I have had an odd rule in my math class for the last decade involving pencils. I don’t allow them. During the first day of class, I specifically tell students that they can ONLY use pen. It is even in my syllabus. This is not a ban that I do not strictly uphold, but most students do follow it. However, when I first explain this rule, students are often shocked that a math teacher would want something like this. They are used to their math teachers wanting student work to be neat and orderly especially my community college students. So why do I dislike students erasing their work?
The main reason I dislike erasing is that any work students show is communication to me, other students, and themselves... even if it is wrong. It shows me their line of thinking both past and present. They might have thought one thing, reflected upon it, and went a different way. Since I have not found a way to read students’ minds yet (sarcasm), their work is the next best thing. It provides an excellent conversation starter when reflecting on their problem solving and critical thinking skills. Metacognition is a powerful habit of mind. Erasing work gets rid of any evidence of that thinking.
Another important reason I dislike erasing is that sometimes students erase the correct solution to a problem for an incorrect solution. If they kept both solutions, this again can be used as reflection for student thinking. Why did they think what they were doing was right? How can they learn from their mistakes? Are there any trends in their second guessing themselves for specific standards, concepts, etc.?
Without Erasing, Won’t Work Be Messy?
Many teachers want neat and orderly work. I am not against that and prefer it actually. However, neat and orderly ≠ erased work. With my erasing ban also comes a scribble ban. Students are NOT allowed to scribble out their work. Putting lines or strikethroughs through discarded work can be neat and orderly. Sometimes, it is even more neat than having erasure remnants.
How Does This Look in Practice?
Promoting this idea to students requires a little work on the teacher’s part. Students need to be given ample space to communicate their thinking without needing to erase to free up space. For any practice problems, activities, or assessment documents, I have students use scratch paper for showing work rather than showing work on the actual document. There are three benefits from doing it this way.
  1. It saves me from giving students space on those documents which cuts down on copy time.
    • I can print documents that 1 page front and back rather than 7-page packets.
  2. It delimits students from only using the space teachers provide.
    • Students need freedom and should not be given hints on how much work they should be showing for a specific problem.
    • Furthermore, how many of us teachers have printed a test that did not have enough space for student work or even too much space? Using scratch paper would get rid of this issue.
  3. Scratch paper puts the focus of organizing work on the students rather than the teacher.
    • Granted, this can be problematic if students are sloppily showing work, but you cannot get rid of a problem like disorganization with less practice.
    • Students need to work on clearly communicating their thoughts with the freedom using as much space as they want.
What About the “Neat Freaks”?
It is important to point out that some students are “neat freaks” and insist on erasing. When this happens, I tend to not fight them on it. I do want students to have choice and be comfortable.

The most important thing going on in a math class involves what is going on in a student’s brain and how that’s communicated. Erasing gets rid of communication which results in less reflection pieces. It is time that we erase the practice of erasing and embrace our mistakes.
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