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I am writing a research paper, and am fairly new to writing. I am working on a research topic that has not been touched too much. There has only been one other paper published regarding the same topic.

In this other paper, they have a fairly strange methodological approach that almost doesn't make use of the method at hand. My paper is an improvement of their approach; I am wondering what would be the best way to criticize their approach to present my own approach.

As Bob et al. failed to notice, we can actually do this...

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There's no need to harshly criticize the authors of the first paper, however strange it seems, even if their approach is plainly wrong. After all, as you say, it appears that they are the only ones who actively worked on that research topic before you.

So, be constructive and build upon what they've done. For instance, you might write something like:

Bob et al. [1] developed an algorithm to square the circle. This algorithm can square the circle in 198 steps. Here we present a modification of the original algorithm which can square the circle in just 87 steps. This modification is based on the observation that blah blah...

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    I would make that 'even if their approach is plainly wrong'. My experience is that it is assumed you will avoid saying outright that something is wrong. In a somewhat related situation I thought I had worded something pretty mildly, but it seems that others took what I wrote to be too strong. – Jessica B Dec 25 '14 at 22:49
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    @JessicaB: agreed! – Massimo Ortolano Dec 25 '14 at 22:58
  • Another thing that I guess I like to add: Bob et al. didn't actually use the method correctly. (ps. Bob et al isn't real..) – ᴇcʜo Dec 26 '14 at 14:53
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    @user26850: No, again no. Are you writing a paper to present your own work? Then present your own work; show the advantages of your approach and show why your approach is an improvement over the previous one. No more than that. If, instead, your aim is just that of criticizing Bob's paper, than submit a comment to their article, so that they can reply on the same journal issue. – Massimo Ortolano Dec 26 '14 at 15:13
  • PS: I've suspected that Bob et al weren't real ;-) – Massimo Ortolano Dec 26 '14 at 15:16

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