We are continuing our series of posts by Beth Guadagni, who shares the strategies she uses in her Colorado classroom. Today, she looks at how she uses interleaving to help students maintain math mastery.
To help students retain math procedures they’ve already learned.
Math problems from previously studied units
I put together review sheets that students complete a few times a week. A simpler approach would be to flip backward in a textbook, choose a few pages at random, and do a problem from each section. Note that students should have a way to check their answers* if they’re going to tackle this independently.
Why This Works:
Like many students, my group generally does a good job of performing newly learned procedures once they’ve had some practice. Performing that procedure a few weeks or months down the road is a different story. To combat this, I use interleaving, one of Dr. Yellin’s most useful and widely applicable strategies.
One thing we know about memory is that we’re able to store a lot more things than we’re able to find easily, rather like a very large, disorganized closet. Brains are good at keeping thought processes efficient, and so information that we have to access often is stored in a place that makes it easier to find. Information we don’t need often, however, takes a lot longer to find, and sometimes we can’t find it at all. Here in Colorado, my students spend a lot of time enjoying the outdoors, so I use a trail analogy to explain this to them. A pathway that is traveled often is well worn, making easy to find and follow. You can hike faster along a trail that’s been traveled a lot, just like one’s brain can quickly find information that has to be accessed frequently. A less popular trail, though, like a seldom-referenced memory, is much more challenging. You might lose it altogether, and if you can follow it, your progress is going to be slowed by rocks and overgrown plants.
Back to math: Constantly circling back to concepts we covered earlier in the year causes my students continually access procedures they’ve stored in their long-term memories, communicating to their brains that this information is important and so the pathways to it need to be efficient. My students complete only a problem or two from each past unit of study at a time, and we spend only five to ten minutes reviewing every few days. This small investment pays off in a big way, though; when I graded their math finals at the end of the last semester, I was pleased to see that they recalled concepts from August just as well as the ones they’d learned in mid-December.
*See our previous post on Photomath, a free app that uses smartphone cameras to scan and solve math problems.
Photo by Matt Gross on Unsplash