I’ve been thinking recently about "teaching slow, then fast, then slow again." I want to try and describe what I mean and what it looks like in practice.
Teaching Slow
When I approach a topic or unit, something larger than a lesson that represents a big idea of 7th grade math, I always remind myself to start slow. That means two big things. First, I take my time making sure students have all the prerequisite knowledge they need to be successful learning some new math. I do a mix of review, mini-lessons on things students might have forgotten, and chunks of practice with those ideas to try and make sure all the prior learning is secure before we get started on new math. Second, I take my time figuring out what students already know about a topic. It depends on the topic, but for a lot of concepts students already have some intuition for what I want them to learn. I spend lots of time seeing what students already know and can do, and getting ready to link that knowledge to what I want them to learn. This might take a couple days before we start the new stuff. That’s fine. It’s worth the time.
Then Fast
This is the part where students learn the big idea of the topic or unit. When I say fast I don't mean that I talk fast and rush. I mean that, when I start slow and make sure students are ready, the learning tends to go much more quickly and smoothly. First, I don't get hung up over and over again realizing in the middle of a lesson that students don't know something I assumed they know. Second, as long as students are ready for it, this is a great place for explicit instruction. Trying to get kids to figure something out or facilitating a big discussion leaves too much to chance; it’s my job to make sure the math is communicated clearly. Third, I try to focus on big ideas. I don't want to go overboard saying "and if the equation looks like this you do this first, and if the equation looks like that you do that other thing first..." There will be time to hash out lots of specifics and edge cases later. The focus in this chunk is helping students understand a big idea that they can apply to lots of different situations in the future.
Then Slow Again
This is the part where students apply what they learned. I always need to spend more time here than I think I will. We solve problems. I introduce more complexity bit by bit. I assess what students know and don't know and respond to it. I figure out who's having a hard time and could use some one-on-one help. We dive into those edge cases. We do mixed practice. We solve more complex problems. This takes time. I often realize students are struggling with something and go back and reteach or adjust. And then we solve more problems and repeat.
Two Examples
When I teach proportions in 7th grade, one big strategy I want students to know is to find a unit rate, and then use that unit rate to solve a problem. We spend a lot of time at the start filling in tables of proportional relationships, calculating unit rates with numbers that work out nicely, and doing calculations with contexts students are familiar with like minutes per mile. With that foundation it becomes pretty quick to introduce students to the "find a unit rate and use it to solve" strategy — they've basically been using it already and they've had a bunch of practice with unit rates in different contexts. If I get the beginning right that part goes quickly. Then, we spend a lot of time practicing and applying the big idea to lots of different situations. Slow, then fast, then slow.
When I teach two-step equations the unit begins months beforehand. Students need a strong grasp of one-step equations and I plan a bunch of mini-lessons and spaced practice in the months before we start working on equations. Then when the unit actually begins we spend time practicing one-step equations, solving simple equation word problems, using tape diagrams to represent equations, and talking about inverse operations. It takes time but students get good at all that introductory stuff. All that makes introducing two-step equations and telling the difference between equations like 3x+6=42 and 3(x+6)=42 much easier. Students don’t master these ideas instantly, but it doesn’t take too long to connect the new equations to the work we’ve been doing using inverse operations, working with tape diagrams, and solving one-step equations. After I introduce the big idea we spend lots of time practicing different types of equations and gradually bringing in more negatives and other weird edge cases that trip students up, with a focus on applying the big idea of inverse operations in all these places. Slow, then fast, then slow.
Closing
The reason I think this slow then fast then slow framing is helpful is that in a lot of the worst teaching in my career I did the opposite. I would jump into a new topic too fast, without checking prerequisite knowledge or figuring out what ideas students had that I could build on. Then my teaching crawled as I tried to fill in those gaps or spent forever trying to lead discussions that would help kids discover ideas for themselves. Students would get a few questions right, I would assume they understood everything, and we would move on before they were ready. That was terrible teaching. The words slow and fast don’t describe how my classroom feels. Hopefully if you came in to visit you wouldn’t say “wow this class is moving slowly” or “wow he’s talking really fast right now.” Those modifiers describe the speed compared to what my intuition tells me I should be doing. I always feel like we should be going faster at the start of a unit, but that time is valuable and I need to be patient. If I get that introduction right the teaching of the big idea always goes faster than I think it will. At the end of a unit I typically feel like we should be ready to move on before students are actually ready, and I need to remind myself to be patient and give students lots of chances to practice in lots of different contexts. Slow, then fast, then slow.