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3 ways to prepare for rigorous math learning

With middle schoolers 11 weeks behind where they would be in a ‘normal year,” teachers should focus on the math skills that trip students up.
By Dr. Gene Kerns, Vice President and Chief Academic Officer, Renaissance
November 24th, 2021

With middle schoolers 11 weeks behind where they would be in a ‘normal year,” teachers should focus on the areas that trip students up

While students across all grades have shown growth during the pandemic-related learning disruptions, that growth hasn’t kept pace with what we’d expect to see in a typical year. According to the most recent data, students in grades 2–8 have fallen an average of 11 percentile points below typical year expectations in math.

In terms of instructional time, it will take approximately 11 weeks to make up that lost ground, though it varies widely from grade to grade. Recouping an 11-percentile point drop in 2nd grade, for example, will require an estimated five weeks, while covering a similar drop in 6th grade will take more like 15 weeks.

The issue is that the math skills we expect students to master do not always increase linearly in terms of difficulty. If math standards and skills are a staircase, most of them are short, relatively uniform steps up—but every once in a while, we expect students to take big leaps in understanding and ability.

Here are three ways to help teachers navigate this crucial time in their students’ education and help them prepare for the rigors ahead as efficiently as possible.

Identifying prerequisite skills

All skills and standards are important, but there is probably not a teacher in the nation who has managed to cover every single math standard for their grade in a single year. This year, students will have greater instructional needs than usual, and teachers will likely have to skip over a few more standards than they would in a typical year. So which math skills are must-haves and which are nice-to-haves that can be a lower priority in a pinch?

The truly essential skills are those that are both the most critical at grade level and prerequisites for future learning. Take, for example, the 7th-grade standard “Multiply or divide integers to solve a problem.” This is a critical prerequisite for a deep understanding of numbers and how they’re used to solve real-world problems. It’s also crucial for success in algebra, geometry, and beyond.

“Estimate the solution to a problem involving the multiplication or division of integers” is also an important 7th-grade skill, but the ability to estimate in this way is not a critical prerequisite for future learning. In fact, it’s a skill most students will even pick up on their own as they practice other math skills.

Focusing on the most challenging math skills

Once a standard has been broken down into discrete skills, these skills can be laid out in teachable order, with the prerequisite skills at the beginning and each skill that builds upon them coming next. Generally, each skill is a bit more difficult than the last, but in math especially, every once in a while the difficulty increases greatly. These are the most challenging math skills to teach because they are both fundamentally important to math progression and typically very challenging for students.

In 3rd grade, for example, teachers ask students to find the area of a rectangle. The formula, length times width, is pretty straightforward to an adult mind. To 3rd-graders, however, it can be quite confusing. They’re just getting their heads around multiplication when suddenly they’re asked to apply it in a novel way. They’re used to measuring things, but it’s generally been along one dimension and now there are two. They understand that a foot is a unit of measurement, but now they need to learn how a square foot is different.

That is a tremendous amount of new and somewhat abstract material coming at a child all at once. It’s about as difficult as skills that 6th-graders work on every day, but educators ask 3rd-graders to do it three years earlier because it’s a prerequisite for other important skills that are themselves prerequisites for future learning.

When those students get to 6th grade themselves, for example, they are going to run into another challenge relating to area, but this time it’s not just length times width. They’ll have to find the area of an irregular shape by breaking down its component shapes, finding the area of each of those, and then putting it all back together again.

Students encounter a whole cluster of relatively difficult to learn skills from the end of 6th grade into the beginning of 7th grade. They start working with fractions a lot more and we ask them to convert decimals, for example. Ask any adult the difference between one-third and .33 and they’re likely to tell you they’re equal, but 6th-graders need to know that .33 is just a little bit smaller than one-third.

Honing in on challenging skills that are also must-haves

By focusing energy on finding the best resources and pairing up with fellow educators to identify the best lessons and practices for teaching these difficult math skills, teachers can help their students acquire the must-have skills for the next level of learning most efficiently.

The most challenging skills that are not prerequisites, on the other hand, may be better left to the side for the time being. For example, students tend to struggle with estimation a great deal more than the other skills they learn at the same time, but it isn’t necessary for most skills they will need to learn later. Given all of the pressure on instructional time this year, it’s not a skill to prioritize.

This approach will help teachers understand both what will matter most to their students’ future growth, and their greatest challenges in teaching them.

About the Author:

Dr. Gene Kerns (@GeneKerns) is vice president and chief academic officer at Renaissance. He is a third-generation educator and has served as a public-school teacher, adjunct faculty member, professional development trainer, district supervisor of academic services, and academic advisor at one of the nation’s top edtech companies. He has trained and consulted internationally and is the co-author of three books. He can be reached at gene.kerns@renaissance.com.