Students should definitely be allowed to redo tests. Drivers test, FAA pilots certification, mechanics licences, bar exams, MCAT (medical school entrance exam), PRAXIS (US teacher certification exam), and CPA exams are all allowed to be redone for full credit. Our goal should be for the student to become proficient in whatever area they are studying. If I say, “you failed this exam but too bad for you because we have more material to cover and need to keep moving” we are essentially saying that my material isn’t very important. It can’t be important if the student doesn’t have to learn it. If “your material” can only be learned for a short period of time and then their are other things to “cover” you have a weak argument. Who says adding two digit numbers has to be learned in two weeks in the middle of October? If a student realizes that they should have studied harder, then it shouldn’t matter what time of the school year it is. What is important is that they learned the material.
To avoid the problem of students thinking, “I’ll just wing it because if I get a bad grade I can just retake the exam” I have various hoops the students need to jump through. These are situationally dependent and include: writing a study guide of what you will study and when and how your going to do it, taking the test during lunch break, giving the second test in a different format (the first test may have been multiple choice but the second one could be an essay).
In response to averaging two test grades I would advise that you use only the second exam. Suppose I don’t know some material and get a 50% on my first test, then I study and learn the material and get a 100% on the second test. Now what grade should I get? I should be graded on how much of the material I know. All 100%. Why should I get a grade that tells me I know 75% of the material when I actually just proved to you that I know all 100%. Some people may interject and say, yea but the dock in percentage teaches them to be studious and responsible. If you want to “punish” them some way for not being studious and responsible you may, you just can’t do it by docking their grade. A students grade measures what they know, not how many presents they bring you, or if they are studious. That should be reported separately. Suppose you fail your drivers test the first time and ace it the second. The state (or province or queen or whoever issues your driver’s licences) doesn’t say that you have to be off the road by dark and are limited to driving 50 kph (not all Americans are illiterate in the superior système international). They trust the validity of the test.