Habits Over Gaps: A New Path to Algebra Readiness

“My class can’t do grade level work. My students can’t multiply. I need to teach multiplication first,” said a middle school math teacher during a recent PD session. 

Math teachers face this challenge every day: students arrive in their classrooms with significant learning gaps. Teachers are left with a hard question: “Do I go back and reteach basic skills, or do I move forward and continue to cover this year’s required content?”  We propose a third path, one that challenges this false dichotomy: teaching foundational skills while teaching grade-level math. We can and should do both.

Some teachers recognize the value of a third option, but they are unsure about how to do it in practice. They are already racing against time, juggling large amounts of content, and working within pacing guides that constantly signal how far behind they might be. Under those conditions, the response is understandable: “Nice idea, but no thank you.”  

We believe that teaching foundational skills while teaching grade-level math requires creating classroom conditions where all students can share their thinking, make mistakes, and learn from one another. So, the question becomes: what kind of professional learning helps teachers create that kind of classroom? 

In our work with middle schools, we provide PD/PLC opportunities that strengthen teachers as mathematicians, not just as lesson facilitators. Our approach bolsters educators’ knowledge and skills in key algebraic readiness standards through active practice of the habits of mathematicians. Teachers actively engage in the habits that help students build a strong math identity both as learners and in their classrooms by (1) making thinking visible by encouraging students to share and reflect on their approaches while normalizing mistakes; (2) using feedback to guide deeper understanding and support self- and peer-evaluation; (3) fostering productive struggle so students persist through challenges and develop a belief in their ability to succeed; and (4) building a trusting classroom culture in which ALL students feel they belong in math, see themselves as experts in their own data story, and share authority for learning. These habits reinforce NCTM’s standards for mathematical practice.

This shows up in practical ways during our sessions. Teachers move around the room during error-analysis gallery walks, examining each other’s work and noticing patterns of reasoning, just as they would with student work. They practice asking assessing versus advancing questions, pausing to consider how their prompts not only gauge what students know (assessing) but can also push their thinking forward (advancing). They reflect on “learning pits,” the moments when students feel stuck, recognizing moments of struggle as opportunities to grow.  In every session, teachers examine student work closely and make sense of how students are approaching math.

As teachers deepen their practice of the habits of mathematicians, we are seeing promising shifts in instruction and student engagement. Teachers and district instructional coaches report strong satisfaction with this approach, describing the strategies as practical, immediately useful, and accessible for all learners. In a recent post-session survey, 100% of teachers said they were ready to try at least one strategy from the session. This work is laying the foundation for classrooms where student thinking is visible, valued, and extended. In communities built on trust, students are supported to share ideas, reason aloud, and build the confidence to engage with complex mathematics.

School leaders play a critical role in strengthening math instruction by ensuring teachers are prepared to support students effectively. Professional learning should go beyond curriculum implementation and content mastery to help teachers challenge deficit-based assumptions about prerequisites, refine their own mathematical thinking, and practice the habits of mind they want students to develop. This honors the fact that every student enters the classroom with valuable assets, experiences, and mathematical ideas, and meaningful instruction builds from there.

Teaching foundational skills while advancing grade-level content is not a contradiction, it is the work to be done. Educators don’t have to choose between addressing unfinished learning and teaching grade-level math. We say, content does matter, but what matters just as much, is how we encourage and equip students to engage with that content. When we build on what students already know and support teachers to think like mathematicians, both can happen together, in the same classroom, every day. Supporting educators to make these shifts in ways that strengthen teaching, expand access, and open new possibilities for student success in algebra and beyond is the promise of our work.