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.

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.

ReplyDeleteI 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.

Delete