Small quizzes, as diagnostic or low-stakes formative assessments, are practical in a wide variety of fields. Since they are really as much worksheets as they are quizzes, academic integrity isn't an issue.
Summative assessment is generally measurement of student learning for record. These can be exams, quizzes, or completed projects where students achieve a score that contribues to their course grade, passing the class, advancing in a program, and graduation. Traditionally, these activities have measured learning effectiveness after the class completes a big chunk of the course, or the whole course itself.
Because of this, professor feedback on summative assessments is usually valuable only in preparing students for future courses or career activities. By definition, summative assessments occur after learning has taken place, and before the course goes on to new material, so within the course students may not get a subsequent chance to improve their mastery of the concepts or skills assessed. The line between formative and summative assessments isn't sharp; courses with cumulative final exams, or where students acquire skills in one lesson that are needed for subsequent lessons, can benefit from an exam that assures students they're on the right track, or admonishes them to revisit the assessed materials. However, many courses move on to other concepts after an exam, so summative assessments may only provide generalized feedback on whether or not student effort is sufficient or well-directed. In any case, strongly formative assessments at intervals between major summative assessments are good practice, because they help students acquire mastery of concepts or skills, in preparation for the "big tests."
Faculty in many fields have abandoned big, cumulative exams or term papers in favor of other projects and exercises they feel better foster critical thinking and analysis skills in their students. Given all that we've discussed previously about activities and assessments in this course, might you scrap your paper exams altogether?
If you are not ready to move away from exams, it's worth briefly considering the mechanics of these online. Often, faculty are skeptical of online tests. What's the point if students will cheat? In one direction, this has led to the rise of costly online proctoring systems usually based on surveilling students using their own webcams, a practice unlikely to foster a sense of community in courses.
But consider what cheating practically is, after the information revolution of the last few decades. Perhaps sequestering students away from information, in order to test their comprehension, skills, or mere memorization, is no longer a relevant exercise? With the internet, the problem is no longer scarcity of information. It's too much information, of varying degrees of quality. Automated, algorithmic search methods don't necessarily yield the best or most relevant results. And information abundance is useless without the analysis skills that are the basis of our disciplines. We now teach students how to find, identify, and curate quality, relevant information to make meaning, build understanding, and develop courses of action (including further inquiry.) Shouldn't we modify traditional testing methods to reflect this?
Another option is what are called "take-home exams" in F2F courses. These may be even more appropriate, not only in an online environment, but also with changing attitudes about what we assess when we assess students.