Above, Coeur D’Alene Elementary first-grader Jayden Vasquez shares his thinking with Tamryn Wilkins visiting from 54th Street Elementary.

As winter changed to spring, kindergartners at Coeur D’Alene Elementary shared stories about changing numbers of eggs and bunny rabbits.

“What if I said there were twelve eggs here, but now you see ten?” teacher Adriana Mackavoy asked her class. “How could we tell that story?”

Coeur D’Alene kindergarten teacher Adriana Mackavoy engages her students in conversations about how numbers change with items they can relate to such as cartons of eggs.

The students pondered the question, talked with one another and then shared their thoughts with the class. Their conversations organically developed into verbalizing thoughts about subtraction.

By encouraging the students to tell stories about numbers, studying their thinking and using that information to guide them in problem solving, Mackavoy was using Congitively Guided Instruction, or CGI, a relatively young approach to teaching math being explored in schools across L.A. Unified.

“CGI is a framework that helps teachers understand how children learn,” said Lisa Ward, coordinator of elementary mathematics in the Division of Instruction. “Our job as educators is to find out what they know so we can guide them in linking new understanding to their existing understanding, and that way math starts to make sense.”

Ward has been working closely with UCLA education professor Megan Franke, who specializes in CGI, to explore its use in teaching math to students from transitional kindergarten through sixth grade.

“What we’re seeing here today is young people listening to each other’s ideas, asking questions and supporting one another in generating ideas about math problems,” said Franke, who recently visited Coeur D’Alene along with hundreds of educators from around the Los Angeles area. “Not only are they thinking really hard about the math, but they are learning how to participate together. Students learn to listen to one another, ask questions and then build on each other’s ideas. While it helps them learn math, it also teaches them to work collaboratively.”

Now in its fifth year using CGI, Coeur D’Alene has become a beacon to educators from other schools who regularly visit the Venice campus to observe how it looks in practice.

“At Coeur D’Alene, our philosophy is that doing things together is better,” principal Andrew Jenkins said. “With CGI math, we are constantly researching what works for our students and making determinations about what to do next based on how they’re learning and ongoing evaluation of their understanding. We are following their lead.”

First-grader Abigael Yemane talks to visitors about how she arrives at estimates of large numbers.

Jenkins says students are now excited about learning math, and parents are excited about enrolling their children at the school.

“We have grown by about 120 students in recent years, taking us from 18 to 24 classrooms,” he said. “And, most of that growth has occurred since we started using CGI.”

Among recent visitors is Ruben Gonzalez who teaches kindergarten at nearby Walgrove Elementary, where CGI is in its first year of practice.

“I can see based on what I have observed here that we are stepping forward in the right direction at Walgrove,” he said. “The kids are having a lot of fun with the program. Every day they are saying ‘when are we doing math?’ It’s opened a lot of new doors for us in terms of teaching math concepts and interactive styles of learning.”

Gonzalez recently spent a morning with a dozen other educators observing Coeur D’Alene first-grade teacher Jacklyn Gonzalez, one of several teachers who were instrumental in bringing the program to the school.

“Traditional ways of teaching math didn’t really provide me with a sense of what my students knew, what they were capable of and what was engaging for them,” she said. “So, my fellow teachers and I looked into alternatives. We heard through our school community about CGI, researched it and took some introductory courses to understand how it works. With this approach, we don’t try to teach students a way of thinking; rather, we pay attention to how they think and then adjust our instruction according to what we see. It has really transformed how our students learn math concepts.”

Observers take note as first-grader Ella Rose Reisig shows her teacher, Jacklyn Gonzalez, and fellow students how she arrived at a solution to a math problem.

Gonzalez’ students eagerly talked with visiting educators about their problem-solving methods.

“We are learning to do estimates,” first-grader Abigael Yemane explained. “We are trying to figure out how many times a soccer player bounced a ball on different parts of his body before the ball hit the ground. I took the numbers and made them into tens and ones and then put them together to find the answer. That’s my favorite part: finding the answers.”

During visits, observers took notes on what they observed in classrooms and then gathered in work groups to discuss their observations and generate ideas about how they can use CGI effectively in their own schools.

The approach is now being used at 60 campuses in L.A. Unified, 10 in each local district. Ward says there are plans to expand to additional campuses next year along with a summer institute for teachers that will blend traditional classroom-led professional development with online courses.

“It’s showing a lot of promise,” she said. “By posing problems in real-life scenarios in high-interest areas, we are able to incorporate students’ interest into what they are learning, provide tools to help them make sense of it and encourage them to explain their thinking to one another. The teacher is then able to share in that network of knowledge and adapt lessons accordingly. It can be done with any curriculum, which is a key reason why it’s been so successful.”