Monday, June 5, 2017

More Reading Fractions as Decimals

Last December, we speculated that many students who are weak in understanding fractions may read them incorrectly as decimals (for example: thinking that 1/2 = 1.2).

For the spring term, I added a question on my first-day diagnostics regarding this topic. Specifically: "Graph the fraction on a number line: 2/3." Four multiple-choice options were given in graphical form: (a) between 0 and 1 [the correct answer], (b) b/w 1 and 2 [at 3/2], (c) b/w 2 and 3 [at 2.3], (d) b/w 3 and 4 [at. 3.2].

Results:
  • Remedial intermediate algebra class (N = 26): (a) 62%, (b) 8%, (c) 23%, (d) 8%.
  • Credit college algebra class (N = 21): (a) 86%, (b) 5%, (c) 10%, (d) 0%.
Conclusions: In both cases, item (c), the result of thinking that 2/3 = 2.3, was indeed the most commonly selected incorrect response. While most students in both classes selected the correct answer, approximately one-quarter of the intermediate algebra class instead picked the location of 2.3. Students registered for the college algebra class clearly had stronger incoming knowledge of fractions.

2 comments:

  1. It might be that they chose (c) simply because the numbers 2 and 3 appear in the question, not because they confused it with 2.3. 3/2 would have been better for this.

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    1. I think that would complicate the issue by warranting a conversion step to mixed form. I'm interested in the more basic question if they know that the proper fraction 2/3 is indeed less than 1.

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