Key points:
- Young students are capable of far deeper mathematical reasoning than we sometimes give them credit for
- Why so many students struggle in math before learning even begins
- The future researcher in every fifth grader: The case for curiosity-first teaching
- For more news on math trends, visit eSN’s Innovative Teaching hub
My first graders ended this school year asking for more math.
I know—I am still surprised myself, not because I ever doubted my students (in my decade of teaching, that has never happened!), but because I spent years teaching in a system that made math feel like something you either got or you didn’t. Not everyone can be a “math person” … right?
What I’ve learned this year is that in math, a student’s final answer can only tell you so much.
In first grade, educators shape the trajectories of how students feel about math. Long before they discover algebra or standardized tests, six- and seven-year-olds are forming beliefs about whether they are “math people,” if their ideas are worth sharing, and what their mistakes say about them as learners. These beliefs are hard to undo later, which means what happens in first grade matters more than we sometimes acknowledge.
For most of my career, math instruction looked like most classrooms: I taught a lesson, students solved problems, I checked answers. My classroom culture has always been positive and relationship-driven, and I know my students well. That said, with a very structured math curriculum and limited time for instruction, I, like most early education teachers, often have an incomplete picture of where every student’s understanding is.
Written (or digital) work can only tell you part of the story. First graders are still building writing stamina, fine motor skills, vocabulary, and confidence. Some know exactly what they mean but cannot yet get it onto paper. Others can complete a math worksheet with 100 percent accuracy but cannot explain why an answer makes sense. A few may get the wrong answer using a strategy that is actually quite sophisticated, one small misconception away from getting it right. If I only look at students’ final answer, I miss all of that.
Research from NCTM shows that young children build stronger math understanding when it connects to their everyday lives. This year, we incorporated more play-based activities tied to things my students know well, like measuring ingredients for a recipe and tallying prices in a pretend toy store. Once math felt like part of the world they already knew, rather than something abstract and separate, learning it actually became fun.
As educators, we often hear what gets measured is what gets taught. In math, especially with limited instructional time and resources, it can be more efficient to skip right to the answer-getting. For young learners, there is so much value in the in-between. This year, I made an intentional shift in my math lessons to regularly ask students to explain their thinking out loud as they worked through problems.
For example, a recent money lesson was a huge hit. Students paired up, each pulled five coins from a bag, counted the value, and compared totals. Whoever had the larger amount won. Then each student recorded a short video explaining how they knew what their coins were worth. This part has been the game changer for my practice.
When I listen to student explanations, I hear things I would never have caught on paper. I heard a student who knew the value of each coin but lost track while skip-counting. I heard several students who were confusing dimes and nickels, not because they didn’t understand value, but because the coins look so similar. I heard another child explain a strategy for adding the total value that was different from the one I had just taught.
Sometimes I watch their videos two or three times because they surprise me. You can literally see something shift as they explain math out loud in their own words to an imagined audience. They start using vocabulary more intentionally, demonstrate confidence as they share with each other, and understand that talking about math is just as important as “doing” math.
In terms of the growth I’ve seen, one student comes to mind immediately. Jazelle is bright, hardworking, and perceptive. At the start of the year, she was reluctant to share what she knew through written work or raising her hand in front of the class. When I watched her first recording, I saw something different. She introduced herself, set up her coins, and walked through her reasoning like she was hosting her own show. She was confident, funny, and ended her video like a TikTok star (“thanks for watching!”). Talking through her thinking gave her another way to show what she understood and once she knew that pathway existed, she really thrived. By spring, she was one of the students asking for more math time.
Making student explanation a regular part of our math practice required intentionality. It needed to be taught, modeled, and made safe. I could not have achieved the shift I saw with a one-off tool or strategy; I had to evolve my practice and get comfortable testing to find what worked. Some students required sentence starters while others needed more time with manipulatives before they were ready to share. Ultimately, we built a culture where students felt safe sharing and making mistakes without feeling like those mistakes defined them.
The technology I used this year captured and analyzed student explanations, which allowed me to “hear” every student in a way that I simply cannot do in real time. With a class of around 20, there’s not enough time in the day, let alone a single lesson, to pull up a chair next to each student and catch misconceptions the moment they happen. After revisiting explanations, I was able to respond faster and identify common patterns and misconceptions across the class.
As AI continues to evolve and make its way into more classrooms, I can tell you that teachers do not need tools that replace our judgment or tell us how to teach. We need supports that help us see our students more clearly so we can use our judgment more effectively. One thing I hope others can learn from my experience is that young children are capable of far deeper mathematical reasoning than we sometimes give them credit for. They will show us if we give them the right conditions to share it.
When a child who began the year hesitant to participate starts asking for more math, that means everything. She was always capable, but she needed the chance to see, hear, and believe it for herself.