By allowing students to retake tests and quizzes, you are encouraging and rewarding learning. When a student is not allowed to make up older assessments, they can show a low grade even when they now understand the content.
Many teachers will complain that it takes a long time to make a new version of the test, or that students will just re-take a quiz, but not spend the time to prepare for it. First you could require the student to provide some type of evidence that they have learned the content. Perhaps have them do a test reflection, where they take each of the questions they got wrong and explained why it was wrong. Second, your retake can be really easy for you. Have a quick one-on-one with the student: "Tell me what you know about this question." A 5 minute conversation can tell you very quickly if they understand!
You can also create an assessment plan for either a unit, semester or year long course. If you have thought ahead as to what/when assessments will be given, and they are assessing similar targets over time, then retakes are not always necessary because you have built in the next opportunities as part of your course. Students should know this in advance and can still find a way to find out what went wrong on a particular assessment, and then knowing they have another chance to show what they know can give them hope.
Why was the work late in the first place? Do you know what situation the student has at home for doing homework? What if the student is responsible for child care or working to support the family? What if they experiencing houselessness?
First off, you could just have a blanket policy that all work can be turned in late with no penalty. This can lead to more grading for you at the end of the term. You could set some limits. "You have two weeks to turn in assignments late." Late work must be submitted with a note explaining what happened.
If we want to encourage and reward learning, then assignments that are done at the end of the unit should be weighted more heavily. This assumes that your curriculum builds on itself and that students are using information from earlier in the unit to solve problems at the end.
You can drop lower (or take the highest) scores if you re-test the same concept later in the term. You can weight tests later in the quarter higher. A reminder that a high score is a good indication that the student has a good grasp on the concept. A low score can be anything from poor understanding to a rough night/day/week. If I see a student score high on an initial assessment and then drop at the end, I know I need to have a conversation with that student to see what is going on.
Often teachers will give a student a zero on an assignment for cheating. First, this may be just fine with the student. If it does not impact the grade (bring the grade down one letter), then they may not care. If their grade is already low, they really don't care because they were going to fail anyway.
Have a parent conference with the student. Never fun for students... Require that the student comes in outside of the class to redo the assignment (lunches work great). Students who are faced with losing their time with friends often will beg for a zero. That tells you how important a grade is vs. their time.
Grading homework, classwork, and other forms of formative assessments lead to a focus on completing assignments instead of learning. Not that learning won't happen, just that the focus will be on completion. Have you ever said, "Just get the assignment in! Partial credit is better than no credit." Grades should be a measure of a student's ability and knowledge, not on completion. It also means less grading for the teacher, so they can spend more time planning and giving quality feedback on summative assignments.
This is an easy one! Just don't assign points to classwork and homework. Make sure that your assignments are tailored to the learning targets on your assessments. Will some students choose not to do your assignments? Yes! But don't some of them already make that choice?
Not all students are good test-takers. Some have people at home that can coach the students on better test-taking strategies and some do not. Some families choose to hire test prep agencies just for learning how to "do better" on tests. When is the last time you had to take a test for your job? The last time for me was 20 years ago when I got my teaching license...
Give students a choice when asking them to demonstrate knowledge. Now that students and teachers are more adept at using computers, allow students to make a recording to show their understanding of the branches of government. I had a student with a writing IEP. He would not write anything because it physically hurt him to write more than 5 minutes. He did a voice recording for all of his tests/quizzes. He would read the question and then he would explain his thinking.
We are trying to know what this student knows. When we grade a whole group, we are not sure who understands what concepts. Maybe one student did the whole project, maybe they did a jigsaw and broke it up into pieces so they each only know one part. We just don't know unless we ask them individually.
I am NOT saying to not do group projects! But instead the group project may be a formative assessment that is followed by an individual summative assessment. You can also grade individuals within a group project based on their presentation!