This is the second in a two-part series. Part one can be found here.
The debate over what early math should look like and what should be included in the Common Core State Standards for math is one of the most contentious in education circles. Bethany Rittle-Johnson is a professor of psychology and human development at Vanderbilt University in Tennessee who studies early math, specifically the importance of teaching young children about patterns. Patterns were mostly left out of the common-core math standards in the early grades (kindergarten and 1st grade) due to a lack of evidence that they helped children understand later math concepts. Rittle-Johnson’s research on what children take away form learning repeating patterns, however, along with the research of several others that has come out since the standards were written, suggests that patterns should be added back in.
We spoke with Rittle-Johnson at length about both her work with patterns and the more wide-ranging question of what math should look like for preschool students. Should students use objects, called manipulatives, to practice addition? At what point should they begin to learn symbols? Is counting important? How do students figure out math rules?
Our conversation was so engaging, that it’s being published on Early Years in two parts. The first part, which ran on February 17, covered best practices for early math classes. We left that conversation just as we were about to discuss the importance of learning repeating patterns. Here’s the rest of our conversation, edited for length and clarity:
Which brings us into your research on patterns, right?
Yes, I’ve been looking at this research on kids thinking about repeating patterns.
Like A, B, C, A, B, C?
That’s right. There are also these things called growing patterns like two, four, six, eight. Growing patterns [are something] that kids deal with at an older age. But you can’t really deal with growing patterns until you have good number skills in place.
Repeating patterns are very accessible to young children though, and kids love patterns. And preschool teachers love patterns. But there’s big concerns that how kids usually deal with patterns isn’t very mathematical because we show them red, blue, red, blue and we ask them what comes next and people say “Well, what are you really paying attention to to do that? You just kind of get a little rhythm. You just match the first item or something.” It wasn’t clear how mathematically relevant it was.
Would you say that those concerns were part of what led to patterns being taken out of the kindergarten common-core math standards?
There was a National Mathematics Advisory Panel that came out with a report in 2008 that was commissioned by the president to look at what math knowledge was important for kids. [The panel] really focused on algebraic competency in high school because being good in algebra seems to be related to getting into college, completing college, earning more money, [etc.]. And so people got worried. What can we do to help kids be better prepared for and more successful in algebra in high school? And so that’s what this National Math Advisory Panel did.
At the time there was no evidence linking repeating pattern knowledge to later math outcomes, and mathematicians were worried. They were like, “What’s mathematical about that?”
Also, five out of the six highest-achieving countries out of the world do not pay attention to repeating patterns in the early grades.
Based on that [the National Math Advisory Panel] said that patterns should receive a lot less attention in the curriculum. As far as I can tell, that’s why the Common Core State Standards dropped it.
Patterning is not there at all in kindergarten right?
Yeah, that’s right. If you look at the math practices in the common core it says look for and make use of structure. [Math practices in the Common Core Standards are lists of skills children should use to help them achieve the standards.] There’s some reference to looking at these kind of patterning ideas in that mathematical practice, but it’s easily missed. Teachers I talk to don’t get that from it at all, and they’re saying, “They’re taking patterning away from us.” This is just anecdotal, but I’ve heard this anecdote from several people.
I’ve heard it in my reporting too, which is why I was interested in your research.
I want to be always really clear that I agree that the common core should be evidence-based, and when they were writing the standards there wasn’t really evidence out there. But in the last eight years or so I think there’s a lot of really nice evidence coming out showing that patterning, even these basic repeating patterns, really are useful and helpful in supporting kids’ mathematical thinking. And so I think that is something that we should add back in.
So what is the evidence that repeating patterns are useful?
So there’s one study by Marina Papic, [a professor at the Macquarie University] in Australia. She did a preschool patterning intervention that does this sophisticated kind of patterning. She found that a year later when these kids have entered kindergarten their numeracy knowledge was better than the kids who hadn’t been in this patterning intervention. Of course, their repeating pattern knowledge was better, but then a year later their numeracy knowledge and their growing pattern knowledge was better too.
Is that maybe because they had practice with simple patterns so the idea of a more complex pattern was an easier leap?
It’s this idea of getting kids to make use of and look for structure. You are trying to think about “What’s the rule? What’s going on here? What’s happening?” Looking for rules and regularities and figuring out things that are happening—that’s what most of math is.
