Like most teachers, I learned the craft on the job, with the help of colleagues. The formal training I received in college was not that useful, with one exception: my short stint as a Community Teaching Fellow (CTF) when I was a math graduate student: I got paid as a Teaching Assistant, but my teaching was 40 minutes a day to third graders in a public school. As part of my training, I observed experienced CTF’s in action, and they watched my class and gave me feedback. Interestingly, the feedback was overwhelmingly about what was happening among the students, not so much about what I said and did. Or rather, it was how my choices affected student participation.
The CTF program was inspired by William F. Johntz’s Project SEED, an approach based on whole-class Socratic teaching techniques, combined with a trust that all students can engage in abstract and logical thinking if given a chance. My third graders in Richmond were comfortable exploring negative numbers, exponentiation, and finite groups — as long as I taught this content using the discovery methods I was learning. Project SEED was an ambitious and effective program, which started in Berkeley in 1963, was deployed nationwide, and finally closed shop in 2016, after having helped hundreds of thousands of underserved students.
In preparing to write this post, I read through Project SEED’s Guidelines for Discovery Teaching, with the intention of sharing with my readers some of what I learned some 50 years ago. I was stunned to discover that many, many of my whole-class teaching techniques originated there. They were so ingrained in my classroom demeanor that I forgot where they came from. When I shared these ideas with colleagues over the years, most assumed (as I did!) that I had created these strategies, that they just reflected my personality. In fact, they originated in Project SEED.
In any case, it is now clear to me that I cannot share all of them in this blog post. I’ll select some — if you want the whole package, go to the Project SEED page on my website.
Hearing from all students
Many teachers, well aware that merely talking at the class is not that effective, try to involve the students by asking questions, and resign themselves to having the same two or three students answering them. Alas, that is not much of an improvement over a straight lecture. It may even be worse, as it gives the impression that students know what’s going on — when in reality it is only those two or three students who are actually on board.
Project SEED proposes a number of techniques to get everyone to engage, and (crucially) to let the teacher know where the class stands. This involves varying the student response mode.
- After asking a question, do not tolerate students blurting out the answer. Ask for “quiet hands”. Count the number of hands. “…five, six, seven… Seven of you have an answer. I’ll give you more time to think.” Or else: “talk to your neighbor about this, and I’ll ask again.” Or: “Who can give a hint to the class? I’m sure more than seven students can figure this out.”
- “Show me the answer on your fingers”. This works best for small non-negative integers, but students enjoy the search for ways to show -2 or 3/4.
- “Point up if the answer is positive, down if it’s negative, make a zero with your fingers if it’s neither.”
- “Graph the function in the air”
- “Thumbs up if you agree, down if you disagree, sideways if you don’t know”
- “Write down the answer” (quickly walk around to see what they wrote)
- If you’re pretty sure almost everyone knows the answer, ask for everyone to answer in chorus — perhaps in a whisper.
In some of these modes students will just imitate other students answers, since they’re visible to all. But the increased involvement overall means it’s worth it, and in any case you can tell if they’re doing that, which is itself useful information. Sometimes I use gestures to tell students to put their hands down as soon as they know I’ve seen their answer — this makes for a bit of excitement.
(More on maximizing participation: Every Minute Counts.)
Assorted discussion-enhancing tricks
Even the best questions are ineffective if students are not paying attention. The board is the visual support for the discussion. Here are some tricks to maximize its usefulness, and to get focus.
- Use color, boxes, circles, and arrows for emphasis.
- Erase strategically. “Oh no! I erased the most important thing! Help!” Or else “I need space. I’m about to erase almost everything. What should I not erease?”
- Use students’ names: “Asa’s formula”, “Lucy’s trick”, “Maria’s theorem”
- Move around the room.
- Every once in a while, teach in total silence. Ask questions by writing them on the board. Hand the marker (or chalk!) to a student so they can answer without speaking.
- If appropriate (e.g. when exploring a pattern), ask “What is my next question?” “Yes! You must be psychic! How did you know?”
- Especially if a student stalls mid-response, or gives an answer that generates many thumbs down: “Pick someone to help you.”
If a lesson is going well:
- “Fasten your seatbelts! This is going to be challenging!”
- “This next problem may be too hard. Last year’s class couldn’t handle it. Maybe I shouldn’t even ask that.” (Then ask it.)
And here are some big-picture principles from Project SEED that have become second nature in my teaching.
- Embed review in new material, rather than going over old content the same old way with promises that it will be useful later. It’s more respectful of the students, and more interesting for everyone.
- Vary the difficulty, rather than going monotonically from easy to hard. This helps keep everyone engaged. (More on this: Geometry: A Guided Inquiry.)
- It’s OK to leave some questions unanswered and return to them in a future class.
- Go back and forth between the general and the specific. Sometimes: “This idea works for small numbers. I wonder if it’s always true.” And sometimes: “Does this idea work for small numbers? Who has a way to test that?”
- Students should be comfortable making mistakes, as it is often a necessary stage on the road to understanding. I wrote about this before: Handling Wrong Answers.
And the biggest principle: if we teach effectively, all students can do math!
And there’s more!
Just to be clear: There is no one way. I do not claim this is the only way to teach math. But combined with other approaches (such as especially group work) the Project SEED techniques are a powerful addition to any math teacher’s toolbox. They add an element of drama to whole-class discussion, and break the hold of the dominant culture (“I explain, you practice.”) Coming across Project SEED’s Socratic method is what convinced me I needed to become a teacher. I have used these ideas for about 50 years at all levels, from counting to calculus, and passed on much of this to colleagues and mentees.
And now it’s your turn: I obtained permission to share Project SEED materials on my website. So it is possible for you to go to the source of all this. I hope it will be as useful to you as it was to me!