Part 2 of Math Intervention Strategies

Addressing unfinished learning in the context of grade-level work

Not all unfinished learning should be treated the same way

As a teacher, I had an understanding of the grade-level math content I was supposed to teach and the belief that students’ new learning had to build from their prior understanding. But the harsh reality was that most of the students in my class were several years below grade level, and I only had one school year to try to catch them up.  At the time, I felt like I had to choose between two pathways — to move forward with grade-level work despite students’ gaps or halt grade-level instruction to build prerequisite knowledge.

Neither of these would provide equitable learning for my students.

In my current role as Director of Math Professional Learning at the Achievement Network (ANet), I’ve learned that I wasn’t the only teacher facing this challenge.  In fact, it’s one of the most widespread challenges we hear from our school partners.  And that’s why I’ve partnered with Astrid Fossum from Student Achievement Partners (SAP) over the past year to think more about what it means to address students’ unfinished learning in the context of grade-level work.

What is unfinished learning?

Unfinished learning refers to any prerequisite knowledge or skills that students need for future work that they don’t have yet.  Previously, I’ve used the term gap or weakness to mean the same thing, but I prefer unfinished learning because it seems to inspire action rather than focusing on student deficits.

Not all unfinished learning has the same effect on students’ ability to access grade-level content.  In some cases, it will simply require more time or effort from students, similar to how road construction affects travel.

For example, a student who is not yet fluent with multiplication (5.NBT.B.5) may need more time or support when solving real-world and mathematical problems involving area, surface area, and volume (6.G.A), but should still be given an opportunity to engage with these types of grade-level problems.

This idea may be counterintuitive at first.  Given the coherent nature of mathematics, I used to think that students couldn’t engage in grade-level work until they’d built all prerequisite skills.  But now I see it differently — as an opportunity to help students “plug holes” or strengthen understanding.

The bridge is up!

On the other hand, there may be situations that require prerequisite knowledge for entry into a lesson or task.  For example, a 7th grader needs to understand the concept of a ratio (6.RP.A.1) in order to analyze proportional relationships and use them to solve real-world and mathematical problems (7.RP.A).  In a case where students lack the former, a teacher may insert one or more lessons to address the gap before moving into grade-level content.

To build on our driving analogy from earlier, we could use the example of a drawbridge being “up,” not allowing cars to pass until it is closed.  In these cases, teachers will need to “close the bridge” before moving ahead with grade-level content so students can access new material in a meaningful way.

Over the past year, I’ve had a chance to explore examples of unfinished learning alongside teachers, and I’ve been surprised to see that cases where lack of the most critical prerequisite understanding actually prevents access to grade-level content are rare.  Instead, far more common are situations where students can both engage in grade-level content and fill gaps simultaneously.

Given this, and the pacing challenges that arise when teachers halt grade-level instruction to teach content from prior grades, I’d encourage teachers to ask, “Is the bridge truly up?” before deciding how to support students.

The flowchart above summarizes an approach you can take to identify and address students’ unfinished learning when planning upcoming lessons or units.  You may enter into this approach at different points, depending on when student gaps are identified, and you will likely cycle between the steps as you work with students, as the double arrows suggest.

As you work to understand the demands of the standards, it may be helpful to try solving problems that align to each standard yourself to help you anticipate areas where students may get stuck and to identify the most critical prerequisite knowledge.  Additionally, the Coherence Map is a helpful tool to understand the progression of learning leading up to grade-level content, as illustrated on page 2 of this 5th grade example.

When possible, use data you already have to diagnose student understanding in order to save yourself time and avoid over-testing students.  See what you can learn from classroom discussion, one-on-one conversations, and written work students complete as part of everyday instruction.  If more information is needed, you may decide to administer a pre-assessment. Page 3 of this 6th grade example shows one teacher’s approach to diagnosing student understanding.

Let the data be your guide as you take action – with whom, when, and on what?  Pages 4-6 of this 8th grade example show one teacher’s approach.  During this phase, it’s important that students understand how the extra support connects to their own grade-level content.  One teacher shared that she posts grade-level problems on the board at the beginning of instruction, explaining that they will return to them after brushing up on a few skills.

There are no silver bullets

As I’ve looked into this topic over the past few years, I’ve realized that there are no silver bullets.  There is no one program or solution to catching kids up who are several years behind.  Instead, it takes deep content knowledge, increased time, and strategic planning to meet students where they are and accelerate their path forward.

While the 3-step approach Understand-Diagnose-Take Action will not magically “finish” students’ unfinished learning,  it can provide some structure to a challenge many teachers continue to face in the classroom.  Reactions to the approach have been positive, and we’ve seen some early successes from teachers who have used it.  If you’re a teacher working to address unfinished learning in the context of grade-level work, please share your ideas and examples by sending us an email or Tweeting at us: @achievethecore and @AchievementNet!

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About the Author: Chrissy Allison is the Director of Math Professional Learning at The Achievement Network (ANet) where she supports teachers, leaders, and ANet coaches to implement strong standards-aligned instruction in math. As a former middle school math teacher and instructional coach in Chicago's Little Village, Englewood, and Auburn-Gresham neighborhoods, Chrissy was drawn to ANet's core value of Advance Equity and the opportunity to bring educators together to learn from one another. Chrissy resides in Chicago with her husband, Dan, and two children, Liviana and Otto.