. Of course, even that idea is quite novel to many students, because mostly they view their math classes as training in following the given step-by-step samples. But back to solving: after you figure out how to solve the problem, you need to write a clean narrative for someone, such as your instructor or grader, who will read it. But our students don't realize that: their idea of working on a math problem is to immediately start writing all over the place, scratching and crossing and correcting as necessary hoping to get to the answer, and they believe that that's what expected as their submission.

So I recently started telling my students that for any work they do, be it homeworks, quizzes, or even in-class tests, they need two stacks of paper: some scratch paper where they figure out a solution, and one clean paper (for in-class tests, it's the test paper itself where space is provided) for writing a clean version of the solution. I can't say that it actually solved their messy writing issue completely, but quite a few students followed my advice and actually started submitting nicely written works!

Besides that, I agree with the excellent answers above. I use some grading penalty too, but not always — depends on the messiness of the paper, difficulty of material, etc.