After a personal look through the currently available literature on the use of self-assessment, my research shows that the majority of literature dates back to only the late 1980s and early 1990s, and that most research is from the past decade.
Because the research behind the implementation of self-assessment in classrooms is so new, there is not very much data supporting whether there is a significant positive link between self-assessment and student success or not (Kostons et al., 2009). In addition to the limited number of studies performed, the majority of studies have only involved fairly small sample sizes of students at a time (Panadero & Courtney, 2014).
Of the research that did find significant links between the use of self-assessment and academic achievement, many postulate that students many not benefit from self-assessment because they do not have the ability to accurately use the tools and strategies to assess themselves (Kostons et al., 2009, 2012). This is especially true for students still in their adolescence who do not possess the cognitive maturity with which to monitor themselves. Kostons et al. describe the cognitive functioning of adolescents as limiting, which makes it difficult for students to focus on both assessing themselves and the process of learning concurrently without getting distracted (2009, 2012).

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Many studies have found that when students are given the opportunity to assess themselves on their work, the results of their assessments is dependent on whether or not the assignments contribute to their grades (Ross, 2006; Panadero et al., 2014; Kostons et al., 2009). The general consensus is that students are more likely to over-estimate their abilities and achievement when the assessments are used as part of their grades (Ross, 2006; Panadero et al., 2014; Kostons et al. 2009). This is one of the greatest setbacks of first trying to implement self-assessment into the classroom because it deviates away from the original purpose of self-assessment, which is to provide the students with an idea of their learning progress and allow for improvement of achievement of learning outcomes rather than serve as an ending point for their learning (MacMillan & Hearn, 2008). An additional result of student over-estimation of achievement level is that students may actually lose motivation over time if the actual results of their learning do not match with what they perceived was their level (Ross, 2006).
Kostons, D., Gog, T.v., & Paas, F. (2009). Self-assessment and task selection in learner-controlled instruction: Differences between effective and ineffective learners. Computers & Education, 54(2010), 932-940.
Kostons, D., Gog, T.V., & Paas, F. (2012). Training self-assessment and task-selection skills: A cognitive approach to improving self-regulated learning. Learning and Instruction, 22, 121-132.
McMillan, J.H. & Hearn.J. 2008. Student self-assessment: The key to stronger student motivation and higher achievement. Educational Horizons, 87(2008), 40-49.
Panadero, E., Brown, G., & Courtney, M. (2014). Teacher’s reasons for using self-assessment: a survey self-report of Spanish teachers. Assessment in Education: Principles, Policy & Practice, 21(4), 365-383.
Ross, J.A. (2006). The reliability, validity, and utility of self-assessment. Practical Assessment Research & Evaluation, 11(10).
Self-assessment can be tricky, especially as a student or someone new to the field, because you do not have enough experience to determine what you know or what you are good at. I think self-assessment is only helpful if there is also another form of assessment/evaluation used with it. Self-assessment is good for forcing one to take a moment and reflect on their experience.
Self-assessment is something I believe to be taken with a grain of salt. While it is important to evaluate yourself for strengths and weaknesses, it is only helpful when another form of assessment is used in conjunction to be used as a comparative tool for performance.