Sachs and Polio (2007) by Kevin

Learners' Uses of Two Types of Written Feedback on a L2 Writing
Revision Task SSLA, 29, 67-100

This study is an attempt to determine the effectiveness of two types of feedback in improving learners written grammatical accuracy. The two types are error correction; here defined as direct correction of student's mistakes with the correct forms provided by the teacher, and reformulation; here defined as maintaining the meaning but not necessarily the form by rewriting the student's incorrect sentences in a more native like way. Reformulations with think-aloud comments were also examined to study student's awareness of their reformulations and the effect that this has on the effectiveness of the reformulation. Because of possible problems with the error correction part of the first study, a second study was done with a larger n size was done to control for these effects. In both studies, error correction was shown to be more effective than both kinds of reformulations in improving students written grammar. In addition, reformulations + think aloud were shown to be of limited use in studying awareness and noticing due to the interfering effect and extra cognitive load that is required to verbally report on awareness.

On the bright side, this article mentions the idea of depth of processing, which is popular among vocabulary acquisition researchers and which we talked about on the second day of class. The researchers believe that this concept should be imported to error correction research in general, which I think may be a good idea. This article also discusses in some detail the idea of how noticing is related to acquisition through error feedback. Examining the role of noticing at the level of awareness (superficial linguistic level) and at the level of understanding (knowledge of linguistic rules and metacognitive linguistic knowledge) is a secondary goal of the research here.
Both depth of processing and a more nuanced notion of noticing are important ideas and this article may prod other researchers into taking a look at these areas. Unfortunately this study doesn't contribute much to the discussion.

In addition to the awkward title of this paper, there are several problems, which for the most part, the authors are aware of and state clearly, with the design of the experiment. While it is interesting that the authors bring up the idea of depth processing, they choose direct reformulations as a way to test their hypothesis. According to the authors, the following sentences are examples of a reformulation and error correction:

As he was jogging, his tammy was shaked ORIGINAL
As he was jogging, his tummy was shaking. REFORMULATION

As he was jogging his tammy(crossed out and rewritten) was shaked(crossed out as rewritten as shaking)

As is obvious, they are very nearly the same thing. The first reformulation would not require much depth of processing and most likely result in students just copying the answer.
At any rate, the results show that error correction is more effective, but the researchers admit that the design of the experiment encouraged students to simply memorize the correct feedback and that the error correction results were better simply because the format, and not the type of feedback was different. So at best, we have superficial, short term improvement of grammar points that may or may not be due to the type of feedback, which doesn't tell us much.
One interesting result of the experiment is that it reinforced the idea that students providing verbal feedback about their state of awareness during error correction interferes with the error correction and should therefore be controlled for.

This was not an especially thrilling read. If you are in love with quantitative statistical analysis (Here is a test, what is the exact definition of a Kruskal-Wallis Test?) then you might be interested in this one because the authors use every trick in the book to make up for the fact that their n size is too small and there is no normal distribution to work with. Otherwise, you will find yourself skipping down to the results and discussion.

I don't recommend this one, but it raises a few good questions.