My school institutes a semesterly cumulative exam in all classes. This "midterm" exam counts as 33.33% of the student's semester grade, averaged against the two quarter grades the student has earned. (Curiously enough, Q2 doesn't end until January, even though the fall midterm is in December. I actually prefer this setup, because it makes it possible for me to give the kids some extra-credit work, should they be on the border of passing/failing for the semester once the midterm grade has been computed and included. But, I only do that for the first semester, as I then tell the kids that they will need to earn their second-semester passing average on their own. It's a bit of a carrot-and-stick approach.)
I am pretty sure there are various people out there lobbying against midterms, and admittedly, these cumulative exams might not be something that works equally well in every subject, but I personally find them to be a valuable opportunity to spiral back to what we've learned and to do a cumulative assessment to see what the students have really retained. So, it's important to me that both my review and my exam reflect that philosophy.
This year, I structured my review as such:
* A few weeks in advance, I posted a list of topics and associated practice problems on the web. The kids could start doing those problems whenever they have free time, and the problems I assigned were either extra practice problems from the textbook that we didn't have time to do during the regular instruction, or they were problems from old exams they've taken. Each problem is aligned with a specific skill in the list of key skills that I think the kids should retain from the first semester. The kids know that if they show excellent math work (which includes verifying their answers with the back of the book) and they complete all assigned problems, they can gain up to 5% extra credit toward the midterm exam.
* During the allotted 3 days of review time in class (this is standard across all of the school), each day I would give the kids a short sheet of practice problems to jog their memory on older, dustier topics and terms. If they are sharp on that stuff and/or are aggressively asking me for help, they can get through those practice problems each day in about 30 minutes, and then use the remaining 30 minutes in class to work on the extra-credit study packet. (See above.) Or, if they're unmotivated and only idly working, they are kept busy reviewing pertinent material for 45 minutes to an hour (since in that case, the worksheet would take them longer to get through), so they're not bothering other people in class. (If they do start misbehaving instead of choosing to work on the extra-credit study packet, obviously you assign them a consequence. Another carrot-and-stick approach.)
* In the end, the midterms I gave were always a mixture of: problems similar to those on old exams; problems similar to those in the extra-credit study guide; and problems similar to those we practiced in class during the review days. I wasn't looking to surprise the kids for the midterm; I don't feel that's quite so fair for a test with so much weight. Plus, I wanted to make the entry point of each problem accessible for every student, so that a kid feels like they have some hope for getting every problem correct, using what they've learned. But, they were definitely asked to show, explain, and apply concepts, so the tests were by no means easy. One kid said, "Wow! We learned a lot of stuff this semester, and every single thing was on the midterm!" And others told me they thought the tests were not difficult, as long as you did your part in reviewing.
The result? Each class had a pretty nice distribution of scores, and in all cases, it was evident to me whether a kid had put in the extra effort to get through the entire study guide of practice problems. :)
I know that sometimes (...many times??) other teachers complain that midterms are a waste of time, but I don't think they have to be, if you see them as an opportunity to further the kids' familiarity with those older topics.
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