Transforming Math Classrooms with Cognitively Guided Instruction

While subjects like language arts and science frequently evolve to meet students’ needs, math instruction has traditionally followed a rigid format: teachers model the problem and students solve for the answer. But does this approach truly support all learners—especially emergent bilingual learners?

The School of Education’s English Language Development/Math (iELD/Math) Project team is committed to building a better classroom model. Through a five-year research study funded by the National Science Foundation and in collaboration with Los Angeles Unified School District (LA Unified), they are working with teachers to employ Cognitively Guided Instruction (CGI) in fraction instruction to foster collaboration, discussion, and deeper mathematical understanding. Their goal: to integrate English language development concepts into math instruction to build students’ competence and confidence in both subjects.

Where Traditional Math Teaching Falls Short
Dr. Rachel Restani, a co-researcher on the project, explains the issue with conventional math lessons. “Traditionally, teachers demonstrate how to solve the problem, and then students turn to page 26 and complete questions 1-15 to practice the procedure. Then the class moves on until the test.”

This method only presents one way to solve a math problem, limiting students’ ability to explore different approaches. It also discourages discussion—making it particularly difficult for emergent bilingual students who must process both the mathematical subject and new terminology on their own.

Supporting Math and Language Learning
The iELD/Math Project team—which includes PI Prof. Tony Albano, Co-PI Prof. Margarita Jimenez-Silva, Prof. Rebecca Ambrose, Prof. Matt Wallace, Prof. Megan Welsh, Dr. Suzanne Abdelrahim, Robin Martin, Dr. Rachel Restani, Ph.D. candidate Valeria C. Zunino-Edelsberg, Hilda Yudess from LA Unified, and other teacher collaborators—is prioritizing CGI in math instruction because it empowers students to engage in math discussions and work with their teachers to uncover the right solutions. By talking about their thinking students have an opportunity to deepen their mathematical understanding while developing their language skills.

By shifting the focus of math instruction from passive learning to active exploration, the team hopes students will:

• Construct their own problem-solving strategies
• Explain their own reasoning and understand their peers’ thinking
• Build confidence in their math abilities

The team reiterated that, “We want to get children talking about math and exploring other students’ thinking, while also explaining their own logic.”

A Pop-Tart Math Problem: CGI in Action
To introduce CGI in classrooms, the iELD/Math team suggests a simple but effective exercise: the “equal share” problem. They encourage teachers to pose the question “Eight friends are going to share five Pop-Tarts so that everyone gets the same amount. How much should each friend get?” Students work to identify potential solutions, including slicing up the Pop-Tarts like a pizza, cutting four Pop-Tarts in half and dividing the final one into eight pieces, or dividing 5 by 8. They then talk to a partner about their work and explore any differences in their approaches.

This exercise enables teachers to step back and observe their students’ reasoning and language use, gaining introductory insights into what students already understand about mathematical concepts, how they communicate problem solving to others, and their confidence levels when participating in math discussions.

Building Stronger Math Identities
A key aspect of the iELD/Math Project team’s work is math identity—a student’s belief about their own ability to engage in math.

“We wanted to create an environment where teachers pay more attention to their students’ math identities,” said Dr. Abdelrahim. “And this close attention has encouraged students to maintain a growth mindset about math learning, while still holding a positive outlook on their own identities.”

This awareness is crucial because students who perceive themselves as “bad at math” often disengage, while those with positive math identities are more likely to actively participate and develop mathematical skills.

Interestingly, many educators also uncovered that their own math identities impacted how they teach problem solving. If they lacked confidence on a particular math subject, they tended to rush through it or avoid deeper discussions. Their personal challenges with math can hold major implications for their students’ learning. As the iELD/Math Project team writes in their resource materials: “Children whose teachers are anxious about math are more likely to develop math anxiety themselves, endorse negative math stereotypes, and learn less math.”

As collaborators on the iELD/Math Project, all of the teacher participants developed a greater appreciation for the ways in which mathematics can operate as an elitist activity where only a few students excel. This motivated the group to create more equitable learning environments where every student felt that they had a contribution to make to the math problem at hand.

Empowering Teachers Through CGI
CGI not only benefits students—it also helps teachers feel more confident in their instruction. Instead of needing to be the sole expert, educators become facilitators, supporting students to use their own problem-solving strategies.

“CGI gives teachers agency,” said Martin. “It honors their expertise while still helping them see their teaching styles in a different light.”

By shifting the focus to student-led learning, CGI reduces pressure on teachers while fostering a more engaging, discussion-based math classrooms that cultivate inclusive learning spaces for all learners.