It all began when I released my third-grade scholars to produce a model for their first math journal in which they had to represent how many legs were on three cats. I had carefully planned my lesson, strategically partnered them during work time, chosen a student to model their thinking for the rest of the class, and checked in for understanding. This was going to be great!
And then it started—the heads down, the hands up, “I don’t know how to do this!” “What does this even mean?” “I suck at math, I can’t do this.” My heart sank. I knew that helping my students experience opportunities to engage with grade-level thinking tasks linked to representations could help them grow their conceptual understanding of operations and numbers, so why did this feel like such a bust?
The enemies that undermined the lesson were the students’ lack of confidence and the presence of math anxiety—two well-researched and documented monsters that live in many a math classroom’s closet. There is much professional development about the “right way” to change these negative feelings in the classroom, but I found an effective daily routine that helped change my students’ perception of themselves, affirmed their thinking, and pushed them for their next steps in learning: cycles of feedback.
Feedback in Action
My journey of incorporating feedback this year has been one of growth and learning. I began with an action research project to see how students connecting representations to procedural and abstract ideas in a math journal would grow their confidence. When I started, I struggled to confer with even three students per session. There were two reasons for this:
- I was physically writing feedback (a glow and grow) for each student I spoke with.
- There were so many hands up before students had even tried to get started.
Students had such little belief in their own abilities that they weren’t even willing to put anything on the page or pick a manipulative to help them until someone else had affirmed their idea. To reach more students, I began to shift my feedback from written to oral. This was when core questions came into play.
Core questions is a term I first saw in the book But Why Does It Work? A core question addresses conceptual understanding rather than recalling information, and it encourages deep connections between context, representations, and number sentences.
For example, rather than saying, “What was the number of groups you made?” I would ask, “Where do you see the factor x in your model?” This questions the students’ understanding and offers a connection between conceptual and procedural knowledge. Additionally, your questions could address the Standards for Mathematical Practice, which helps build mathematical thinkers. The important thing about core questions is that they are planned, so you avoid those in-the-moment leading or recall questions.
Here are some examples of core questions:
- Where do you see addition in your representation?
- What does the denominator represent, and where can you see this in your thinking?
- What strategy did you use? How could your reader see this in your visual?
- What tool did you choose and why?
The Shift From Panic to Problem-Solving
As time went on, I saw a shift in my students. They began to get started on their tasks right away because they wanted feedback, adjusted their thinking, and took more academic risks after their conference. What I realized was that while this was great, I had no evidence of data from this oral feedback. This was where I made my final shift in practice and began coding along with my oral feedback.
We agreed as a class that a star would indicate where I saw their thinking and had affirmed it: “I see you were able to accurately represent your numerator,” “I notice that you chose to decompose this factor into 3 and 10,” or “I see that you chose to use an area model to solve this problem.” I also told them, “A pair of glasses (they knew how much I love the Harry Potter books) is where I want you to focus based on our conferring.” This not only gave me the opportunity to talk with them but also gave me the chance to look back over where the glasses were and see if they had made adjustments based on our discussion.
The data I collected at the end of three months to measure confidence showed a noticeable shift:
- Students who raised their hands for help before attempting went down from 42 to 11 percent.
- Students who remained on task for a duration of more than three minutes without prompting went from 23 to almost 100 percent, with 75 percent of students at the end of the three months of data collection remaining on task for the entire time given.
- One hundred percent of students included a model to represent their thinking when appropriate to the learning task.
By utilizing coding while giving oral feedback, I’m now able to reach almost all 18 of my students in a 10-minute period of time in each of my three sections daily. That’s 52 affirmations and 52 pushes every day. It requires no extra time on my weekends and leaves students feeling accomplished and intelligent. This practice also gives me the opportunity to address trends of misconceptions on the spot rather than planning an entire reteach.
The goal at the end of my project was to see an increase in student confidence as measured by anxiety, efficacy, and self-concept. What I saw happen in our math classroom was a complete shift from learned helplessness and the need for affirmation to students’ believing in their own abilities and being willing to take academic risks and try at least one strategy before asking for help.
How Can You Get This Started?
The next time you’re planning your math lesson, examine the task your students will be working on and start by doing the math yourself. Think about possible student responses. What questions might you ask that will help them connect context to representations? What questions might help them explain their use of an operation? In doing this, you can begin to plan your own core questions. Keep them in your pocket on a note card so you don’t lose them in the moment.
Next, check in with students who have started right away. This will encourage other students to try on their own because, let’s face it, we all know they want their individual moments to shine. And of course, save the best for last and watch as your mathematicians begin to increase in confidence, decrease in anxiety, and become independent problem solvers.