To some people there's this Platonic ideal of a lesson where the entire class from the moment students walk in builds toward the objective.
This is one of the questions on an observation tool that my school uses. I bet lots of other schools look at lessons through a similar lens. I've had principals or assistant principals come into my room and comment on whether what we're doing is tied to the lesson goal, or ask me to write my lesson goal on the board every day. All of that comes from this assumption that each lesson should have exactly one goal, and everything that happens should be in service of that goal.
My teaching is moving away from that assumption. I am doing more and more things in a typical lesson that aren't tied to one goal. I do think goals are important, but I think of them differently: each chunk of my lesson — whether it's 5 minutes or 25 minutes — should have a clear goal. But those goals don't need to all connect together. Here are a bunch of possible goals that are separate from "learn today's math concept."
Retrieval practice. My lesson from yesterday or last week could've been perfect, but if I never ask students to retrieve what they learned they are less likely to remember it. Retrieval practice is best in short chunks with a variety of problems. It doesn't fit nicely into a lesson goal but it's an important ingredient in teaching.
Create positive momentum early in a lesson. I want students to participate and share their thinking early in a lesson. One example of that is a routine — I do these right after my retrieval practice Do Now — to get students talking and trying something accessible. I like for these to be short, accessible, and interesting. I pick one routine, do it for a few weeks, then move on to a new one as it gets old. I just finished a round of estimation. I give a quick estimation task, students make an estimate, share with a partner, and then I call on a few students to share their ideas with the class. It’s quick, it’s interesting, and it gets students talking and participating early in the lesson. That’s momentum I can build on, even if the estimation task doesn’t connect to what we do next.
Formative assessment. I don't find exit tickets very helpful. After spending a lesson working on a skill there will be a lot of false positives. I get a better sense of what students understand by doing a check for understanding at the start of the next lesson. These fit together in different ways depending on how yesterday's topic and today's topic connect. Sometimes I do a little check for understanding of something that's not connected to the day's lesson at all. I might do a little reteach right there if necessary, or file it away to follow up on in the future.
Cover for individual followup. Ok so I've done that formative assessment. On some days, in particular for key skills that play a big role in the future, I give students a practice assignment to work on that is pretty accessible and won't require much support from me. While students are working, I check in with students who made mistakes on the formative assessment from a few minutes before, try and figure out where they're hung up, and help them out. If I want to work one-on-one with a few students, I need to keep others busy with a task that isn’t essential to the lesson. I won’t be able to provide much support, and the students I’m working with won’t have as much time to work on it.
Method selection. One unintended consequence of the idea that every lesson should be laser-focused on a clear, specific goal is a lack of mixed practice. A strategy I love is what Craig Barton calls SSDD, or same surface different deep, problems. I do these by writing four problems that look similar on the surface — maybe they use the same numbers or the same context — but require students to use different math for each problem. This type of mixed practice is valuable in helping students to think about which method they should use, and leads to interesting discussions and misconceptions.
Prerequisite skills. There are lots of little skills students need in order to access a given day's lesson. Maybe it's putting negative numbers on number lines to add and subtract with negative integers, or knowing the different inequality symbols before solving inequalities. More and more I spend time checking for understanding and reteaching these skills before the first lesson where they come up. This gives me time. If my little reteach doesn't work I can figure out where the hangup is and do something about it without having to blow up my lesson for the day. I might be assessing and reteaching a quick number line skill while the rest of the lesson focuses on percentages, but that quick reteach will set me up for success in the future.
Stretching skills out. Learning isn't some neat and tidy thing where students learn something in one day and never need to revisit it. I often spend a few minutes of a class previewing a future topic, often by showing how what we're doing that day connects to something they will learn in the future. Similarly, there are often a few loose ends from a previous day that I want to wrap up in a future lesson but don’t take the entire class.
Practice for priority skills. There are a handful of skills that are so essential they require extra practice. For instance, integer addition and subtraction are 7th grade skills that will come up over and over again in the future, and take lots of time to get good at. Do I also care whether students learn complementary angles? Yes, absolutely. But I won’t mix in complementary angles practice every week for the rest of the year. I’ll mix those problems in from time to time, but if that learning doesn’t stick life will go on. I care way more whether students get good at integer addition and subtraction, and I mix it in literally every week for the rest of the year after that unit.
Final Thoughts
I’m not opposed to goals. When I was learning how to teach my program described this thing to avoid called “activity planning” that I still think about. Activity planning means saying to yourself, “oh this activity would be fun” and lesson planning by picking fun activities, rather than putting together a thoughtful sequence with clear goals to help students learn things. Goals are important! I don’t mean to disparage goals or encourage activity planning. I want to point out that there are lots of reasonable goals for a portion of class that aren’t tied to the day’s learning objective. If a teacher plans every class so that everything they do is tied to the day’s objective, they are missing out on a bunch of important aspects of teaching and learning.
Flashbacks to my education professors warning us of the “Taylorization” of teaching — the gradual transformation of a creative human art into a gearwork process ruthlessly
I really appreciate this post!
First of all, thank you for the link to the SSDD problems - I've already found a set that I am planning on incorporating into a future lesson I'm planning for a tutoring student!
Second - this might be fairly obvious, but - I feel like everything that you said underscores yet again, why it would be impossible/impractical/detrimental to keep pushing for teachers to be replaced with AI or purely digital learning platforms. There is so much flexibility and recursive planning that we do that would not be able to be duplicated by an AI platform... which would probably be more purely "goal-focused" on the surface.
Last but not least - in the past five years, one phrase that that I've used a lot when talking about math to my students and colleagues is that math is truly an "open middle" discipline. As in, it is true that there is often *one* correct answer, but there is almost always a multitude of ways to get to that answer. In some cases, perhaps there is a "fastest" method to get to that answer... but the "fastest"doesn't necessarily mean "best" - that the "best" way is ultimately the way that allows you to solve the problem in using a method that is the most efficient and accurate for you. (Also, for my advanced math students, I often want them to be able to solve problems using a multitude of methods!) I've found that this allows students to take the space to explore and actually understand what's happening instead of mimicking a process that they don't really understand. Similarly, there are obviously a set of "goals/understandings" you'd like to reach for your class by the end of the year... but I think there should be a lot of flexibility in the road you take to get there. Sometimes it may seem like you're going "backwards" so to speak, but that might be what the students need to truly understand the next step.