Review, ad infinitum…

In elementary school, I used to get excited right around when we reached p.100 of our math books, because that’s when we would really start doing stuff.  Those triple digits meant that lessons would no longer be about practicing addition and subtraction, or rehashing things we were supposed to have learned the year before.  Maybe that first month or so of the school year taught me patience, otherwise, I would have gone mad.  Unfortunately, as a teacher, I’d fallen into the same trap of needing to do that all-important review as the first unit of the school year.  What better way to kill the potential energy built up over the summer and bring whatever momentum had built up to a grinding halt?  In retrospect, it seems that “review” seems to make students who already got it last year either check out or get lulled into a sense of complacency.  For students who didn’t “get it” last year, instead of starting with a clean slate, it instead drives home the message that this year will be more of the same.

This is not to say that review isn’t important or necessary, but what makes the difference is the way that it is done.  This year, a colleague and I rearranged the sequence of topics in the PreCalculus courses that we taught (different schools in the same district).  Instead of first semester being largely a rehash of Algebra 2, we started with Trigonometry first.  This is the fifth year that I’ve been fortunate enough to teach PreCalculus, and I’m kicking myself for not coming to this realization sooner.  Even though we’re starting with a topic that’s new for most students, we’re still able to secretly review solving equations, working with exponents, and working with fractions, all in the context of doing trig.  Instead of two separate groups (those who got it last year and those who didn’t), everyone was learning something new, on equal footing, and with a clean slate.  I don’t think that there’s anything intrinsically different about the makeup of students this year, but with the new approach, we’ve been able to keep the momentum going from the beginning of the school year when students come back from summer, eager to learn something new.  We’ve been able to cover more material, go into more depth, and maintain a healthy pace, especially compared to previous years.

I’m slated to teach Algebra 1 next year and am hoping that this idea is something the team will be willing to run with, or at least consider.


About Clint

Looking for answers and enjoying the journey.
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4 Responses to Review, ad infinitum…

  1. Paul Hawking says:

    I’ve printed out a copy of this post and plan to share it with some of my colleagues. Your approach gives all of the students a chance to be engaged from day one and simultaneously incorporates needed review.

    Were you able to “bank” the days originally set aside for review and use them to slow down the pace for challenging units, add a project, or add an additional test review day before a challenging test? It’s a great idea, even if it didn’t translate to a net gain of free days.

    Now you have me thinking of how I would re-sequence the first few weeks of Algebra 1 next year 🙂

    Paul Hawking
    The Challenge of Teaching Math
    Latest post:
    Posts I really like from (Math Be Brave)

    • Clint says:

      Hi Paul,

      Sorry I’m soooo late in responding to your comment! Regarding how we used the days originally set aside for review… Using the old model, usually the most complicated topics would come at the end of the quarter or end of the semester because we did the “easy” topics up front. With the new model, I found that while we were able to cover a few more topics, really most of the “extra” days were used giving the complicated topics the time they should have gotten, rather than rushing through or cutting them short at the end of the term. As an example, graphing and solving trig equations were covered fairly early 1st semester, then those topics could continue to be “reviewed” on subsequent homework assignments periodically during the rest of the semester. Also, leading off with trig identities second semester, I didn’t feel that we were rushed through it and we were able to give it sufficient time. In past years, we’d hit the trig identities chapter right in the middle of our standardized testing season (and AP testing shortly thereafter).

      Let me know if you have any questions. Also, if you’re interested in following the resequencing of Algebra 1 that my colleagues and I will be working on later this summer, I can give you access to our internal site ( in exchange for any suggestions and feedback you have as we do this work.


      • Paul Hawking says:

        Hey, thanks for the reply, Clint. I think you did exactly what I would have done: too often, the hardest topics get short shrift because you’re building up to them without enough time at the end of semester to do them justice.

        No worries on the wait time: it was a pleasant surprise to find the “Hey, you’ve got a reply” email from WordPress in my inbox.

        I would love to see what you’ve done with the Algebra 1 re-sequencing and would be happy to chime in with my feedback, for whatever it’s worth. You can contact me via email with the access particulars, if you’d like. My email is listed in my blogger profile under “Contact”, which you can access here:

        Paul Hawking

  2. Jeremy Touzel Hansuvadha says:

    Yeah. Glad you put this up. I couldn’t agree more.

    Reviewing to start the semester is a lose/lose proposition. It’s a lose for the kids because blah–review. And it’s a lose for the teacher because IT DOESN’T WORK ANYWAY! (Sorry to go all caps there, but there was no way of getting around it.) I mean, a few weeks after reviewing, the same kids will still screw up fractions/order of operations/solving equations/properties of exponents/whatever.

    And like you alluded–another downfall of reviewing is that it merely serves to stratify the class by status.

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