“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.
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