Monday, January 7, 2013

Should I Even Bother Reviewing For Final Exams?

Happy New Year, everyone!

It's been a while since I last released one of my incoherent ramblings into the wild jungles of cyberspace, and I have much to talk about, so expect to see a few more posts in the coming days. (And if you don't see said posts materialize, please nag me until I get them done.)

(As a side note, as of this writing, my blog has about 25,000 views accumulated since my first post in July. 20,000 of those views are attributed to a post I wrote in August about the ninja board. Apparently Google likes ninjas.)

My school resumed classes today, and 1st semester final exams are coming up in a week and a half. That means the time has come to start reviewing for finals.

I've been wondering about this lately, the idea of spending a week and a half of class time reviewing for final exams.  I'm not completely sure I ever do it the right way. Actually, I often wonder if there even is a right way.  

Does it even do any good to review for final exams?

Every semester, I take the last week and a half or so before final exams to review with my students everything that we learned over the prior 16-17 weeks, tell them what kinds of questions to expect on the final exam and how many, give them time to work on review packets/assignments/flaming obstacle courses, etc. and so forth.

I've tried various ways of helping my students to take stock of what they learned (or were supposed to learn) over the semester. We've done the "review for finals process" as a project (with a rubric and everything) where students had to develop and publish their own study guides. We've done the classic "Jeopardy!"-style review game. We've done notecards that students were allowed to use on the final. We've done review assignments with the final exam questions literally lifted from the exam itself, with the numbers changed.

And what bothers me is this: Not once, that I can recall, in the four years I've spent teaching so far, have I been able to discern whether or not these methods of reviewing have done any good to any of my students.

What appears to happen is that the students who more or less have been "getting it" (or have been perpetually on the cusp of "getting it") all along are best equipped to understand and solve the problems set before them on the review assignments. Students who have been struggling all semester -- for whatever reason -- also struggle to find success on review assignments. It strikes me as a situation where the students who benefit the most from reviewing for finals are also the ones who need it the least, and the ones who benefit the least are the ones who need it the most.

I don't know why this appears to happen. (Or, if I'm really being honest, if it actually is what happens.) Maybe I haven't been making enough of an effort to find out. Maybe it's some bizarre phenomenon that can't be explained, like Honey Boo Boo. Maybe I suck at teaching. (Okay, maybe not.)

I was discussing this matter with my lovely wife the other night, and she asked me, "well, how do you know whether or not it's helping your students?" I thought about it, couldn't come up with a great answer, got childishly frustrated then stammered something like, "it's just based on what I've observed in class, I don't know how to explain it!" Then I pouted and decided to go do something else, because I'm so mature.

The bottom line is, I've never really been confident in my approach to reviewing for finals. I haven't made it easy for myself to tell whether or not my approach has a positive (or negative) effect. Maybe that's what makes me wonder if reviewing does any actual good.

Perhaps in the naivety of being a young teacher, I've been thinking of it the wrong way.  I think the best way to describe how I've approached reviewing for finals is that I've seen it as an eleventh-hour scaffolding activity, intended to give students one last hope at having a mathematical epiphany, a lifeboat that will float them safely through the perilous, shark-infested tides of the final exam.

It never seems to really work that way. No lifeboats. Sharks with happy tummies.

Maybe I should be looking at reviewing for the final exam as part of the cumulative assessment itself. Reviewing should really be more of a time for reflection and fine-tuning, not making a last-ditch effort for comprehending something for the first time. That's not to say there won't be a few students that do get that benefit from reviewing, but that shouldn't be the point. The point should be to look back at all of the work we've done all semester, take stock of what we've learned and what we still have questions about, address areas that still need addressed, and perhaps even celebrate.

My angst aside, here's what I'm trying this time around. The other day, I remembered something I read on David Coffey's blog about giving students the answers to the problems and having them explain how to get that answer. In my case, I'm going to provide students with a set of problems that are similar to what's on the final exam, give them all of the answers, and require them to explain how to get each answer. This way, they focus on how to solve the problem as opposed to focusing on getting the right answer.

I don't really know if this will be any better or any worse than what I've tried in the past. But, I think it will at least alleviate some of the anxiety and second-guessing that comes with reviewing for final exams. We have a week and a half, which should be plenty of time to address any questions or concerns that arise as students work through their review assignments, particularly since I am putting the focus on articulating their mathematical thought processes.

Will it do any good? Your guess is as good as mine.


  1. A couple thoughts... the first of which is sadistic. Review with one class, don't review with another, and see how it goes. I can just imagine the scuttlebutt in the hallway! Secondly, last year I took the approach of "let's build a notecard together." I had each kid bring in at least 3 things (I'm upping it to 5 this year) that they think they need to remember for the exam. Then we put them on the whiteboard as if it was a big notecard. They covered everything pretty well - a formula here, a notation there, an example, things to remember, etc. We're down another day before midterms now - water main break at our school today means no school tomorrow. Oh well. Who needs to actually GO to school?

      I nominated you, Get back to work!
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  2. I'll be interested to hear how it goes after the review week! I only have about 3 days to review with my students but I also give them a packet reviewing all concepts from the year with answers at the end. Students in the past have told me they love that it has answers so if they're working on it at home then they know they are solving the problems correctly.

    Also, I think we need a ninja board update!

  3. What has helped my students more than review sessions is having more than one chance to take the test. In pre-calc, they can take most tests as many times as they want. In Calculus, they can take each test at least twice, including the final. They have taken on the responsibility for learning how to study better.

  4. Been reading your blog for a while, but not much posting. Thought I'd chime in here... (altho' I'm a science teacher, not math)

    No answers here for you, sorry. I agree with you - how do we know that reviewing actually helps? I think finals are just a state's way of having standardized scores. I don't care much for finals myself (or any standardized testing for that matter). The grade I use in class is an attempt to reflect a student's actual and (somewhat) current science abilities. If I don't have to give an exam, I don't. If the school requires me to, I will.

    The exam just proves either you know it or you don't.

  5. Jeff,
    I too spent a week or more reviewing for the final with the same results. I did not see a significant change in math scores over previous semesters. It's a question of active vs. passive learning. If I walked through examples on the board, or even had the class break up into groups and review problems, there were those who worked the problems and those who watched. The is a difference between “I see what you are doing and can follow your steps” and “I can work problems myself and see the steps to finding a solution”

    My math anxious students, in particular, are almost afraid to try for themselves. They watch me work a problem and figure they understand it if they can follow the steps. They get to the exam with numbers changed or problems worded differently, and they can’t do them. In one case, I put several questions on the exam exactly as those in the review. They still couldn’t do them.

    What makes a difference is getting the students engaged in projects that require active participation. It is changing mind sets, study habits and other engrained behavioral traits, and it doesn’t happen over night. I still like reviews, it gives students one more exposure to the subject matter, and repetition, if done right, does help students reach a deeper understanding. The difference is teaching my students how to recognize destructive learning behaviors, and then helping them find the resources and learning opportunities to overcome them and develop true problem solving skills.

    Your posts, as always are thoughtful and informative.

  6. Here's my perspective as a college instructor:

    1) When we hold review sessions it's the students who don't really need to be there who show up while the ones who really could use it don't. I don't offer review sessions very often for this reason.

    2) By reviewing with them you are teaching them a valuable skill that they can use in college when they have to review for their exams on their own. Maybe tell them that. I've often found that telling them the reasons for things gets them to value them a little more.

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