Teachers face unprecedented challenges in accelerating students’ math learning since the pandemic, and teacher trainer Christina Tondevold said the stress can make it harder for teachers to plan ways to fill students’ learning gaps without resorting to rote drills.
“It is a huge, huge concern that kids are falling behind. We feel like we’ve got to catch them up, but there’s so much [to make up] that we actually need to slow down and make sure that there’s a solid foundation there,” said Tondevold of the professional development organization Build Math Minds.
A veteran K-8 math teacher and self-proclaimed “recovering traditionalist” when it comes to math instruction, Tondevold said it’s crucial for teachers to boost students’ prior-year skills within the context of learning new grade-level concepts. That’s necessary, she said, to avoid widening academic gaps over time.
“It’s often ingrained that the way that you teach is by telling the kids, ‘These are the steps to do it. Now follow that and memorize it and you’ll get the answer,’ ” she said.
“But math connects more deeply to [students] if you’re able to let their understanding of the mathematics happen,” she said, and streamline those connections and help them learn to write their understanding in a mathematical way.
Tondevold spoke with Education Week about how teachers can accelerate K-8 math instruction while maintaining rigor. Her answers have been edited for length and clarity.
How can teachers keep from becoming overwhelmed if many of their students have a lot of holes in prior skills and content?
We all feel that rush—I’ve gotta go, I gotta go, I gotta go—and [students] are not getting a deep understanding of anything because we’re just throwing so much at them. We’ve got to look at the really big ideas, what is essential at each of these grade levels. If [students] don’t have some of the prerequisite stuff needed to understand those ideas, we do need to bring that in—but there are ways that we could bring it in 5-10 minute mini-lessons throughout [the grade-level content] and not feel like we’ve spent the whole first half of the year doing stuff that was from the grade before.
How should teachers restructure their pacing to allow for this sort of acceleration?
Teachers need to take a hard look at their instructional time. I’ll ask teachers, how many days do you have when you’re teaching mathematics? They’ll say 180 [the average required number of school days in most states]. And I’m like, no, let’s be realistic here, because you have days where there’s a field trip, you have days where there’s a class party, you have tests and all that.
So we start laying it all out there and looking at how many days do you actually have to do lessons. Then we say, OK, so if we’re down to 120 days—hopefully we don’t lose 60 days, but just for the sake of argument—60 percent to 80 percent of those [days] need to be spent on the major standards for that grade level. How many days do you think you’re spending on those things right now? How can we change that? And how do we fit in all the supporting stuff?
How can teachers find the time to fit those mini-lessons needed to catch students up into their regular pacing?
For far too long, mathematics has not been taught as a connected web of concepts. Everything has been seen as these isolated sets of skills. When I was teaching middle school, the thing that bugged me the most was we would have a unit on fractions, and a separate unit on decimals, and a separate unit on percentages. Those are all one and the same, right? If we do a fraction/decimal/percent unit, we can connect those concepts. The more connections we can make for kids, the easier it is for them to recall that information.
So for instance, in 3rd grade, finding the area of shapes is a supporting standard; it supports the major standard of multiplication in 3rd grade. So if you are teaching [students about] finding an area of a rectangle, it should be embedded in the work you’re doing around multiplication.
What’s the most common mistake you see teachers making in trying to teach these mini-lessons?
So, the style of teaching right now is we let [students] solve a problem in their own way, then we have kids share some of the ways that they solve the problem. One of the dangers of that form of teaching is that can be too slow and sometimes it can end up like a show-and-tell: [Students] get up, they show their strategy up on the board, they tell us exactly what they did, and then they go sit down. Then the next kid would come up and do their show-and-tell, and the next kid, and everybody else’s eyes were glazing over and not paying attention.
If you let five different kids get up there and share and kids see five different ways that this one problem was solved, that becomes really overwhelming and confusing. We want [students] to see that they don’t have to learn all five ways, but they do need to see the patterns in the strategies, the repeatability and the ways they are all connected.
We’ve got to shorten that up to only two or three shares, and there needs to be a purpose for the share. I would let a kid put their strategy up, but then I would let somebody else explain it. And then more of the discussion time was spent on connecting those strategies.
Are there particular math topics that teachers find challenging to accelerate?
Through all my experience dealing with elementary teachers, almost all the math topics are things they’re not comfortable doing. I’ve worked with thousands and thousands of teachers, and I’ve had so many comments from teachers saying, ‘Yeah, I went into kindergarten so I wouldn’t have to do math.’ They were taught that if you’re not good at following these rules or you’re not good at memorizing, you’re not good at math. So they have this feeling of math anxiety, and then to be able to teach math becomes an even harder thing.