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Counting Sheep: New Math in Richmond

Teachers at table
Teachers became students as Richmond Public Schools introduced a new curriculum for math education. Many teachers initially viewed the curriculum with skepticism, but there is a growing acceptance, especially among teachers who attend trainings in 'new math' techniques. (Photo: Megan Pauly/VPM News)

For years, students in Richmond Public Schools have scored among the lowest in Virginia on state math exams. The district recently adopted a new math curriculum, ‘Eureka Math,’ in an effort to turn those scores around. 

If you ask the district’s senior leadership team, they’ll tell you the new curriculum is about much more than test scores. They say a lot of teachers across RPS were making up their own lesson plans. That means when kids switch schools, possibly due to housing instability or their parents getting a new job,  they have to learn math a whole new way. So it’s about all kids across the district having access to the same learning materials.

It’s also about making sure students are prepared with the math skills they need to excel after high school. Many students graduate from this district without those skills. Last fall, about a third of students at one of the largest community colleges in the Richmond area were recommended for remedial math classes, low-level math courses for struggling students.

Before the coronavirus pandemic shut down school, RPS Superintendent Jason Kamras, who used to teach 7th and 8th grade math, led a training for elementary school teachers in early March. The goal for the training, one of many conducted over two years to roll out the new math curriculum, was to learn different methods of adding and subtracting fractions. 

“Now I know, kids usually freak out about fractions,” Kamras said after introductions. “But I think they’re fantastic and super useful. And I really love the way this curriculum approaches them, it’s very visual.”

Kamras came to Richmond from DC Public Schools in early 2018. The top priority for his five year strategic plan for RPS: Increase rigor in the classroom. For him, the Eureka Math curriculum, which falls into the category of what some people call “new math,” is a big step toward doing that.

Traditional math methods focus mostly on memorization of algorithms. Instead, Eureka was founded on the premise that students need a conceptual understanding of what numbers mean. 

Cognitive psychologist at the University of Virginia Daniel Willingham says math researchers usually distinguish between three types of knowledge that you need in order to be successful in math: factual, procedural and conceptual knowledge. Willingham says conceptual knowledge is the most difficult to engender in students.

“Math is so abstract. So understanding what's going on conceptually is very difficult,” Willingham said. “And so the visual model serves as an analogy.”

Kamras summarized it this way: “It’s about making what's going on in your head visible, so that we can ensure there's deep understanding. When you make it visible, then you can see, ‘ah, that's where they're going off,’ or ‘wow, that was a new way of doing it I didn't even think of!’”

Using a projector, Kamras worked through a word problem with the teachers.

“All right, Winnie went shopping and spent two-fifths of the money that was on a gift card,” Kamras said. “So she spent two-fifths of the money that was on a gift card, what fraction of the money was left on the card?”

Traditionally, you’d identify that there’s a common denominator here: 5. Then it’s just a simple subtraction problem of 5 minus 2 equals 3. Three-fifths of the money is left on the gift card. But that’s not the new math way of doing things. Kamras asked the teachers to use something called a number bond, a drawing depicting the problem, to show their thinking. 

Kamras highlighted one teacher’s drawing, which includes five circles, each representing one part of the whole. She’d circled three of these circles, showing how she’s gotten three fifths. Kamras acknowledged you’re not going to want to do all problems with fractions this way. 

“Now do we want kids to be able to do the algorithm? Absolutely. Because when it’s 9/16ths minus 4/27ths that’s a whole lot of bonds and drawings, right? So we want them to eventually get there,” Kamras said. “But right now I want them to think, oh, one whole is five-fifths. And if I do my bond or if I do my number line I can see how easily I can knock off two-fifths.”

The Eureka Math curriculum, created by the nonprofit Great Minds, came to Richmond in fall 2018, as part of a pilot program at several schools. It has since expanded to all schools K-8 except Patrick Henry Elementary.

The district says it’s already been a success, pointing to Westover Hills Elementary on the city’s Southside. Westover teacher Abbie Radcliffe and her daughter Niomi, a student at the school, spoke to VPM about the curriculum.

Second-grader Niomi explained how she’s using some of the math, reciting from memory: “I also remember one of my strategies was counting by fives and tens and twos. I kinda did it in my brain, so like 5, 10, 15, 20…..”

Abbie Radcliffe has taught kindergarten at Westover Hills for the past two years, and is teaching first grade at the school this year. She’s a veteran teacher who’s been teaching in Richmond for 12 years. She started using the number bond strategy when the new math pilot started at her school. 

