It is a serious mistake to present important concepts only once, and move on. Most students need extended and repeated exposure to challenging ideas before those sink in. As I became more and more aware of this in the course of my decades in the classroom, I started to think in terms of a “preview / view / review” cycle for any important ideas. A crucial change in my practice was to extend student exposure to concepts by using the strategies I outlined in Reaching the Full Range. This includes lagging homework and assessments, and allowing test corrections for “points”. These techniques turned out to be relatively easy to implement, and in fact to reduce the need for review. (Reduce, not eliminate!) One technique I suggest in there is separating related topics, precisely because doing that provides an opportunity for non-intrusive review. To quote myself:
If you separate related topics, when you get to the second topic, you have a built-in review of the first one, perhaps in homework. And thus you’ve created forward motion (moving on to something else after introducing the first topic), and extended exposure (revisiting the first topic when working on the second.) Another advantage of this approach is that it communicates to the student that they are learning for the long run: any important topic may and will come back.
In any case, because many if not most lessons rely on previous knowledge, it is often a good idea to review old material. The question is how to do it well. Here are two thoughts on that.
Do not start a course, or a unit, with review of old material. I know this is counter-intuitive, but starting that way can be demoralizing. The student who doesn’t need the review resents it as a waste of time. The student who needs it may be reminded of the trouble they had with this topic. So it is almost sure to set the wrong tone. Instead, start with an engaging and relevant anchor activity. An anchor activity, ideally, gets to the big ideas of the unit, is interesting, and does not rely on many prerequisites. I discussed anchors in these posts: Towards Inquiry, Sequencing, and First Day of School. See also Big Picture Planning on my website.
If not at the start, then when should review happen?
- If your students do homework, that’s one place to put review. Use short assignments that hit the key ideas they will need.
- If only a few students need the review, how much of it can be done outside of class in some sort of support system offered by you and your colleagues? (At my school, we had “Math Café”, a lunch-time help period staffed by teachers on a rotating basis.)
- If most students need the review, it will be obvious to all and it will not be resented. It should happen as soon as the need arises.
Approaching the same idea the same way is not effective, no matter how many times you do it. It becomes boring and students tune out, which undermines the goal of the repetition. Instead of blaming the students for not benefiting from my broken-record performances, I chose to expand my teaching repertoire, and refine my teaching practice. It is necessary to know multiple ways to teach important topics. The key idea is multiple representations:
- Manipulatives (or virtual manipulatives — not quite as good, but better than nothing)
- Traditional paper-pencil work
- Technology (electronic graphers, interactive geometry, …)
And within each representation, there are multiple approaches possible. If your textbook does not include that sort of variety, you’ll have to learn new things outside the textbook (including from other textbooks)! This cannot be rushed, as there’s only so much time in the day and the week, but you can gradually expand your horizons by attending conferences and workshops, by internet searches, and especially by talking to colleagues. Learning new ways to teach the same content is a career-long project.