Abstract
Many students enter middle school viewing decimal and percent as independent and unrelated concepts rather than as being natural extensions of the standard base-ten system in use today. This commonly held perception generally reflects a lack of basic numeracy on the part of the students concerning the foundations of number and number representations. This is a problem which must be directly addressed in initial instruction if advancement is to be made in developing decimal and percent. These are two new types of number from the perspective of such students, but are really natural extensions of ideas dating back elementary school activities.
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- 1.
It is not uncommon for middle school students at this point to notice that the “shape” of the Hundred is a square and that 102 is often called “ten-squared”. Likewise, that the “shape” of the Thousand is a cube and that 103 is often called “ten-cubed”. This recognition serves the student well when encountering terms such as x2 or “x-squared”, and x3 or “x-cubed”.
- 2.
It is important that students are able to meaningfully interpret how the numbers displayed in their calculator, or through other technologies, relate to the problems they are working on. Otherwise, these various representational methods will be unconnected in the students minds causing a disconnect in their application.
- 3.
Richard Dedekind (1831–1916)—a German mathematician.
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Abramovich, S., Connell, M.L. (2021). Decimal and Percent Representation of Rational Numbers. In: Developing Deep Knowledge in Middle School Mathematics. Springer Texts in Education. Springer, Cham. https://doi.org/10.1007/978-3-030-68564-5_5
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DOI: https://doi.org/10.1007/978-3-030-68564-5_5
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