This blog post was originally published on Mindful Math Coach, which aims to support secondary math educators to provide equitable learning experiences for students of color, leading to equitable outcomes. The site offers a variety of free resources for educators such as The Mindful Math Podcast, videos, and guides for educators to use in classrooms.
“My kids can’t do that!” How do you respond when teachers say this in regard to grade-level math work? Teaching grade-level content when students have significant unfinished learning is a tricky topic, at best. Back in 2016, I spent hours solving problems and making lists of prerequisite skills students would need to solve those problems from start to finish. The lists were long— very, very long—and at first, a little daunting.
But then I had an aha moment: I realized that I was asking the wrong question. Instead of asking what skills and understanding students needed to be able to complete a task correctly, I should have been asking, “What is the minimum students need to be able to enter into the task and engage in the problem-solving process in a meaningful way?” And when I say “minimum,” I’m talking about the most critical prerequisite skills and understanding. When I asked the question this way, the list became much, much smaller. I was able to pare it down, and it felt way more manageable.
So, at the end of this investigation, I must admit that I was a little surprised by what I had discovered. I’d gone into the exercise under the assumption that most of the middle school tasks would be impossible for students to do without intervention from the teacher ahead of time. It simply wasn’t true, especially if you ask the right question.
Since that time back in fall of 2016 when I decided to really dig into the topic of unfinished learning, I’ve continued exploring and experimenting with ways to increase accessibility to grade-level tasks using somewhat of an “action research” approach.
First, I partnered with Astrid Fossum, Senior Mathematics Specialist at Student Achievement Partners, to investigate the topic. We spent over a year in deep discussion, comparing notes and brainstorming the most common pitfalls we’d seen schools fall into when it comes to math intervention. We identified alternatives that align to the Math Shifts of focus, coherence, and rigor. And we’ve shared them publicly through Achieve the Core’s Aligned blog, in newsletters, and at several conferences, including the National Council of Supervisors of Mathematics Conference in Spring of 2018. Here are links to the blog posts in case you want to check them out:
- Designing Shifts-Aligned Interventions in the Math Classroom
- Addressing Unfinished Learning in the Context of Grade-Level Work
After that, I started working with a handful of teachers and math coaches one-on-one to help increase students’ access to grade-level math in the face of significant unfinished learning. Together, we learned which approaches increased accessibility, engagement, and understanding and which ones didn’t. We saw students get excited about the problem that was presented to them and engage in ways they hadn’t before – and this was noted by both teachers and leaders. I’d like to share a few ideas that have come from that work:
1. “Is the bridge really up?”
I like to use an analogy of a drawbridge to describe the degree to which unfinished learning affects access to grade-level content. Imagine you are trying to cross a drawbridge and there is heavy traffic or construction. What will happen? Can you get across? Sure, it’s just that your speed will be a bit slower. However, what if the drawbridge was up to let a boat cross? Different scenario, right? The takeaway? Not all unfinished learning has the same impact on students’ ability to engage in the task. Sometimes it will be like traffic or construction and cause the students or the teacher or the lesson to slow down. Other times, the “bridge will be up” and you’ll need to hold on and wait until the bridge is down before you proceed across. So, here’s the first of two great questions to ask when you’re planning for unfinished learning. When you consider what students are “missing” from previous grades, does it cause the “bridge” to be up? When you do this, I bet you’ll see for yourself what I saw – that “the bridge isn’t up” nearly as often as we might think.
2. “What can I do to ensure all of my students have entry into the task?”
This one is related to the phrase I mentioned earlier that I hope we can strip out of our language once and for all: “My kids can’t do that.” Oftentimes when teachers say this, what they really mean is, “I don’t have confidence that all of my students will be able to complete the entire task by themselves with 100 percent accuracy.” That’s probably true with any class of students! The problem is that this is the wrong question to ask on the front end of a learning task. Sure, you want all students to solve rigorous problems accurately and independently by the time the state summative rolls around, but that’s a completely different situation than a math task that you’re using as part of the learning experience. Instead, let’s ask, “What can I do to ensure all of my students have entry into the task?”
In other words, how can you design or launch or scaffold the task in a way where all of your students can make sense of the task and begin exploring a solution pathway of their choosing? What can you do to open the door for students to engage in the task, and to welcome them in?
Remember that we’re trying to decide what the most essential skills and understandings are—the most critical prerequisites students need—in order to access the task, not solve it with 100 percent proficiency by themselves, the first time through.
One tip I’ll offer is that it’s worth taking time to solve the task yourself as part of the planning process. Solve it and list out the skills and understandings students need, then identify which ones truly need to be in place before students can begin the problem versus the ones that can be folded in during work time or the discussion that follows.
3. The two implications of access.
Teachers and school or district leaders tend to have varying perspectives about the challenge of supporting unfinished learning. We have to take into account both implications of “access.” First, students need access to grade-level content, meaning that they need consistent opportunities to engage in grade-level work. This should be the focus of the majority of instructional time. Second, we must support students to access the content, meaning we need to make sure students have an entry point into the task, and that you as a teacher have ensured there is an “accessibility bridge” in place if necessary.