LA Looks to Expand Popular Math Program Without Clear Evidence of Effectiveness

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Twenty kindergartners at Los Angeles Unified’s Coeur d’Alene Avenue School sit on a multi-colored carpet, listening to their teacher present the day’s math lesson. 

Projected on the whiteboard are clip art images of a gold coin and a pot of gold against a rainbow background. St. Patrick’s Day is just around the corner, and the students at the neighborhood school in Venice are getting ready. 

The story goes like this: A leprechaun has two pots of gold, each with ten coins in it. 

So far, so good. The students have seen this type of problem before. But their teacher, Adriana Mackavoy, adds a twist. In addition to the pots, the leprechaun has three extra coins. 

“I see those looks you guys are giving me,” says Mackavoy. “I’m sorry I didn’t tell you earlier.” 

With two pots of ten, plus three extra, how many coins does the leprechaun have? 

Compared to California’s math standards, the multi-step problem is relatively complex for a kindergartner. But some students solve it quickly. A girl in a faux-sheepskin vest displays her worksheet, which consists of a drawing — two clusters of ten circles, with three on the side — and her answer: 23. 

Her tablemate, however, is stuck. 

He stares at the worksheet, his blond bangs in his face. He’s gotten most of the way there — he knows there are 20 gold coins in the pots. But the extra bit isn’t making sense. The school’s principal, who’s observing, kneels down to help, but at no point intervenes to show the boy how to solve the problem.

And that is quite intentional. 

Coeur d’Alene is one of 220 elementary and preschools at LAUSD in a nearly $6 million pilot math program called Cognitively Guided Instruction, or CGI. Administered through a partnership with the UCLA Mathematics Project, CGI trains teachers to let student instincts guide math class, often resulting in hands-off instruction.

LAUSD’s 2022-26 Strategic Plan calls for moving elementary and middle school students an average of 40 points closer to proficiency in math on the Smarter Balanced Assessment. 

And L.A. Unified’s continued investment in CGI comes as districts nationwide try to recover after math scores saw unprecedented declines during the pandemic.

The district would like to expand CGI. But there are doubts about the wisdom of making young learners with little math foundation solve new problems with minimal guidance. The debate echoes the recent reckoning over balanced literacy, an approach to reading instruction that often deemphasized basic skills like phonics. 

LAUSD board members are asking for evidence that CGI improves math achievement at pilot schools. So far, there isn’t any. In fact, as in all district elementary schools, math scores at CGI locations remain low. 

Beyond L.A. Unified, education researchers say that a student-guided approach like CGI, when taken to an extreme, can be less effective for struggling learners than more explicit, step-by-step instruction.

“Is it fair to let some students flounder while other students succeed when we know that with just a little bit of teacher intervention or teacher modeling, all students could likely succeed?” said Sarah Powell, an associate professor of special education at the University of Texas-Austin who spends a lot of time with math students like the kindergartner at Coeur d’Alene. 

Powell is also the founder of an advocacy group that seeks to raise awareness of research-based math instruction — much like the science of reading movement has done for literacy, resulting in efforts to move away from balanced literacy.

There is evidence that CGI, which is primarily a teacher-training program, helps math teachers feel more confident and creative in their practice. Some research into its potential impact on student achievement is ongoing. But Powell points out that it’s hard to measure the effect of teacher training on student performance.

“It’s quite easy to impact the people that you directly work with,” she said. “But it’s much harder to see those results diffuse to another level of people, and many times that’s students.”

Other California schools also use CGI, including some in Riverside County and Downey Unified School District. The California Math Framework lists CGI as one of seven “general instructional models” that teachers might use to help their students reach standards. CGI is also used in Florida schools, such as those in Okaloosa County and Lee County. 

At LAUSD, the program is extremely popular among teachers and administrators. By deemphasizing the rote memorization of facts and algorithms in favor of conceptual understanding, they say, CGI welcomes students who might otherwise come to dread math class. 

“CGI is a movement. You feel the passion right in people,” said LAUSD administrator of elementary instruction Carlen Powell at a January 26 presentation before the school board’s curriculum and instruction committee.

“It’s not a religion, but it’s something,” she said. 

The nation’s second-largest school district, where just over a quarter of fifth-graders met or exceeded math standards in 2022 state testing, is considering bringing CGI to all its elementary schools at an estimated cost of $10.3 million. 

Board members, however, would like to see more data. Board president Jackie Goldberg and Tanya Ortiz Franklin have asked for a comparison between CGI and non-CGI schools. 

“I wouldn’t want to encourage growing the program if we can’t compare,” said Ortiz Franklin at a recent curriculum and instruction committee meeting. “Just looking forward to a little further analysis there.”

Research background and LAUSD data

CGI is based on research from the 20th century about how young students approach math operations.  

The program was articulated in a series of papers in the 1980s and ‘90s. An early study involving 40 classrooms in Wisconsin showed a small positive effect on student achievement. A core intention of CGI, and one that today’s practitioners emphasize, is to empower young people to see themselves as good at math.

At LAUSD, CGI started at 10 schools in 2016 and has since expanded to 220 of the district’s nearly 600 elementary schools and preschools. Teachers and principals at participating sites receive year-round training in how to recognize children’s ideas about math and leverage them for problem-solving.

