A great lesson doesn’t not need all of these elements, but as teachers we need to understand the lens we use when selecting what our students will spend their time doing. So with that:
Great lessons …
… have a low floor and a high ceiling. I was reading a Desmos blog post about how they think about great digit activities and they wrote:
“Create activities that are easy to start and difficult to finish”
I like that a lot. But what makes a low floor? Probably depends, but you must make sure that every student in your class can participate in the beginning of the lesson. The more interesting the hook the better. Can you get a debate going during the introduction of the lesson?
The simplest metric here might be “Can they make estimates on the answer before beginning the lesson?”
… have more than one way to figure it out. It doesn’t have to have lots of ways – even if there are only two ways that’s still good. It’s important to be able to compare and contrast approaches. Sometimes this “open middle” if you will is only apparent for part of the lesson. For example, I have students measure the height of our stadium lights using an inclinometer. They take measurements from two different distances. This lesson is awesome, but there is only one way to do it. After they get their two answers (one from each distance) I ask them “Which distant do you think is more accurate?” Now we have opened up that problem a lot. The main content outcome had only one way but you can bring in an openness by the questions you ask throughout.
… are ones where you don’t immediately know how to do it, but you think you can figure it out. This is a subtle place. The book “Make It Stick” labels this as “desirable difficulty”. It’s hard to put your figure on what makes this true but there are definitely questions that students get where they say ‘I don’t know how to do this and it’s too difficult for me to figure out”. And that is not a clear constant line for every student but you don’t want anyone in the room thinking that at the beginning of a lesson.
Ms Pac Man hits this mark pretty good. Students generally don’t know how to get her all along that path but they believe they can do it. So when they hit that first turn where she reflects and rotates they are like “this is strange”, and they immediately move into trying to figure out that turn. They believe they can do it with effort and collaboration.
Pro – tip. You must help them without thinking for them. So you must know how they are thinking…. so you must listen to them and not assume that you already know what they are thinking.
Lastly, frame all hints as “break throughs” and attribute them to the students and groups where the idea emerged from.
… have a surprise ending. Anytime our intuition turns out wrong become intrigued. Almost like we don’t believe it or something (“No way – this can’t be right”). One of my favorite examples of this occurs during Mathalicous lesson “As The World Turns”. After students calculate the speed someone on the equator is moving due to the earths rotation you point them to where they are located on the graph and ask “Are we traveling at the same speed, faster, or slower than someone on the equator?” The students who believe we are traveling at the same speed eventually sit at the edge of their seats when they learn they are wrong. It’s time to be convincing and go for that ride.
I’m a bit of time so here are a few more ideas that I’ll present without explanation:
… allow for conversations that are important irrespective of the mathematics, use technology, have manipulatives, ask students to measure and collect data, have students create something, connect art & mathematics, ….
It’s interesting, I have having some trouble differentiating between the elements of a great lesson, and elements of great teacher moves. Most of the ideas that are coming to mind feel more like teacher moves rather than static elements that exist naturally within a lesson.