In mathematics, the coherence of the standards helps. The standards tell the story of mathematics, following a progression of concepts and procedures across grade levels. If teachers know the story, then they know how to work with students who have missed part of it. They don’t have to go back to where the story left off and go through it again. Instead, teachers can identify prior grade-level dependencies for each standards-based curriculum unit and, if needed, add lessons just in time in a coherent manner throughout the year. To balance the number of school days, they can analyze each unit to identify lessons that can be adjusted, combined, or skipped.

2. Use assessments meaningfully, yet sparingly, to make instructional decisions.

Assessment is important, but deciding how and how much to assess is a struggle, even in a typical school year. It would be inefficient to teach everything that was missed in the previous grade before starting grade-level work. Similarly, if too much time is spent administering formal assessments, valuable instructional time is lost. Often, it makes more sense to wait until students are approaching a unit to visit the material they will need to understand those concepts.

One advantage of waiting to introduce ideas from missed learning is a greater opportunity to get to know students and their needs — without over-testing. Embedded formative assessments and a focus on student-generated solutions should illuminate what students need. For example, a unit diagnostic can check student readiness and provide information about where it is necessary to weave in material from earlier units or courses. That way, any remediation can serve in accessing the grade-level topic.

When giving students just-in-time content, it can also be helpful to insert small formative assessments along the way. This allows teachers to build on what students know while moving forward with grade-level material. For example, using a formative mini-assessment — one or two math problems after a lesson as a cool-down — teachers can check in and support students’ learning toward the grade-level standards, and determine if they will be able to engage in the beginning lessons of the next section in a unit.

3. Integrate practice and review into the teaching of current grade-level content.

Tackling unfinished learning in mathematics

After a formative assessment or mini-assessment, there may be students who need extra practice with the knowledge and skills covered in the previous unit or previous grade level. Yet, students will never get through their current material if they are continually stopping to relearn prior material. To keep the learning going, teachers can leverage the coherence of the standards to align and integrate targeted practice into the current grade-level unit. When teachers and students are using a mathematics curriculum that develops concepts and representations coherently along a mathematical progression — again, like telling a story — it becomes much easier to integrate practice from prior units or grade levels directly into current lessons, without disrupting them.

To support students in feeling confident and successful after they have experienced so much recent change and uncertainty, it is critical to ensure they are building on their current understandings as they progress through grade-level content — and in a way that is inviting and safe. Without student engagement in the learning experience, no amount of testing or technology will help.

About the Author:

Dr. William G. McCallum is a Distinguished University Professor Emeritus of Mathematics, one of the lead writers for the Common Core State Standards in Mathematics, and the co-founder and CEO of the nonprofit organization Illustrative Mathematics (IM). Kate Nowak is the vice president of product strategy, Kristin Gray is the director of K–5 curriculum and professional learning, Kevin Liner is a K–5 professional learning lead, and David Petersen is a lead curriculum writer for IM. IM is the developer of IM Math, a problem-based core mathematics curriculum for grades K–12.

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