Here’s a statement that I expect some folks will disagree with.
I don’t believe that students necessarily learn better when they figure things out for themselves.
To clarify, I’m not trying to argue that kids shouldn’t have a chance to figure things out, or that it’s inherently bad. Just that, in and of itself, student discovery is not a particular priority for me. Some reasons:
Cognitive Load Theory
Cognitive Load Theory is fascinating to me. It’s also interpreted lots of different ways. Fundamentally, it says that while trying to figure something out, working memory resources are consumed in such a way that it is difficult to move information to long term memory. I’ve definitely seen this happen. Kids spend a great deal of effort searching for a possible solution to a problem and meet various dead ends along the way. By the time they reach a viable strategy, much of their thinking has been spent at cross purposes with the goal of the lesson. That realization they make at the end is just one synapse firing over a long lesson and isn’t particularly durable.
I’m skeptical this is the case in every instance, and I think there’s a lot more subtlety to things than “increased cognitive load of discovery = bad”. But it’s something important to think about — in the words of Ben Blum-Smith, “any thoughtful teacher with any experience has seen students get overwhelmed by the demands of a problem and lose the forest for the trees”.
How much does one activity matter?
I tried hard to create powerful discovery experiences early in my career. An implicit belief embedded in that instruction was the idea that, if I could just find the perfect way to introduce students to an idea, they would remember it and be able to apply it in the future. At best I had mixed success. One activity, no matter how clever it is, never makes as much of a difference as I might think. The sum of student experiences — from the introduction of an idea, through practice activities, to opportunities to transfer that understanding to new contexts — are what make a difference for learning. I’m much more interested in focusing my energy on a range of activities that allow students to practice and extend the ideas we’re learning about than putting all my eggs in the “they discovered it so they’ll remember it” basket. Here’s my core value: it matters less how a student figures our something new than what they do with that knowledge in the future.
I do still use discovery-oriented activities. Here are two goals I have that this type of lesson can effectively support.
One idea that pushes back against an aspect of Cognitive Load Theory is the generation effect. In short, trying to figure something out before learning it leads to more durable learning. I want learning to be active for students whenever possible. I want to avoid overwhelming them, but I prefer active tasks whenever possible, and if the task is within students’ reach, I’m likely to use it. In addition, I want to create some intellectual need for what students are going to learn. If struggling with a problem makes students aware of what they don’t know and what that knowledge might be useful for, they are well-positioned for future learning.
Neither of these strategies requires that students actually reach the big ideas of a lesson on their own or struggle for a great deal of time; they just argue that attempting to do so to begin a lesson can lead to more durable learning. And, in both cases, the sequence ends with an opportunity to make the learning explicit and consolidate understanding. That explicit instruction doesn’t have to come from me. One way I often do this is to use group work to provide opportunities for students to share strategies, and lead into a full-class discussion sharing those strategies and consolidating the big ideas that students need to move forward. That discussion can be largely student driven. But the consolidation is essential; it’s incredibly rare for me to see every student figure something out in a discovery lesson. And, honoring the principles of Cognitive Load Theory, even if many students figure something out on their own, further clarification and exposure beyond a discovery activity is essential to further cement their understanding.
I love doing math because of the joy of learning something new through discovery. This doesn’t mean that students necessarily feel the same way or learn best that way. But it does mean I want students to have the opportunity to experience the wonder and joy of mathematics. Even if creating these experiences is an inefficient use of class time or leads to less learning, it’s a priority for me. Not every day and often not every week, either. Being judicious with how often I use these activities allows me to focus on the ones I do and do them right. And watching a student light up when they have that moment of insight is a special thing to see and a special thing to experience.
Conditions for Discovery
- A discovery activity should either focus on an incremental, manageable step forward or something so mathematically spectacular that it is worth significant effort
- I must be willing to cut an activity short if it’s clear we’re hitting a dead end
- An activity has to end with time spent consolidating understanding, either student driven or teacher driven
- I won’t choose a discovery activity at the expense of time spent on practice activities that allow students to deepen their understanding, and allow me to see who understands and who doesn’t and adjust future instruction appropriately
I don’t mean to get too down on discovery. Instead, I want to clarify more specific and concrete goals than “students figure things out themselves”. For me, the goals of intellectual need and wonder are worth working toward, and are much more connected to experiences and outcomes I care about than discovery for its own sake.