To introduce the concept to students, Radcliffe had them stand in hula hoops to represent the numbers, forming the number bonds. She said, “We lay hula hoops out on the floor and use painters’ tape or some sort of tape to connect them.”

There’s one hula hoop at the top, and two below it. They form a triangle. The hula hoop at the top represents the whole number. Like, for example 5. The two hula hoops below represent parts of the whole, in this case 2 and 3.

“And so we would make up a story, and two children would stand in one part and three in the other part, and then they had to walk up the path,” Radcliffe said. “And then when they get to the top, that's the whole so we would start out that way.”

Gradually, she’ll start shifting away from kids walking between the hula hoops to drawings to the number symbols themselves. Researchers say this progression from the concrete to the abstract can be effective in helping students better understand math. 

“And then we might use stuffed animals in the hula hoops. And then we move to the table, drawing them out and using cubes or little toy animals. And then we move from that to drawing,” Radcliffe said. “And then from that to actually using the numbers and then from that to using the equations.”

Radcliffe described another new strategy called the “say 10” way. She gives an example: She holds up two cards, one with 10 dots on it and one with two dots on it. 

“This would be, not 12. This is 10, 2 because I know that I need a 10 and a 2 to make 12. One and two makes three, but 10 and two makes 12,” she said.

Radcliffe really likes this one because she thinks it helps students understand that “twelve” includes a 10-unit and two more. And as they get older, they can take a difficult addition problem and come up with an easier problem to solve instead. 

Radcliffe was pretty skeptical of this new way of teaching math at first, as were a lot of Richmond teachers, including Janice Gray. Gray, a fellow kindergarten teacher at Westover who has since moved to a different school, has been teaching for 26 years. 

“My first impression personally was that I was hoping that this was going to be the curriculum, that we didn’t just use it for a little bit and then change,” Gray said.

It was another new thing coming at teachers. There’s been a lot of change when it comes to curriculum and leadership, something you’ll find in a lot of schools across the country. In the last decade, the district has had three different superintendents.

But, like several other teachers at Westover Hills, Gray came to accept this new math curriculum. 

“It hasn't been too bad,” Gray said. “I think it has to do with your own personality. Because I'm the type of person I can adjust.”

Gray said students can still use traditional ways to solve the problem. Usually some kind of formula. But, they could also use a number bond. She says it’s OK if students don’t all use the same method to find the right answer. 

“I remember introducing to them that concept of, more than one right way to get to the answer. I kind of told them a little story, like: I'm on my way to work. And the way that I usually go was blocked because there was construction,” Gray said. “So I had to go another way, I had to cut through a neighborhood, I had to cut through here. I said but guess what, I'm here. So was that okay for me to go a different way? They were like, ‘yeah!’ So I think it allowed them to, on a test or on some type of assessment, if they got stuck, instead of giving up, they could figure out a way to get it or to understand the question without it having to be the way that most people did it.”

And, she says, her students started to get used to the idea that they could get to an answer however they want as long as they show how they got there. 

“They knew if they raised their hand, if we talked about it, they had to explain, how did you get to that answer? So it was more, they knew, like, okay, I get to tell my story, I get to tell how I got to this answer,” Gray said.

"She would do all this kind of like in her head and out loud. And I was like, wow, that's pretty impressive.”

- Parent Jody Lyle

One of Gray’s students is 6-year-old Ellie. She explained how she solved a math problem while baking cookies with her mom for friends. Based on the size of the batch and the number of goodie bags they wanted to make, Ellie helped her mom figure out how many cookies to put in each bag. 

To do that, she mapped out the groups of cookies on the fridge, using dry erase markers to draw rows of circles to represent the cookies. 

“First I wrote one on every line. Then I wrote one again on every line, then I wrote one again on every line,” Ellie said. “Until I realized that we have the number of cookies. That’s how I realized it was 4...and a ton of other 4s.”

Ellie’s mom likes the curriculum. Another mom at the same school, Jody Lyle, says the principal hosted a parent night to help parents like her learn more about the curriculum. 

“That was so helpful. She had a couple teachers come from different grade levels and explain, like, what would be happening in the year and these grade levels and they were showing us, like all these different ways that Eureka math is taught,” Lyle said. “It’s so much, like, new terminology and different vocabulary to learn. They use things called tape diagrams, and I was like what is a tape diagram?”

Even in second grade, Lyle said her daughter was able to do impressive calculations in her head. “My daughter came home and I would say, like, well, what’s 74 plus 39. And she would make the 74...she would add six to it to make it 80, so take away six from the 39 to make it 33,” Lyle said. “And then she'd be like, Oh, 80 plus 33 would be 90 100 103, 113. Like, and she would do all this kind of like in her head and out loud. And I was like, wow, that's pretty impressive.” 

