Something I’ve been thinking about for the last year is whether or not learning should be easy. I can think of times when I learned a great deal and it didn’t feel difficult at all. I can think of other times that learning was difficult and I didn’t feel like I learned very much. These are a few of the questions that bounce through my mind.
- Is there some kind of payoff for learning something that is difficult to learn, beyond simply the thing you learned?
- Is everything we learn ultimately worth learning, regardless of how difficult it was to learn?
- If we teach things that are consistently difficult to learn then how do make sure those learning experiences end up being valuable?
I try to think about these questions from my students’ perspective. For instance, I dragged my extended (slow pace) algebra II students through a unit on quadratics. Realistically speaking my students were never going to use most of the mathematical concepts that we covered, at least not directly. So why do we teach them these things that are so difficult for many of them to learn (especially at a conceptual level)? Or maybe a better question is what do we tell them about learning when we teach them concepts they’ll never use and find difficult? What message are we sending about learning? A lot of algebra II (a requirement for every student in the state of Michigan) is an absolute struggle for many students, so how do we make this struggle meaningful?
In my mind we have a couple of options. The first option is to try to reduce the curriculum to it’s simplest form. We give the students the tricks, shortcuts, calculator programs, and everything we can to get them to put the correct answer in the blank on the assessments. This way we can get as many kids through the curriculum as painlessly as possible. This method is fairly attractive and I know I’ve been guilty of it on several occasions. The glaring problem with it is that we are essentially wasting the students’ time. We are not creating opportunities for them to think critically or grow as learners (not to mention how this destroys the beauty of mathematics). Also, it’s been my experience that students don’t retain the concepts over the long term.
With this, I often consider another path. Maybe instead we take an approach that encourages critical and independent thinking. A model that allows students to construct the concepts within learning experiences that, although seemingly more difficult, allows them to grow as learners and mathematical thinkers. This route is more difficult for a number of reasons. First, developing these kinds of tasks is difficult. (Although, to be fair, it is getting easier. Consider the MTBOS search engine this list of Common Core aligned problem based curriculum maps or the power of online professional learning networks.) Second, students hate it. (Okay, maybe hate’s a strong word, maybe it’s not every student, and I think the culture of the classroom can make them hate it less, but I’ll have more on that in another post.) In addition, there is a concern that we won’t get through all the content. If you teach in trimesters, where a student might have a different teacher from trimester to trimester, this becomes especially important. From a teacher’s perspective this option can seem daunting. We are going to take kids that already (probably) don’t like a subject partially because they find it difficult and then we make it more difficult for them. For many educators this choice is simple. Go for option number one.
I would add one note about the second option. We wouldn’t be making the content more difficult because we are evil. We’d be trying to create valuable struggle. The idea would be that we help them build the concepts so students would be doing more thinking during class and the teacher would stop giving away the interesting stuff so frequently.
I think most educators, given infinite time and patience, would pick the second option to implement. So the big question becomes:
If the second option is more difficult for both the student and the teacher, does the payoff (if there is any) outweigh the difficulties in implementing it?
To be honest with you I don’t know the answer. My idealism pulls me hard towards the second option but my practicality pulls me in the other direction. Also, not having infinite time and patience is a big factor. I apologize if this post doesn’t feel like it has a resolution. It doesn’t, because I don’t. However I’d love if it started a conversation. I think this is something that all math teachers and departments should be having an open discussion about.