Supporting Incomplete Math Learning in the General Education Classroom

As students have returned to school in the fall of 2021, we are recognizing the variety of ways in which students have been impacted by the pandemic. One commonplace issue surrounds students’ incomplete learning of grade-level mathematics standards over the past year and half. The following brief has some recommendations for supporting students with incomplete math learning in the general education classroom.

Recommendation #1: Stick to grade level standards.

Educators may be naturally inclined to try to identify the mathematics from prior grade levels where students have ‘holes’ in their understanding, and to start instruction here. We call this just-in-case instruction. In the general education classroom, we recommend starting instruction with grade level standards and scaffolding back to areas of incomplete learning. We call this just-in-time instruction. 

Recommendation #2: Use just-in-time instruction to catch up on incomplete knowledge.

Just-in-time instruction can mean a brief review of math content from previous grade-levels or units just prior to teaching a grade-level lesson. Below we have an example of a task that addresses the Grade 6 Domain: Apply and extend previous understandings of numbers to the system of rational numbers that relies on students’ understanding of several concepts from previous grades.

A grade 6 teacher using just-in-time instruction would recognize the likelihood that students may need a quick review of understanding fractions, decimals, and/or integers from a visual perspective prior to engaging with the task.

Recommendation #3: Use visual models to frame instruction around just-in-time learning.

Visual models of mathematics (e.g., bar models, area models, number lines, etc.) are especially useful in helping  students make meaningful connections, particularly in situations where their learning may be incomplete or procedural. For example, for the task above the following two mini-tasks could be used to review understandings for some of the concepts embedded within this original task.

Once students have engaged in these two tasks with visual models, they will be primed to think about how to meaningfully engage in the original Ordering Rational Numbers task. This intentional use of just-in-time instruction to assist students is an excellent strategy to address incomplete learning from the pandemic —and the usefulness of the strategy extends well beyond.

A few items to note, 

• If a significant amount of just-in-time instruction needs to occur throughout the year, it may be necessary to consider systematically (not at the individual teacher level) prioritizing standards and paring down the content teachers are required to address within a year.

• For some students, additional instructional time and resources may be required to address their incomplete learning. 

• Identifying incomplete learning is a complex task that requires multiple data sources, including high-quality classroom formative assessments in conjunction with summative assessment data.

These items and others will be the focus of future posts. Please comment below with additional thoughts and questions.

Several of the ideas from this blog are borrowed from Addressing Unfinished Learning after COVID-19 School Closures from the Council for Great City Schools. We highly recommend you read it for more information.

By Michele Carney @ Boise State University

The Math Education Collective (MEC) at Boise State University is focused on providing high-quality mathematics education resources and services in partnership with Idaho’s school districts.