Westover Hills Elementary principal Allison El Koubi has a contagious smile. She started the job in 2018, the year the Eureka curriculum was first piloted. The year before she arrived, math test scores had dropped significantly. 

Only around a quarter of students in the school were proficient in math. That was about half the district average. It’s hard to know why the scores dropped, but it was El Koubi’s job to get things back on track. So when the district administration asked if she wanted to “opt in” to the new math pilot, El Koubi agreed. 

“There's not a lot of bells and whistles, it's not flashy, there's not like bright colors, but it really gets into the math and gets kids really thinking about it and gets the adults really thinking about it,” El Koubi said.

RPS holds up Westover as an example of success of the new math. That’s because after the pilot, spring 2019, its test scores jumped a whopping 30 percentage points. The school went from about a quarter of students passing to more than half. 

“I would say that switching to this [new math curriculum] was the main thing that improved our scores,” El Koubi said. 

But looking at the numbers, it’s not so clear. The year before El Koubi arrived, test scores fell 20 points. So down 20 one year, then up 30 the next. A net gain of 10 percentage points isn’t uncommon when you look at other schools in the district.

And it wasn’t the only change made under El Koubi, who created new programs to involve families in education and launched a school spirit campaign. “We named our mascot, we got a new mascot costume,” El Koubi said. “So Justin Beaver, we're the Beavers.”

Experts say it’s hard to pinpoint to what degree the new curriculum improved test scores. Research shows that curricula in general does have an impact on student achievement. In fact, that’s why this matters so much. But it’s nearly impossible to isolate the role any singular curriculum plays in student achievement. In addition to factors like school culture and family involvement, there are just too many curriculum-related factors: to what degree teachers use the material, teacher training and more.

In fall 2019, the Eureka pilot expanded to nearly all kindergarten through sixth grade classrooms in the district. VPM heard from a few principals about how it went. One said they liked the prior curriculum and didn’t see much value added from Eureka. 

Another principal didn’t know whether a new curriculum was needed or not, but just said the way the pilot was rolled out wasn’t good.

Ultimately, a couple of schools asked for permission to put the pilot on hold. One of them was Holton Elementary, on Richmond’s Northside. Walking in, the building feels relatively new, at least when compared to most other schools in the district. 

The roof is covered with solar panels, and there’s a rain garden in the middle of the parking lot. Francis Johnson has taught fourth grade here for five years. When the school started piloting Eureka math materials in fall 2019 he felt lost. 

“I guess it would be like being taught English your entire life and then all of a sudden being expected to speak Spanish,” Johnson said. “Like, you understand that it's still a language, but you're having trouble approaching it.”

Part of the problem is that there were more training opportunities to learn directly from curriculum developers in the first year of the pilot than the second year. Johnson says another problem was teachers were trying to learn and teach the material at the same time. 

“You'd have students that were like ... 'Oh, I'm good at math," ... and now they're saying, 'I'm not good at math.'”

- Teacher Francis Johnson

“And usually, as a teacher, you have at least some sort of a foundation in what you're teaching before you start teaching it to the students,” Johnson said.

Johnson said his students were lost, too. Some just weren’t picking up on the new concepts, and it frustrated them.

“That was one of the biggest things that I had noticed,” he said. “You'd have students that were like, always say things like, oh, I'm good at math, or I used to think I'm good at math. And then now they're saying I'm not good at math anymore.” 

Some of Sydney Bauman’s students didn’t like the new math, either. She teaches fifth grade at Holton. Like many teachers, she’s used to making up some of her own lessons. In fact, less than a quarter of teachers across the country use a textbook without bringing in their own materials. Many use websites like Teachers Pay Teachers, which lets teachers buy material from one another.

“I find a lot of my things [through] Teachers Pay Teachers, because that's a lot of colleagues, basically, who are posting what they like,” Bauman said.

She also picks things up at the grocery store, like coupon pamphlets, when she has an idea about how they can help students understand a math concept.

“If I wanted to buy potatoes and broccoli and whatever else, how much is it going to be? Or like giving them a budget and telling them they have to pick things from that,” Bauman said. “So it's kind of a mix of like, what I kind of come up with on my own or finding things online.”

When her school started rolling out the Eureka curriculum, she too didn’t feel like she’d had enough training. And she was only able to get through a few problems in each lesson. 