The practice of thinking about repeating patterns helps kids look for patterns in numbers and look for patterns in other things. And so they’re starting with shapes because blocks and colors are what’s most easy for a 4-year-old to do. It gets them looking for those patterns and thinking about rules, and that’s what they need to do to learn a bunch of other math.
And then there’s more evidence that [George Mason University professors] Julie Kidd, and Robert Pasnak [discovered]. They did work in the U.S. with these 1st graders who were struggling with patterning. Their classroom teachers worked in small groups doing patterning with them or they did a variety of other things like reading activities or math activities that were pretty varied. At the end of the school year the kids who did the patterning activities did better in math achievement on a standardized math test, than most of the other kids. They were better or equal to the kids who did the math work, and they were definitely better than the kids who did the reading work.
It sounds like the thing that is most clear then about working with repeating patterns at a young age is that it helps children understand the idea that there is structure and there might be a rule governing the pattern and therefore their brain starts to figure out “Oh, I should be looking for rules. I should be looking for patterns.” And then that continues to be helpful throughout their math learning.
That’s what we think is going on.
And there’s more evidence for that than you knew there was before.
Yes. These studies came out in 2011, 2014, so it’s really new. And the things those studies share is they didn’t do the really simple patterning work that preschool teachers oftentimes do, which is like what comes next or just like red/blue/red/blue/red/blue and now can you copy it?
Can you give me an example of what they did do in the studies?
My favorite example is we asked kids to come up with the same kinds of patterns, but using new materials. So if I show you red/blue/blue/red/blue/blue, now I give you shapes and triangles and I ask you to make the same kind of pattern using circles and triangles.
So now you have to do circle/triangle/triangle/circle/triangle/triangle?
Yes. And so the idea is kids can succeed at easier tasks by matching. They can do it in a simple way that we’re not sure is really pushing them to think about rules and regulations.
When you do this activity where you [tell kids], “Okay, do the same kind of pattern,” then kids have to think about it. I’ve found in my own work that from the beginning of the preschool year to the end of the preschool year, kids got a lot better at that, even though their teachers were doing a lot of patterning but not a lot of that more sophisticated patterning. So I think it’s very accessible to 4-year-olds, and [the studies I mentioned] used this more-sophisticated stuff that’s pushing kids to think about rules. You have to really pay attention to the rule and the structure and do something with it.
Also, I don’t think you can do that with 3-year-olds. I mean, I’m sure there’s a 3-year-old out there, but in general, you first have to get easier tasks.
You’re saying they need to progress to the more difficult ones to really have an impact.
By the time they’re 4, they’re ready for that. Now, we haven’t actually any evidence before they’re 4, but I think this would be rough going if I was doing this with kids who hadn’t really seen patterns and hadn’t really talked about patterns. Like when I say, “Look at the pattern,” no kid has ever said to me, “What do you mean?”
It’s clear, when I survey the teachers I work with, they report doing 10 patterning activities a week on average. Now, of course, preschool teachers aren’t directly affected by the Common Core State Standards, but I think it’s going to push down.
If you could give just one thing that parents or preschool teachers could do with their young children at home—we’ll talk about 4-year-olds—that would help them be ready for kindergarten and 1st grade math, what would it be?
I’m going to encourage them to do this pattern abstraction. Make a pattern with one set of materials and ask kids to make the same kind of pattern, but using new materials so that they have to really be thinking about that rule. I think it’s going to really help. There are other things that help too, but this is something that most parents and teachers have never thought about.
Oh, and have you heard about Bedtime Math?
It’s [an app] by this mom who’s also a Ph.D. in biochemistry or something. Essentially in addition to reading a story at night, it’s a math problem for your kids to do at night.
The idea is doing this informal thing just gets kids thinking about math. There’s a really nice study that just came out by Susan Levine in Science, that shows doing this bedtime math project with math-anxious parents reduced the anxiety of the parent and the anxiety of the kids. Because I think the idea is that you realize math isn’t this scary thing off in school, right? It’s just this real-world problem-solving thing I do all the time.
Just this little puzzle we’re going to do together.
Exactly. I think it’s a really important idea, especially for math-anxious parents.
Photo: Child works on the types of patterns Rittle-Johnson studies. Courtesy Bethany Rittle-Johnson.
A version of this news article first appeared in the Early Years blog.