Teaching in the Long Period

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by Henri Picciotto

Math 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.

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. In this article, I will argue that the long period supports better teaching.

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My Experience

I was a teacher and department chair at the Urban School of San Francisco from 1981 to 2013. The school's schedule went through various revisions over that time, and has continued to change since my retirement. However one thing remained constant: students take four classes in any one term, periods are significantly longer than the classic 50 minutes, and a weekly double period takes up about half a school day.

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 such trimester 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 a long period prep takes substantially more time than a short period prep, for reasons that will become clear if you read on.)

As the chief architect and tweaker 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. I will start this article with general observations, applicable to any discipline, before zeroing in on math instruction.

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 obviously well suited to science and art where labs, trips, and hands-on work are essential. Bringing this broad range of pedagogical modes to all the disciplines allows us to reach a broader range of students, and also to give more depth of understanding to all. A well-designed lab can enhance a math or science class. A well-chosen field trip can enrich a history or biology class. In-class writing or watching an entire play can transform an English class. And so on. (For more on broadening one's pedagogical range, see my article "Nothing Works", and the accompanying "Art of Teaching" activity.)

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 usually 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.

For 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 this 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 increased 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

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 useful concept for working with heterogeneous classes.)

At Urban, we have found that teaching fewer things in more depth has gone hand in hand with students taking a fourth year of math. So for many students, 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.

Math in the Long Period

Many math teachers resist the transition to a block schedule because of their deep-seated belief that math is best taught is small daily doses. Here are my answers to some questions frequently asked by those teachers.

Do students have the necessary attention span to remain engaged during a long period?

Yes, they do, if you break the period into two or more chunks. Few activities will work well for the duration of a long period. In your planning, get used to breaking it up. Here are two possible templates, and a blank one if you don’t like either of them:

long-period-templates

(These templates are intended for a 70-minute period. Adjust as necessary.)

The opener can be a transitional piece into the day’s work. What I did was have students go over the homework in their groups. Another possibility would be a well-chosen warm-up or “do now” which will help set up the main topic of the next segment. (See for example: Think First)

The One Main Activity template is good for a lab or collaborative project, the sort of thing one doesn’t have time for in a shorter period.

The Basic Routine template is one way to set up a daily rhythm. The central segment is where you’re forging ahead with new material. The last segment is where you might review some past work, apply new ideas, or preview some future topics. It is not to do homework or have a study hall, and should be planned just as seriously as anything else.

Breaking up the period is only partly about content. The main point is to use different formats:
◊ whole class / groups / pairs / individual
◊ paper-pencil / verbal / hands-on / technology
◊ formal / informal
◊ watching / reading / writing / making
Format-switching helps students stay focused, and in any case is better teaching, as it increases engagement, motivation, and understanding. (See my Art of Teaching worksheet to help you think about broadening your pedagogical horizons.)
Use this worksheet to draft possible long periods:
◊ generic for your department or all your classes
◊ special versions for different grade levels and courses
◊ actual implementation for a particular day
…or all three. Whatever would be most useful.

Can students remember what they learn if they don’t have math every day?

They will if you rely on understanding rather than memorization. One way to do that is to teach the most important topics in multiple representations, and/or with the help of technological or manipulative tools. Take advantage of the long period to diversify your toolbox, and use your new tools strategically on the key topics. Longer periods make it possible to build interesting review into your course. (Teaching the same thing the same way is the worst possible kind of review, as it is boring for students who got it the first time, and usually unhelpful to the ones who didn’t.)

I recommend other strategies to strengthen retention: lagging homework, separating related topics, and generally extending exposure. I discussed all this in Reaching the Full Range. See also some practical advice on implementing these ideas.

Will I be able to cover as much material in a block schedule?

Probably not, because even if you see students for the same number of minutes, there’s only so much they can learn in each school day. If your goal is to teach for understanding, you will need to prioritize the most important topics, as suggested above. To do that will require eliminating or giving less time to other, less crucial topics. I share some guidelines for pruning the curriculum in Big Picture Planning.

But even then, you still run a risk of not covering even a pruned curriculum if you allow your classes to be too leisurely. Do not let long periods lull you into a false sense that there is plenty of time. There isn’t. As suggested above, I do believe in eternal review, if it is done well, but the other side of that coin is constant forward motion.

Constant forward motion is helped by lagging homework and the other strategies listed above. Another way to keep moving forward is to pursue two units at a time. I realize that is truly countercultural, but my department has done this for years, and it’s worked very well for us. For one thing, if you’re pursuing two units, you can use that to break up your period into chunks as suggested above. Also, if things bog down in one of them you can switch the emphasis to the other one while you figure out what to do. Finally, pursuing two units forces students to be alert and not turn into automatons.

Ideally, the units would be unrelated, and as different from each other as possible as to their “feel”. For example, a unit on the properties of special quadrilaterals can be run concurrently with one on right triangle trigonometry. Or, a unit on systems of equations along with one on the Pythagorean theorem. And so on.

Will I be able to change my habits?

I cannot answer that for you. I’ll just say that the long period is unforgiving: if you don’t heed at least some of the above suggestions, it will feel endless, and you’ll conclude that “it doesn’t work”. On the other hand, the long period can be a motivation and an opportunity for ongoing professional growth. In my own career, it has both required and facilitated my becoming a better teacher. If you’re up for the challenge, the long period is a wonderful gift to you and your students.

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