Warm-ups in Math Education

Interviewer (looks at Sarah over her glasses): “Based on your research and personal philosophy, what is the purpose of warm-ups in your classroom?”

Sarah (taps her lip thoughfully before replying, then leans forward a touch): "Funny you should ask, madam. Indeed, using warm-ups at the beginning of a class period are useful for a number of reasons. For one, having students work on some problems as soon as they enter class gives the teacher a few minutes in which to take roll and complete other “housekeeping” duties. This is doubly beneficial, because rather than talking and not settling down, the students are almost immediately engaged (in other words, none of their time is wasted) and the teacher will be more quickly able to move onto the lesson for the day.

Moreover, warm-ups are appropriate for daily classwork because they are designed to meet at least one of the following targets: activate prior knowledge, review material from the day before (repeat and reinforce learning), introduce new material, check for understanding or lack thereof, and/or get students ready for jumping into the next set of activities. An activity, for instance, that references a concept that students should have learned the previous year, will ensure that students are better able to remember it (we “learn” through repetition) and will help the teacher check for any instances of lack of knowledge (so that he/she can scaffold those students who are lacking in an area). An activity that reviews material from the day before creates a sense of continuity from one day to the next and ensures that students are less likely to forget material from lack of exposure to it. Also, students have had the night to process new information overnight and are better able to tackle any misunderstandings. Because the work time on warm-ups is short, it helps get students settled into the correct frame of mind for beginning the next lesson or activity or for getting back into a lesson that has spilled over from the day before—in other words, it makes students think about math before listening to the teacher lecture again.

(brief pause, as though considering whether to say more)

However, I do argue that the most important of the above stated reasons is the one regarding repetition and reinforcement. We cannot expect students to internalize new knowledge in one day. Our brains need time to process and store that information, but if it is not “activated” within a short period of time, the likelihood of retaining that knowledge is greatly lessened. Not only for their own general benefit, but also for passing tests, this repetition is the key to the students’ success. Students must be able to remember things that they were taught at the beginning of a semester when they are taking tests, and if the teacher was unkind enough only to teach it once and never reference it again, it is quite possible that a high number of students will not recall that information. If I had only spent one day learning the alphabet when I was a child, it would be unlikely that, four months hence, I could tell you it in its entirety. It would even be possible that I forgot all of it. By extension, we can easily assume that most children will not run home after math or science class and eagerly do problems for entertainment, so we have to address all learning as it happens in the classroom. As a result, repetition and reinforcement are the primary reasons for having warm-ups in a classroom to begin with.