I was recently asked, “what happens after a problem based lesson? Don’t we need to practice the skills we just used? And learn how to apply them in different scenarios?” The answer is, of course, a resounding “yes.” No one experiences something one time and has immediately learned it permanently. Humans need to experience things multiple times in the same and in varying circumstances in order to fully understand a topic. To use a tortured analogy, coaches don’t give their players the playbook and then call it a day. They hone their skills with a bunch of practice. Now, sometimes that practice can kill the joy of the sport and that’s where we need to be mindful; but in order to learn something fully, practice is essential.
While I don’t feel that’s a controversial statement, I wonder – when I hear such questions – if teachers are operating from a position of fear: fear of not being hip enough, reform-y enough, growth-mindset-y enough, innovative enough. Skills practice can seem so retrograde. The entirely appropriate reaction against “minute math” and “tricks” might scare teachers off of skills practice entirely. And this fear might be enhanced from the messaging and professional development offered by the district. District PD is often focused on more authenticity and bigger thinking. It’s rare that a district PD (either led by district employees or consultants) focus on the smaller things. You’re not often going to attend professional development that helps you better structure individual or group skills practice time. You may have even received the message that that’s not a good use of class time. Consider this post – not that I have any authority – permission to practice.
There are legit concerns about how practice time looks in… practice. Having students silently complete dozens of problems individually, followed by a right-or-wrong assessment isn’t particularly good instruction. And I’m not convinced that that scenario results in the more permanent learning we’re after.
So what does the time after a problem based lesson look like to ensure deep understanding? Here are a few options:
Offer another, follow-up task incorporating similar concepts to groups with less scaffolding. If you designed your problem based lesson from, say, the Application Problem section of a textbook (a practice a highly recommend), consider grabbing another problem in that same section. You can even apply similar adaptation methods, including audiblizing.
Practice problems, even in packet form. There’s nothing inherently wrong with practice problems. These can actually be nice times for students to collaborate on smaller, bite sized tasks. Students can support one another, give pointers, and develop camaraderie by working through practice problems together. Provided your classroom has the requisite culture of uplifting one another, use this time to boost understanding. I would recommend structuring the practice problem time so it’s not a free-for-all.
Another benefit of using this semi-structured time for practice is that you can naturally differentiate via the workshop model. In this model, you can pull out specific students to become the “expert” for any tricky problems.
Use a card sort. Card sorts are among my favorite methods to develop conceptual understanding. A tactile matching activity – even though it really is just a glorified version of a set of practice problems – engenders natural conversation and checking one another’s’ work. The downside is card sorts are a bit of a pain to prepare for. The Desmos card sorts help with that aspect, but I find that digital card sorts don’t have the same energy that tactile ones do (that might be my own Old-Man-Yells-At-Cloud bias though).
I recommend you also check out my friend Kevin’s blog post on what to do during student work time. While that blog post is centered on what happens during the work time of a Project Based experience, many of the same practices can apply to time spent honing skills.
It might also help you conceptualize the classroom time by running through my mini-series on Routines, Lessons, Problems and Projects. There I attempted to develop a framework of what type of mathematical teaching happens in a classroom to better understand the balance between teaching, facilitating, letting students innovate, etc.
In a typical week in which we meet with students all five days, I might spend two days on a Problem Based Lesson and the remainder reinforcing what I had hoped to get across during that lesson or preparing for the next one. According to my calculations, that means I spend over half my time in what some might dub teaching “traditionally.” Personally, I’d call it more “psuedo-traditional” because even within those days in which I’m lecturing or providing time for practice, I’m trying to employ learner centered facilitation moves, both long term and short term.
I’m trying to demonstrate active caring, even when students are working through a problem set. And at this point the traditional vs. non-traditional distinction is meaningless. Students are learning math in a safe, supportive environment, hopefully applying the lessons learned from our problem based experience. And if an administrator or district person gives you guff about it (especially if they’ve never taught mathematics), send ‘em my way.
emergent math 