The evidence says no
What research I'm aware of is all about how giving any overall data about their own performance is actively harmful in promoting further learning. They learn considerably more from instruction about what to do differently in the absence of a grade or numerical score. To repeat; individual scores discourage learning! (Explanations for this correlation are about strong students relaxing and weak students giving up, all students concentrating on an emotional rather than academic response and ignoring any pointers.) The data says don't grade if you want more learning, instead instruct.
In my experience the earlier you do this correction/instruction-only feedback, the better. I've been delighted with the change in attitude its early use has resulted in, with students preferring to re-test than give up, and much higher pass rates (our course is assessed by a national externally marked test). Later in the course I've been able to mark tests with numbers, particularly near exams, but the foundational practice builds a culture of improvement post-testing rather than finality.
Note: To improve learning, provide instructions for how to improve work, without a mark
Warning: the research shows that any grading nullifies correctional/improvement feedback - don't bother doing both.
To clearly separate research findings from my own experience: research says the presence of any summative grade/percentage/score nullifies the effect of any formative advice/feedback/instruction, and that such feedback is far more effective at improving performance. My experience says that building an improvement culture early on by providing advice-only feedback with resits for underperformers can have a lasting impact on approach to learning, which allows them to ride out our numerical common test scores with their "not there yet, let's fix it" approach. We got the culture right first.
I like to tell them "You are not an arrow! If an arrow misses its target, it lies helplessly on the floor. You are a human - you have legs and a brain! If you missed the target, keep going. If you fell on your face, get up!"
Alternatives to grading
You absolutely need to check they've done the work and made a reasonable attempt at it. As some of our students pointed out in a candid after-the-exams conversation, "If we think there's a chance you won't check we did the work, we'll take that gamble, every time."
This checking only takes seconds per student. The good news is Dylan William, an advocate of using feedback to improve learning says feedback should be more work for the student than for you, but what are some alternatives to marking and grading?
There are loads of ideas, but here are three.
Comment-only marking: a medal and a mission
Don't mark everything, point out a medal and a mission: something they did well, one thing to improve. If I came in your class and listed everything you did wrong as an educator you would be dejected and find your list of failings to rectify overwhelming. If instead I praise something and then tell you the most important thing to improve, you can handle that, and may well actually do it! Students are the same.
Next you should...
Quickly read through and assess where you think the student is at (eg strong & accurate, OK but error prone, clueless), and have a follow-up task or resource, but just set a few questions based on their ability: strong and accurate students get harder problems, clueless students get basic technique drill. If all students get the same number of follow up questions no-one feels penalised for what they did.
Done well with thorough in-class training this can teach students to understand how they will be graded in the terminal exams, but more generally it spreads the mathematical authority around so that it's "is this valid mathematics?" as opposed to "did I write what the teacher wanted?"
Disadvantage: it's hard to train students to give good feedback that's not binary or numerical, and as I say, the number often drowns the improvement message in emotional response.
What is and isn't worth grading?
In my view, homework is for learning - I expect students to seek help (phone a friend, ask the internet, watch a video, read a book) and find out how to answer questions if they don't know. As a result their performance on homework is a very poor indicator of what they can do unaided, so formally grading it is misleading for you and them.
Tests under test conditions are a better indicator of what you can do in an exam, and giving good feedback about how to improve (i.e. not a number, letter and judgement, but something they can work on) is important and relevant, so I don't object to marking tests, I'm just very aware that summative numerical feedback or grading can encourage students to stop learning, and have found success through avoiding it in the first part of the course.
There's no reason to suppose I won't find holding out for longer even more effective in the future. (I won't hold out indefinitely, since one of my aims is that students understand how they will be assessed, and peer marking is the best way of teaching that. It's hard not to get numerical feedback out of a mark scheme!)
NCTM:Five “Key Strategies” for Effective Formative Assessment says:
The research on feedback shows that much of the feedback that students receive has, at best, no impact on learning and can actually be counterproductive. Kluger and DeNisi (1996) reviewed more than three thousand research reports on the effects of feedback in schools, colleges, and workplaces and found that only 131 studies were scientifically rigorous. In 50 of these studies, feedback actually made people’s performance worse than it would have been without feedback. The principal feature of these studies was that feedback was, in the psychological jargon, “ego-involving.” In other words, the feedback focused attention on the person rather than on the quality of the work——for example, by giving scores, grades, or other forms of report that encouraged comparison with others. The studies where feedback was most effective were those in which the feedback told participants not just what to do to improve but also how to go about it.
A nice introduction to comment only marking on a good blog here
'Inside the Black Box: Raising Standards Through Classroom Assessment' (Paul Black and Dylan Wiliam, Kings College, London, 1998).
People seem to reference Butler, R. (1988). 'Enhancing and undermining intrinsic motivation: The effects of task-involving and ego-involving evaluation on interest and performance.' British Journal of Educational Psychology, 58,1-14. a lot but I haven't read it.
Search terms: Assessment for Learning (AfL), comment-only marking.
See here for an intro to AfL generally.
Where's the evidence?
(In response to comments challenging my statements about the existence or content of evidence.)
There are a number of educational researchers who advocate what is referred to as evidence based education. They have high standards for what constitutes a good study (you can read their selection criteria in their work) and review a large number of studies, and concentrate on effect size. Dylan William is a good example as he specialises to mathematics a great deal, and I recall his description of the comment-only evidence but have read too many papers, talks etc by him to locate which one(s) make the reference. John Hattie is another evidence-based education expert, and I'll quote him for those seeking reassurance beyond my experience in class and my recollection of the literature I've read.
In The Power of Feedback (Review of Educational Research March 2007, Vol. 77, No. 1, pp. 81-112 DOI: 10.3102/00346543029848)
John Hattie introduces some shorthand:
Thus, there is a distinction between feedback about the task (FT), about the processing of the task (FP), about self-regulation (FR), and about the self as a person (FS). We argue that FS is the least effective, FR and FP are powerful in terms of deep processing and mastery of tasks, and FT is powerful when the task information subsequently is useful for improving strategy processing or enhancing self-regulation (which it too rarely does).
before going on to talk about where the evidence for comment-only marking, against grades, and the nullification of the effectiveness of comments by the presence of grades can be found:
The effectiveness of marks or written comments has also been investigated. There is considerable evidence that providing written comments (specific FT) is more effective than providing grades (Black & Wiliam, 1998; Crooks, 1988). In one of the early and influential studies, Page (1958) found that feedback in the form of short written comments rather than grades alone significantly improved the test performance of students in 74 classrooms (see also Cardelle & Como, 1981; Elawar & Como, 1985; McLaughlin, 1974). R. Butler (1987) demonstrated that grades can increase involvement, but they do not affect performance (relative to a no-FT condition). She also showed (R. Butler, 1988) that feedback through comments alone led to learning gains, whereas marks alone or comments accompanied by marks or giving praise did not. She claimed that such results called in question the whole classroom culture of marks, grades, gold stars, merit awards, competition rather than personal improvement. As will become a theme later in this article, feedback that mixes FS with FT is less effective than FT by itself.
The paper includes a considerable bibliography including of course the studies referenced in this extract, and if you'd like to delve further into the evidence than references you should download the paper and start investigating.