“It was a lot to handle,” Bauman said. “We spent a really, really, really long time on certain concepts. Like we spent, like a month on multiplying and dividing decimals by 10, which is basically just moving the decimal point. And we were supposed to use a place value chart, and nobody knew how to use a place value chart. So we had to teach the kids how to use the place value chart. And then it was just like a month on this one skill. So, when you are spending that much time on something that is a fairly simple skill, when you compare it to something like fractions, it wasn't working for us.”

Another problem is that her fifth graders were having to learn these new Eureka concepts that were very different from the way they were taught when they were younger. Bauman and some other teachers at Holton eventually approached the administration with their concerns and asked for more training. Holton’s principal got permission from district officials to temporarily put the Eureka pilot on hold, at least for some grades. 

In a training for principals this past February, RPS Chief Academic Officer Tracy Epp admitted that the rollout that year, the second year of the new math curriculum pilot, was messy. There were delays in getting materials to teachers. And when teachers did get them, some lessons weren’t fully aligned to Virginia’s state testing standards. 

That was earlier this year. Then came the coronavirus pandemic, and everyone was caught completely off guard. Schools closed quickly, and the district scrambled to put out virtual lessons. It was chaotic, as it was in a lot of places. The district put up some videos on Youtube, some included Eureka lessons, others didn’t. 

At this point, the school district was trying to make a decision about whether or not to invest in this curriculum for good, for all students grades K-8. Some teachers didn't want them to commit during a pandemic, and asked for a pause on the adoption. Other educators said the opposite. The school board's vice chair, Cheryl Burke,  supported the new curricula.

“Yes, we are experiencing the COVID-19, we're experiencing ongoing systemic racism, poverty,” Burke said when she announced her support. “However, it is our job to keep the main thing the main thing, as Dr. Joyner, retired Richmond Public Schools principal used to say. And the main thing is making sure that we provide a sound foundation - educational foundation - for every child. We can’t wait!”

The school board voted to formally adopt the new curriculum, starting this year. That means all elementary and middle schools - except for Patrick Henry Elementary - are expected to use Eureka in the virtual classroom this fall. VPM asked Superintendent Kamras over Zoom how he’ll be enforcing that. And the answer is, it’s really difficult. 

“There are no, like, curriculum cops or anything,” Kamras said. “But I mean look, this is the expectation.” 

At the end of the day, Kamras says, it’s about equity: ensuring all students have access to the same materials. Some creativity in lesson planning is OK, but teachers should still be building off the standard curriculum. But that’s easier said than done.

“It's not like we know how to bake apple pie, and we're having to learn to bake bread. It's like we know how to bake apple pie and now we need to learn how to sail a 50-foot yacht around the world."

- Principal Allison El Koubi

In early August, schools were still gearing up for the fall. Westover Hills principal Allison El Koubi remained optimistic she could make this work with the new curriculum and online learning. But she admits this spring there were a lot of challenges. 

“It's not like we know how to bake apple pie, and we're having to learn to bake bread,” El Koubi said. “It's like we know how to bake apple pie and now we need to learn how to sail a 50-foot yacht around the world, you know, like, it's so different.”

It’s not just how difficult it is to teach online, but she’s concerned about the kids. Do they have a chromebook? Do they have someone at home to help them with learning? El Koubi wasn’t sure how many students hadn’t been online learning.

Unlike the spring, this fall the district planned to have some time when students and teachers are online at the same time. The district’s virtual learning plan for elementary students outlines two “math blocks,” a 30 minute math lesson before lunch, and a longer one after lunch and recess. 

There are other lessons that are available online but up to parents and kids to do on their own. But remember Abbie Radcliffe’s class, where kids were jumping in hula hoops? You can’t do that on a computer screen. There are some aspects of this curriculum that just don’t work online.  

The pandemic is going to make understanding the effectiveness of this curriculum difficult. And it’s always been hard to understand how well a curriculum works anyway, even in the best of times. What we do know is that a teacher's understanding of what they’re trying to teach is crucial. They can’t teach something they don’t understand themselves. It takes a lot of time and practice to completely teach yourself a whole new way to think about math instruction.

Some teachers, including Francis Johnson at Holton Elementary, feel more comfortable with Eureka now, after the district provided a lot of additional professional development sessions over the summer. 

But, at the end of the day, teachers are going to do what they feel is best for their students. Some of that might include Eureka math, some might not. Or like one veteran teacher told VPM: They might, “eat the watermelon and spit out the seeds.” 

This story was made possible thanks to a grant from the Education Writers Association.
Special thanks to Emily Hanford for editorial guidance, and Ryan Katz for editing, fact-checking and mixing help.


Megan Pauly reports on early childhood and higher education news in Virginia
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