3 Ways Instructional Materials Help to Address Unfinished Learning in Math

This article was originally published on the Thomas B. Fordham Flypaper blog. 

A few months ago, I wrote an article about COVID-19 learning loss and the many ways that our instructional materials can (and should) support us as we try to accelerate learning for all students.

As an educator and a parent, I know that mathematics teachers are still facing unprecedented difficulties, especially when it comes to unfinished learning. Today, I’m thinking about the obstacles in educators’ paths as we try to bring our students up to speed and how we can rise above those obstacles.

For the most part, districts have figured out the logistics of remote schooling—how and where to meet online, which learning management systems to use, etc.—but they haven’t fully addressed the instructional core (students, teachers, and content) within the classroom. Until all students have access to the aligned, quality materials that can help accelerate the learning of grade-level content, teachers will continue to be asked to do an impossible job without the resources they need and deserve.

Key Obstacles in the Remote Mathematics Classroom

I know personally that there are myriad challenges when it comes to keeping students focused in an online environment. Obstacles I’ve encountered include, but are not limited to:

• Disruptions in Routine: One of the primary obstacles for educators and students right now is the disruption to regular school routines, which of course leads to disruption in learning. Teachers and schools had to make a rapid transition to remote learning in spring 2020, often without the necessary resources, and those disruptions continued well into the 2020–21 school year.
  
  
• Lack of Peer Interaction and individual attention: Students are missing opportunities to interact and work with their peers. Because of the quick switch to online learning, most students aren’t getting open-ended math tasks to work on, or the chance to work through problems and develop conceptual understanding of the content. What’s more, students may not be receiving individual attention or be exposed to materials that offer scaffolding and differentiation opportunities.
  
  
• Incoherent materials: In terms of materials, many schools lack coherent resources across all grade levels for mathematics teachers. Given the massive disruption of the regular school routine, there’s no guarantee that students have been exposed to continuous coherent instruction from one grade to the next. Even if students are back in classrooms full time, they will bring with them the unfinished learning of previous months, and teachers are at a disadvantage to accelerate current learning if they do not have aligned, coherent materials.

All Students are at Risk for Unfinished Learning

First thing’s first: What is unfinished learning? Simply put, teachers expect incoming students to know certain standards based on the previously completed grade levels. When a student within that group does not know all the standards from previous grade levels, they have not finished their learning.

Unfinished learning is a problem at any age and at any grade level. Some grades might see a bit more of a struggle because they include introduction of major topics. In third grade, for example, students are formally introduced to fractions, which is a major foundational piece for much of the mathematics that follows. If a student does not grasp fractions, they will likely struggle with concepts moving forward.

But what we know is that unfinished learning can happen at any time, even if we’re most aware of it in the transitions from elementary to middle school or middle to high school. And, as we’ve seen, unfinished learning is an issue now more than ever due to the impact of the COVID-19 pandemic.

How Materials Help Accelerate Learning

As teachers continue to figure out how to support students in hybrid and remote environments, many of them are creating their own materials or sourcing them piecemeal from unvetted sites such as TeachersPayTeachers and Pinterest. This practice often leads to a glaring lack of standards alignment and coherence for their own grade—let alone across grade levels. To find and address unfinished learning, mathematics teachers need high-quality, aligned instructional materials.

Coherence is critical for accelerating learning of grade-level content and addressing unfinished learning. Quality instructional materials offer a range of supports for teachers at the classroom level to do just this.

1. Quality materials support teachers in understanding and identifying the academic standards that previous grade levels are built on. To begin to address unfinished learning, it is critical to understand the concepts and skills from previous grades as these will be the same concepts the current grade will be expanding on.
   
   
2. Quality materials can help to identify where students have unfinished learning through curriculum-embedded, formative assessments. Formative assessments built into the curriculum are great tools for teachers and can contribute to addressing unfinished learning in two ways. First, formative assessments, especially those often given at the beginning of a unit, can look at prior, grade-level standards to see what students already know. In addition, assessments should be ongoing to capture current learning in real time. As students begin to learn on-grade-level content, the best assessments are designed to be attentive to evaluating current standards and the previous standards the new learning is built on. For example, if third graders are being introduced to fractions for the first time, assessments should consider both the third-grade standards as well as the relevant K–2 standards that have led to the introduction of fractions. This allows teachers to see exactly where the gaps are if students are struggling.
   
   
3.  Quality materials offer clear supports for teachers to determine potential misconceptions and strategies for differentiation. Aligned, coherent materials provide teachers with specific resources and supports to identify and begin to address unfinished learning from the previous grade, diagnose where students are struggling in the current grade, and to accelerate learning so students can catch up. Quality materials offer suggestions for follow-up around assessment results, rubrics for grading, and help in identifying misconceptions students have.

What’s more, we know that students are individuals, and a one-size fits all approach does not work. Materials should provide strategies for sequencing and scaffolding lessons in order to meet the needs of a range of learners. As materials are considered, it’s important to assess the explicit supports teachers are given to differentiate grade-level content so all students have access.

Closing the Gap With Coherent Mathematics Materials

Instructional materials are not a silver bullet. However, materials can be a way to help overcome the challenges of unfinished learning as well as additional obstacles the COVID-19 pandemic has exacerbated such as disruption in the classroom, lack of manipulatives, and lack of opportunities for differentiation. Ensuring teachers have access to, and training on, high-quality coherent materials is an essential step to setting up students for success now and long after the pandemic comes to an end.