When Is Feedback Helpful

It is amazing that being told of whether one's answer is correct or not after solving a math problem may actually hurt learning. The human brain has limited working capacity such that feedback that is redundant only impedes processing of information. In addition, feedback can be taken as a threat to one's ego forcing a return to old and trusted, but incorrect ways of addressing math problems. A recent study shows that feedback only helps when the learner has no prior knowledge. Feedback apparently is good only when the student has not been taught yet. Feedback appears to help only true novices.

The study, Feedback Both Helps and Hinders Learning: The CausalRole of Prior Knowledge, is scheduled to be published in the Journal of Educational Psychology. The authors from Vanderbilt University, Emily R. Fyfe and Bethany Rittle-Johnson, summarize their findings:
In conclusion, the present study provides causal evidence for a specific moderator that can help explain both positive and negative effects of some types of feedback. In particular, children with no knowledge of a correct strategy benefited from verification feedback during problem solving. In contrast, children with induced knowledge of a correct strategy learned more from problem solving alone. The latter result is consistent with recent research on the need for “productive struggle” during learning. The idea is that students benefit from periods of exploration during which they engage with relevant problems with minimal external guidance. This need for productive struggle also has been recognized by the National Council of Teachers of Mathematics.
The study focused on math problems such as the one shown below:
4 + 5 + 3 = 4 + ___ .
More than one hundred children from second- and third-grade classrooms participated. Initial screening was performed to ensure that all participants were beginners on this type of math problems. All went through a one-on-one experiment with one of the authors, Emily Fyfe. This one-on-one session included instruction, an assessment of the instruction, problem solving, and an immediate posttest. Some of the students received instruction on correct strategies that can be used to solve the math problems to create a sample that had prior knowledge (Induced Strategy Knowledge group). Those who received this instruction were assessed to check if these students did learn the strategies. Those who did not receive instruction specific to the math problems in the test took lessons and performed activities unrelated to the math problems. All students went through a problem solving session. During this problem session, some students received feedback (e.g., “Good job! You got the right answer.”/ “Good try, but you did not get the right answer.”) while others did not receive any feedback. After this session, a posttest was administered. The following graph summarizes the results:

Above copied from
Fyfe, E. R., & Rittle-Johnson, B. (2015, June 8). Feedback Both Helps and Hinders Learning: The Causal Role of Prior Knowledge. Journal of Educational Psychology. Advance online publication. http://dx.doi.org/10.1037/edu0000053
Students who did not receive specific instruction on strategies benefited from feedback. Feedback prevented these students from getting stuck on using a wrong strategy. Feedback allowed these students to explore other options. On the other hand, the students who received specific instructions were hurt by feedback. Those who did not receive feedback performed better in the posttest. 

Direct instruction worked since students who were taught performed better but during the problem solving activity after the instruction, feedback was not helpful. The authors have also tried a summative (instead of immediate) feedback and this likewise harmed children who were knowledgeable. 

This study shows why teaching is not really an easy task especially when teaching something new. It really requires an awareness of how a learner's mind works. The students in the study are not yet experts. They are all beginners and some were taught specifically on the problems to be tested. And apparently, feedback was harmful to those who have learned.