This one is really interesting. We’ve got both a sample of student work, and on the left the student has crossed out \frac{5}{1}. We also have a record of the following student question:

Kid: [Raises hand.]

Teacher: “What’s up?”

Kid: “Are you looking for a 1 or, like, the number 1?”

What is the student’s question, and what does it reflect about what he knows and thinks? How would you help?

[The submission also comes with an answer, yielded by the teacher through further questioning, revealed in the comments.]


  • mpershan

    The teacher reports: “The kid seemed to think that a “1” referred to a whole number. So the student was left confused: was the question asking for a whole number, or a fraction that was equivalent to the number 1. I’d never seen this sort of language used before to describe whole numbers. Has anyone else? Where did this come from?”

  • Perhaps the student recalls that a whole number can be written as a fraction with a denominator of 1, so he thinks that the question means to write a whole number as a fraction with a denominator of 1. Most likely he does not understand the word “equivalent”.

    • Per Rosing Mogensen

      I think you’re on the right track here. If you look up the word “equivalent” it seems likely that the student understood it in an ambiguous everyday sense:
      Math may be internally unambiguous, but it is still communicated and expressed through ambiguous language and if a student has not internalized the definitive usage of “equivalent” in math it would make sense to me that the unclear daily usage of the word would be used and that it would lead to confusion.

  • Peter Tompkins

    Great post. Good to stop and reflect on what is happening inside their heads.
    Not sure where the language comes from but when teaching place value I often hear teachers refer to the “hundreds” the “tens” and the “units”. Some though refer to the “units” as the “ones”.