Rogelio Alvarado remembers realizing his teaching practice had changed.
A fourth grade teacher in the Lost Hills Union Elementary District in California, Alvarado had been trained to teach math via direct instruction: Writing a problem on the board, then asking students a series of step-by-step, closed-ended questions to which students would answer yes or no.
In the fall of 2021, Alvarado joined other Lost Hills teachers in working with Harvard CEPR’s Mathematical Quality Instruction (MQI) e-coaching.
MQI matches teachers with an expert coach for virtual, one-on-one coaching based on video of their own instruction. E-coaching is customized to meet a teacher’s goals and helps them self-identify areas for instructional growth. Coaches guide teachers to develop realistic and actionable next steps to improve their math instruction.
Lost Hills, an hour’s drive west of Bakersfield, served 263 students in the 2021-2022 school year. Sixty percent of its students are English language learners, and most qualify as economically disadvantaged. The district partnered with MQI e-coaching because it wanted to improve students' math achievement and support the teacher’s development.
The beginning of the process — learning how to film class and self-reflect using that video— took some adjustment, Alvarado said. But conversations with his coach soon had him considering new ways to engage with students.
He found himself asking more open-ended questions that let students lead the class discussion. Yes or no answers mattered less than why.
“I spent a good amount of years doing direct instruction and I didn’t really get to hear students’ thoughts,” Alvarado remembers. “It was eye-opening to hear the solutions they had in mind. Every kid has a different pace of learning. As they built their math vocabulary, I understood where they were and where they needed help to master a subject.”
Alvarado’s coach encouraged him to make small changes rather than trying to change his entire teaching style overnight. But by the end of the year, said he was a different, and more confident, teacher. His students evolved with him, as they got used to explaining the processes behind their work rather than just giving a final solution.
The Mathematical Quality of Instruction (MQI) breaks down concepts like “student engagement” into math-specific definitions and methods that are specific and concrete. This rubric gives teachers and coaches a shared language to help translate intentions into practice. When combined with classroom videos, the MQI allows coach and teacher to identify actionable steps to improve math instruction, and in the case of Alvarado that was getting students to contribute in mathematically substantive ways.
"I talk to a lot of district leaders who are trying to make the shift to more student-centered instruction. This change is hard, and they are realizing that the typical large group, one-off, professional development format is not sufficient,” said Samantha Booth, MQI Associate Director. “What we know from the research is that one-on-one coaching that is focused on observation and feedback over time is more likely to shift practice. We designed the MQI e-coaching process so teachers can test out different approaches and build new skills with the support of an experienced math coach throughout the year.”
Alvarado’s class wasn’t the only one at Lost Hills making progress. The percentage of students who met or exceeded math standards on California standardized tests rose by 17 percentage points in 2022. It felt like a breakthrough for the district, which had been trying to boost math achievement with different interventions for the previous five years without significant movement.
Based on the feedback from teachers and the test scores, Lost Hills Principal Veronica Gregory not only decided to extend the MQI e-coaching partnership in the 2022-2023 school year, she signed up to go through the program herself.
“It’s like having a leadership coach that you can go back and reflect with,” Gregory said. “My coach has talked about taking baby steps. These ideas get engraved in your head, and you remember, I’m not going to take a one-word answer, I’m going to see how I can elevate this lesson.”
The results have not been confined to math class, Gregory said.
“It’s changed the culture of our school,” Gregory said. “It has a spillover with other areas and subjects. We’re asking our students to explain their thinking more, because we’ve heard them, and we have higher expectations.”
Alvarado and Gregory agreed that the benefit of MQI e-coaching isn’t just about improving math performance, it’s about preparing their students to succeed in life.
“These are lifelong skills,” Alvarado said. “We want our kids to have a solid foundation for doing math, thinking critically, and having fun.”