Last January, I addressed a blog post to a “young teacher”. Actually, it applied to beginners — whether young or not so young. The post was largely about big-picture thoughts on becoming a math teacher. It generated a thoughtful and heartfelt response from another veteran educator. If you’re a beginner, I encourage you to check out that post, and to continue reading this one. Today, I zero in on a central aspect of your new career: the classroom.

There are many, many ways to manage your classroom. I list many choices we all have to make every term, and every day, on this worksheet: The Art of Teaching. In general, there is no one choice that is *always* the right one. Sometimes, we should rely on a trusted and familiar routine; but sometimes it is important to go for variety and a change of pace. Sometimes we should use technology, or manipulatives; but sometimes students should work on paper, or do “mental math”. And so on. Growing as a teacher is all about increasing our repertoire of techniques.

Still, there are some overarching realities that dictate limits outside of which it is not possible to be an effective teacher.

### Teacher leadership

No matter what the current lesson plan entails, it is essential that the teacher be in charge. This is often called “classroom management”, which makes some sense, since the teacher needs to manage the classroom. But those words carry an implication that the goal is mostly student compliance. I prefer “teacher leadership”, which to me implies that the goal is student learning.

Our students have a lot going on in their life. Learning math, for many of them, is low on the list of priorities. Moreover, even for those students who are eager to learn, they don’t necessarily know the best way to accomplish that. Thus, the teacher needs to be in control. Sometimes it means micromanaging (“get your book out”, “write this down”, “pull your chair in”, etc.) Hopefully over time it means letting go and giving students the space to take responsibility — but the only way to get there is to build healthy work habits.

### Formal vs. informal atmosphere

There are some societal expectations of classroom decorum. A teacher cannot take a nap. A student cannot burst into song. A visitor cannot make a phone call. And so on. But within that there is a range of possibilities. My sense is that instead of searching for a happy medium, it is best to clearly delineate two distinct modes.

The *formal mode* is reserved for whole-class discussion, for teacher explanations of various sorts, and for quizzes and tests. When in the formal mode, students stay in their seats, do not go to the bathroom, and do not speak until they are called on. When the teacher or a fellow student is addressing the class, they listen respectfully. If some students are distracted, the teacher waits until they have everyone’s attention.

The *informal mode* is reserved for times when students are working individually or in groups, or doing an activity using technology or manipulatives. They need not be silent, as long as their conversation is about the work at hand. They can go to the bathroom if they must. Then can ask for help from teacher or peers.

In both modes, students are expected to focus on math the whole time. If they stray, the teacher can gently and supportively put them back on track. In particular, if they try to ask irrelevant questions (“is there a quiz this week?”, “can we do something fun tomorrow?”, “where did you go to college?”) the teacher should not be derailed. They should tell the student to meet them after class — and proceed with the lesson.

Of course, each teacher needs to adjust these guidelines to the realities of their personality and their departmental and school expectations. But once they have some clarity on this, they need to make their policies clear to the students.

### Student intellectual engagement

The whole point of such behavioral norms is to make it possible for students to engage intellectually. “There is no royal road to geometry.” Intellectual engagement is the only way to learn math, but it not possible for most students if the teacher abdicates their leadership role.

As teachers, it is tempting to shield ourselves from reality by doing most of the talking. We ask “Are there any questions?”, and hearing none, we deceive ourselves into believing that the students are listening to us and understanding what we are saying. One way we extend our self-deception is by emphasizing and prioritizing the memorization of various techniques instead of problem solving and multiple representations. Such memorization can temporarily mask lack of understanding.

To teach effectively, we need to constantly get a sense of what students actually know and can do. Are they thinking or just parroting? Some of that depends on what materials we use. But some of it has to do with how we teach. Here are some ways to keep track of the reality of student understanding — every day.

- In group work: Group Work, Random Groups and The Thinking Classroom.
- In whole-class discussions: Every Minute Counts and Project SEED.

### Conclusion

I titled this post “Classroom Basics” because I think these ideas are foundational to effective teaching. Unfortunately, the fact that they are basic does not mean they are easy for beginners to implement. The best way to get there is to work with colleagues. Observe their classes, and ask them to observe yours — with a focus on these questions: are all students engaged intellectually? what can I do to make sure they engage? am I enforcing my formal and informal behavioral norms?

Good luck as you work on all this! It will take some effort, but it will be worth it.

— Henri