By Emily Freitag

In my last post, I shared that supporting unfinished learning requires complex and unsexy work and that we risk harm when we try to oversimplify the task.

This week, we start a tour of real examples from different disciplines about what it takes to support unfinished learning well. We’ll start with math.

Too often math is treated like a linear sequence of learning or a checklist of skills. What I learned from conversations with math experts and practitioners led me to think about teaching math like helping students build a house. Some walls are load-bearing and need to be strong before moving up a level; other walls can be useful for connections but should not be considered prerequisites.

Let’s trace a fourth-grade math example. Fourth grade has some big and important concepts—multiplication and division of whole numbers, really getting into fraction equivalence—while making connections to geometric shapes and area concepts. There are some load-bearing walls for multiplication and division (things like place value and fluency with addition and subtraction).

So what do teachers really need to do to support this learning?

We worked with several districts this year to test different approaches and found a series of key instructional moves needed in the year-long plan, in the unit plan, and at the lesson level. I’m going to walk through the learnings below, but I also put together a video that you can watch here:

Looking at the year . . .

1. Up front, teachers need a strong understanding of the arc of the year.

2. Teachers need to identify which units/modules focus on this priority content. Student Achievement Partners released helpful priority content guidance to support this identification. For example, in the fourth-grade EngageNY units, modules 1, 3, 5, and 6 contain more than 50% priority content:

Example of a table of EngageNY modules with priority standards highlighted.

3. Teachers need to create MORE time in the units/modules with priority content to support unfinished learning. They do this by looking at where other units can be streamlined. For example, teachers need more time for module 3 (multiplication/division) and module 5 (fractions). This time can be found by merging lessons in modules 2 (metric conversions) and 6 (decimals).

Table organizing modules between "Greater than 50% focus on the major work of the grade" and "Less than 50% focused on the major work of the grade"

Looking at a unit/module . . .

4. Teachers need to understand the story of the unit/module. For example, module 1 of fourth-grade math in EngageNY focuses on addition and subtraction with whole numbers.

5. Teachers need to understand the load-bearing walls for the grade-level standards in that unit/module. To be ready for module 1, students need an understanding of how to add and subtract using place value and some key problem-solving strategies (e.g., how to use a number line).

Example of a table identifying foundational standards in EngageNY modules.

6. Teachers need to develop/select pre-unit assessment questions aligned to those load-bearing standards. This is not a pre-test/post-test, but rather a couple of targeted, open-ended questions on the prerequisite load-bearing walls.

Criteria for success Conceptual understanding: Rounding numbers Adding and subtracting using place value operations Problem-solving strategy: Vertical number line Tape diagram (strip)

Moving into the unit/module . . .

7. Teachers need to review student work from the pre-unit assessment. This shows them which load-bearing concepts and strategies students know and which will need support in order for students to be able to access the grade-level content.

Example of a flow chart students can use to review student work from the pre-unit assessment

8. If students need support to access the grade-level content, teachers can plan to use the extra time they already created to support access. This can be done with a bridge task, a mini lesson, or a full lesson (for example, find the third-grade lesson on the key load-bearing concept and teach it the day before).

Bridge task: Data reflect evidence that the class has access to the conceptual understanding necessary to access the grade-level concept. Mini-lesson: Data reflect limited evidence that the class has access to the conceptual understanding necessary to access the grade-level concept. Full lesson: Data reflect no evidence the class has access to the conceptual understanding necessary to access the grade-level concept.

What you do NOT see in this approach is a full unit of third-grade learning before starting fourth-grade work. In mathematics, unfinished learning is better supported when embedded within the relevant grade-level units.

Complex? Yes. Impossible? No.

This is the work good teaching always requires. It takes time and focus and patience to prepare for the year and prepare for each unit/module.

Here are the resources we used in this example:

Instruction Partners will be testing additional support approaches, especially within the unit launch, this summer and throughout next year, and we will share as we go. (If you or someone you know wants to sign up for these resources, click here.)

And remember: What works in math does not necessarily apply to other disciplines.

Up next: science.

Credit where credit is due: This work was driven by Instruction Partners team members Cammie Mabry, Melissa Chipman, Molly Shields, Rebecca Few, Julia Dezen, Carla Seeger, and Kelsey Hendricks.