# My Math Education Blog

"There is no one way"

## Monday, November 16, 2009

### Teaching in the Long Period

Here are some thoughts on teaching in the long period. By long period, I mean a class period of an hour or more, that is typically available under so-called block schedules. I've been intending to write something on this for my Math Education Page for a very long time. Some version of this article will eventually go up on the site, but I thought I'd post a draft here now. [A somewhat edited and updated version of this post is now at http://www.mathedpage.org/teaching/long.html.]

Of course, excellent teaching can happen in a variety of time settings. It is part of every teacher's responsibility to navigate the specific constraints at their school. And yes, every schedule involves trade-offs, and it is foolish to be dogmatic about such matters. Still, all schedules are not equivalent.

The Urban School Schedule

For each course, the Urban School schedule is based on a weekly rhythm of one 70-minute period, one double period (actually 70 + 60 minutes), and one 70-minute period. In addition, during some weeks, you have an extra 70-minute period. This arrangement is possible because students only take four classes at a time, in three trimesters. The trimesters are "real" in the sense that new courses begin every term. (Some schools have one-year classes, divided into trimesters for grading purposes. Those are not real trimesters in this sense.) For any given course, one of our trimesters is more or less equivalent to one semester at another school.

Because students only take four classes at any one time, they are better able to focus on each one. Full-time teachers teach three classes at any one time, typically two preps. (However preparing for a long period takes more time than one might expect.)

As the chief architect of this schedule for about 25 years, and as a teacher working in it, I have given a lot of thought to the long period. My points in this article are applicable to a wide range of block schedules, not just Urban's. They should be relevant to all the academic disciplines, but I will focus on math, which I know best.

Pedagogical Challenges and Opportunities

The long period offers both challenges and opportunities. It supports such approaches as experiential education and cooperative learning, and such practices as in-class reading, discussion, and writing. It is a boon for courses that involve labs, field trips, and hands-on work of any sort. Thus, it is well suited to science and art. However bringing this broad range of pedagogical modes to all the disciplines allows us to reach a broader range of learners, and also to give more depth of understanding to all students. A well-designed lab can enhance a math class. A well-chosen field trip can enrich a history class. In-class writing can transform an art class. And so on. (For more on broadening one's pedagogical range, see my article "Nothing Works".)

The long period undermines over-reliance on lecturing. Long periods do not work well if they are just like short periods, except longer. You cannot lecture at teenagers for 70 minutes and expect them to be able to maintain an appearance of engagement, something they can barely manage in a 50-minute period. Thus, a teacher who believes that giving whole-period lectures is the only way to teach their subject legitimately would consider the long period a threat. However, for a teacher who has been eager to broaden their pedagogical repertoire, the long period is wonderful. (And it certainly does not exclude the use of lectures, which remain a very important tool under any schedule.)

Because the long period is of necessity associated with greater gaps between class sessions, it undermines shallow teaching-to-the-test. If students' grasp of a technique or concept is superficial, it will not survive breaks of a few days between class sessions, or a few months between trimesters. But if our teaching is so ineffective that students cannot retain what we teach beyond a few days or a few months, why are we teaching at all?

Variety

I'll never forget the 9th grade girl who came up to me at the end of the second or third day of Algebra 1 near the beginning of my high school career. She asked "Is every day going to be like this?" I had a horrible feeling, because yes, every day would consist of my going over the homework, explaining a new micro-technique, having the students practice it, and perhaps starting the next homework assignment. Every day, every week, every term, every year... Fortunately, in the subsequent years I've expanded my repertoire, and have a much healthier balance in my classes between routine and variety. The long period was in part what made this possible: if I was teaching 45-minute periods, I probably could have gotten away with the monotony, and would have excused it by pointing out there was no time for any deviations.

Typically, in my classes, students spend the beginning of the period (10 to 15 minutes) going over homework in their groups. I walk around the room, assessing where the big question marks are, and recording who did and didn't do the work. If there are problems many people missed, I might lead a class discussion about those.

Here are some of the ways I organize the rest of the period. I almost always plan two or more parts to the day's work:
Class discussion / group work
Paper-pencil / technology
Paper-pencil / manipulatives
Paper-pencil / make a poster
Quiz / lesson
and so on... Sometimes the first item expands to fill the whole period, but that's OK, given the overall variety of the program.

If you're a math teacher at a school transitioning into a longer period, please look through my Web site for non-traditional approaches involving manipulatives, technology, and big problems. In fact, you can get such ideas all over the Web, and at most professional conferences. Of course, this will work better if you are ready to escape from the textbook on a regular basis. And even better if you make this transition an opportunity for close collaboration with your colleagues.

If you make those changes, under any schedule, you will not regret it -- and your students will thank you for it.

Coverage

All this variety in approaches does help reach more students, and yields more understanding. But one price you pay is some reduction in "coverage", and some reduction in opportunities to practice skills. There is only so much that students will absorb on a given day, and having fewer class meetings, even if they are longer, almost certainly means fewer topics addressed, and fewer homework opportunities. One way to attenuate these problems of the long period is by making sure to do some new and some old material every day. My slogan is "constant forward motion, eternal review." (This is also a great strategy for working with heterogeneous classes.)

At Urban, we have found that teaching fewer things in more depth has gone hand in hand with greater enrollment in calculus, and more students taking a fourth year of math. So there is actually a huge net gain if you look at total "coverage". But even if that were not the case, it is more important to discover and uncover than to "cover": students with deep understandings are better able to continue learning on their own, while students with broad but shallow understandings will have trouble gaining additional depth.

Time issues

More in-class time means less time wasted on overhead (taking attendance, making announcements, and the like), and more time available for big in-class activities, group work and special assignments. Instead of students' brain transitioning from the previous class at the beginning, and thinking ahead to the next class at the end, there is more time for genuine engagement, especially if you have substantial breaks between classes.

However days off and absences will have a bigger negative impact. Also, unless the teacher is vigilant, the relaxed atmosphere can lead to a too-leisurely pace, and a loss of instructional time. Still, a major consequence of the long period is a less frantic atmosphere. The comfortable feel of each day and each period is one of the things visitors to Urban comment on the most.

Conclusion

The long period provides a powerful vehicle to improve teaching at any school, even an excellent one. It demands variety, flexibility, and craft from the teacher. Used well, it offers a more humane pace, deeper understanding, and authentic engagement to the student.

--Henri