LAUSD administrators and board members have expressed interest in growing the program, but the division of instruction is waiting on data to justify further investment. 

The data they do have are basic and preliminary, and district officials caution that there’s not a causal relationship between CGI and test scores.

At schools that have been using the CGI approach for five or more years, 30.28% of students met or exceeded standards on the math portion of state tests. LAUSD officials declined to share specifics on that figure, but for the purposes of a rough comparison, in 2022, 37.23% of third graders, 30.7% of fourth-graders, and 25.24% of fifth graders in all LAUSD schools (excluding charters) met or exceeded the standard. 

“Thirty percent’s not that great,” conceded Frances Baez, LAUSD’s chief academic officer.

“But overall, L.A. Unified, and across the nation, there is a need to improve outcomes for students in math,” she added. “And so CGI is looking promising, but there’s more to be done in terms of revamping our math program.” 

The program’s promise, she said, is based on its popularity among teachers who use it and high appeal for teachers who don’t. “Schools that don’t have it are seeking it out,” she said.

Baez also said the district is waiting on a study from the Los Angeles Education Research Institute at UCLA, or LAERI, to decide whether the pilot is worth scaling. However, a representative from LAERI, which is not involved in administering the pilot, said the study is not yet sure to happen.

“We are currently exploring the feasibility of an evaluation,” wrote LAERI’s associate director Carrie Miller in an email. 

Beyond LAUSD, what does the research say? 

Decades of research into math instruction suggest that a more hands-off approach like what might be found in a CGI classroom is not the most effective way to teach when embraced at the expense of other teaching methods. 

The hands-off approach requires “extensive planning” from teachers, said Russell Gersten, a professor emeritus at the University of Oregon’s College of Education and executive director of the Instructional Research Group. 

But for “many teachers, it just doesn’t work, the implementation can just be problematic. And that’s been more or less the history of these approaches,” he said.

A 2008 research review published by the U.S. Department of Education found that explicit instruction involving “clear examples” and “extensive practice” had consistently positive effects for students who struggle with math. Other studies and research reviews have found that struggling math learners benefit from more explicit instruction as opposed to less. 

Depending on how LAUSD teachers implement their training, students at CGI schools might not receive that explicit instruction.

Robert Schoen, an associate professor of math education at Florida State University, appears to be the only researcher currently studying the effectiveness of CGI through large randomized controlled trials.

Since 2018, Schoen and his research teams have published four studies on the effects of CGI training on students’ math achievement. 

One study found that the program had a potentially positive effect on first-grade achievement and a potentially negative effect on second-grade achievement, though neither were statistically significant. Two other studies measured significant positive effects on some grade levels, but not others. The fourth study found no significant effects. 

Schoen looks forward to producing more conclusive research, even if it doesn’t answer what he calls the “billion dollar question”: Determining the right balance between the open-ended and explicit instruction, and how to adjust it based on the situation. 

“I think everybody is trying to figure out, where’s that balance between intervening and telling versus staying back and letting [students] be where they are and on their own journey,” he said. 

At LAUSD, not all CGI classrooms are the same

Educators at LAUSD grapple with the question of balance too, and the result is that not all CGI classrooms look the same. 

The district’s chief academic officer Baez described CGI as a “supplement” to the district’s adopted elementary math curricula, Eureka and Illustrative Mathematics. 

That’s how Kiana Cotton, a second-grade teacher at Lovelia P. Flournoy Elementary, uses CGI. She uses the Eureka curriculum’s more structured approach as a way to build upon concepts her students might have explored during more open-ended, CGI-informed instruction at the beginning of the lesson.

“It’s going pretty good,” said Cotton. “I see the students taking ownership of the strategies. They get excited about coming up to present. They want to show their work.”

Other pilot sites, like Coeur d’Alene Avenue School, embrace the student-guided approach more tightly.

After the kindergarten class, The 74 visited a fourth- and first-grade lesson, which proceeded similarly.

The teacher presented the problem. The students worked on it independently. Some solved the problem — some quickly and creatively — while others were stumped. Then they conferred with their classmates. The teacher might have stepped in to guide a struggling student, but gave no explicit direction on how to solve the problem.

“We don’t really, like, push in and say, ‘This is how you do it: step one, step two, step three,’” said Danielle Grasso, Coeur d’Alene’s principal. 

The future of the CGI program

Were the LAUSD to expand the CGI pilot today, its main justification would be the huge popularity of the program among teachers and administrators. 

This enthusiasm was especially evident at a January 26 meeting at which the school board’s curriculum and instruction committee heard from UCLA leaders and district administrators about the pilot. 

LAUSD principals spoke about CGI’s influence on teacher morale. CGI is “a mindset,” not “a curriculum,” said Christina Garcia of the Amanecer Primary Center. Cynthia Braley of Coldwater Canyon Elementary spoke about the pandemic’s damaging effect on student math performance, but said of CGI that “we just can’t live without it.” 

Board president Jackie Goldberg called the presentation “inspiring” and said she’d been recently impressed observing students solving problems at a CGI school — though, along with Ortiz Franklin, she did request more data. 

“We have people clamoring to be a part of the work,” said Carlen Powell, the administrator of elementary instruction. 

“The work,” said Powell, “speaks for itself.”

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