Providing feedback in the classroom

In my previous post, I discussed some current and ongoing research on effective pedagogical approaches to STEM education. The problems in STEM education have gained much attention recently due to the growing gap between demand and skill in American STEM jobs, likely due at least in part to lack of interest or discouragement among American students. I pointed out a number of key findings for effective learning. In this post I would like to focus specifically on the last key finding given in the fantastic source How People Learn: Brain, Mind, Experience, and School.  I summarize the point and the few words I gave from my previous post:

A ‘metacognitive’ approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them.” (p.18)

Monitoring progress … should involve many levels of evaluation and feedback. During class time it is important to give some feedback and to encourage a try-fail-receive feedback-try again cycle and atmosphere for exploration. These small evaluations should not be summative. It is always important for feedback to be timely and at an appropriate level. It is hard to achieve both things, but it equips students with the appropriate sense of metacognition crucial for improving from novice to expert.

Providing feedback that is both appropriate and timely is not a straightforward task. This can be especially true of more creative work that involves more than a correct answer, but a clear and well-formulated answer. Drawing upon my own experience, I am thinking in particular about proof-based or algorithms problems. In these cases feedback could involve more than technical corrections. Feedback on style, clarity, completeness and conciseness are all equally important. But how can such involved feedback be done in a timely manner?

After consulting the sources and, again, considering my own experience, the key to this seems to be a good grading rubric. There are many styles of rubric, but the main qualities that contribute to a good rubric are (1) it should facilitate consistent grading, (2) it should provide or at least allow for understandable and meaningful feedback/comments to the students, and (3) it should facilitate timely grading. I would venture to say that these three are equally important, but you may disagree.

A grading rubric that has all three qualities is a so-called grid rubric (sometimes just called an evaluation grid). This style of rubric goes beyond the typical “this is worth 5 points, and this is worth 3.” The grid starts with a set of criterion the grader deems important for a good solution. The grid then has a scale for each of these criteria, typically along four or five points corresponding to an A/B/C/D/F scale. Below is an example of a grid rubric I particularly like from Jadrian Miles’ algorithms course:


Criterion Great Good So-So Poor

All components are completely correct. (9)

At least one component contains a minor error. (7)

At least one component contains a major error. (4)

Multiple major errors, or an entirely incorrect response. (0)


A professional, polished tone and format are maintained throughout the solution. (3)

Minor issues of tone, voice, spelling, punctuation, or formatting. (2)

Major tone or presentation issues. (1)

Exceedingly terse, sloppy, or otherwise unpolished writing. (0)


All components are clear, organized, and easy to follow. (4)

Occasional or minor issues of clarity, causing confusion that can be overcome by careful reading and charitable interpretation by the reader. (3)

Truly confusing writing that can only be interpreted with significant effort. (1)

Exceedingly confusing writing. (0)


No meaningful ambiguity. (4)

Occasional or minor issues of precision, causing meaningful ambiguity that can be overcome by charitable interpretation by the reader. (3)

Major precision errors that cause meaningful ambiguity in the interpretation of the solution, which can only be resolved with difficulty (if at all). (1)

Severely underspecified instructions, definitions, claims, or arguments. (0)


Direct and to the point, without sacrificing appropriate clarity or precision. (3)

Occasional extraneous writing.(2)

Very long-winded, redundant, or extraneous writing. (1)

Exceedingly longer writing than is necessary for the clear, precise expression of the ideas in the solution. (0)

For each of the criteria, corresponding to a row in the grid, the rubric provides a quality scale along the columns – Great, Good, So-So, and Poor. Further, the rubric provides a description of what defines each quality type in the corresponding square. Within each square is also a score. The grader then grades along the rows, circling the square in each row that best describes the quality of the particular criterion being considered in that row. The grade is then simply the sum of the scores in each row.

This system is hugely beneficial with respect to (1) consistency and (3) timeliness. Since each quality is explicitly described in the grid, it should be straight forward for a single grader to stay consistent across different answers. And with a finite grid of grading options, the time involved in grading a solution, and further a stack of solutions, is greatly reduced. In fact, it is even better if the grader can hand back a printout of the grid for each solution with the appropriate items circled.

I will remark that this system may not be consistent across graders. Whether an issue is “major” or “minor,” for instance, is a subjective decision.

The grid rubric is also great for (2) providing understandable and meaningful comments to students. The rubric of this example points out the criteria of a good algorithms solution. The “components” referred to in the grid are the essential components of a solution to a computation problem: a description of an algorithm, a proof of correctness, and an analysis of complexity. The rubric emphasizes that a good solution is above all correct, but also clear, precise, concise, and well presented. The students’ scores on the grid indicate which of these can be improved upon. This allows students to identify goals for themselves and monitor progress.

One may choose to include specific comments, and should if time allows. However, sometimes the volume of problems to grade can prohibit this. For this reason having the rubric available to students for reference is crucial for conveying feedback, and making sense of raw scores. It is a good idea to publish rubrics. It is an even better idea to publish rubrics before the assignment is due. And even better yet is to publish solution guidelines and a feedback key along with the rubric.

This system of grading is hugely relieving to me. One of the hardest solutions for me to grade is one that is technically incorrect, but in which the student demonstrated effort, consideration, and care. Can they receive any credit if the answer is wrong? The rubric above provides the answer.

Providing students with meaningful and appropriate feedback can greatly impact their experience in a class. If they can monitor themselves and observe their improvement, they are more likely to be encouraged to pursue a subject further. If we as educators focus on this, we might be able to encourage a new generation of STEM scholars.

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