I did not become deeply interested in mathematics because it always came easily to me. My interest grew from trying to understand why it had not.
For much of my early education, mathematics felt like something I was expected to perform correctly. I could memorize rules and follow procedures, but my understanding often felt fragmented. It was only when I decided to pursue computer science that I realized I needed to take my mathematical foundations more seriously.
When failure became information
Programming changed my relationship with not knowing. When my code failed, the failure gave me information. I could inspect the output, locate the error, revise my reasoning, and try again. Confusion became part of a feedback loop rather than proof that I was incapable. I began wondering why mathematics had rarely felt the same way.
CTL1120, Effective Teaching Strategies in Elementary Mathematics: Research and Practice, gave me research through which I could revisit that question. In my final paper, From Debugging Code to Debugging Mathematical Thinking, I explored how self-regulation, mathematical identity, classroom discussion, and conceptual language shape a student’s ability to learn mathematics.
Teaching students what to do when a strategy fails
Zimmerman’s work on self-regulated learning helped me recognize the habits I had developed through programming. I was planning, testing strategies, monitoring results, and reflecting before trying again. These habits had often been expected in mathematics, but they had not always been explicitly taught. Students may be told to “show their work” or correct an answer without learning how to use that work to locate a misunderstanding.
A student who says, “I am not good at math,” may actually be saying, “I do not know what to do when my first strategy fails.”
This distinction matters to me. That response is not necessarily a problem of ability or effort. It may reflect a learning environment that has not shown the student how to examine and revise their thinking.
How classrooms shape mathematical identity
Bishop’s research on mathematical identity added another layer to my understanding. Mathematics is not learned privately. Students learn who they are as mathematical thinkers through everyday classroom interactions: whose answers receive attention, who is considered naturally capable, and whether uncertainty is treated as curiosity or weakness. My own schooling had often associated mathematical competence with speed, correctness, and visible confidence. Under those conditions, asking questions could feel socially risky.
A few teachers disrupted that pattern. My advanced functions teacher, Mr. Francis, cared about whether our reasoning made sense, not only whether we reached the correct answer. Later, proof-based university courses showed me that uncertainty, debate, and revision are part of serious mathematical work. These experiences helped me see that struggle does not automatically damage confidence. What matters is how the learning community interprets and responds to it.
Making reasoning visible through talk and language
The course also introduced me to Fuson and Leinwand’s work on Math Talk Classrooms. When students explain, compare, and defend strategies, their thinking becomes available for examination. They can begin to see that mathematics is not simply a race toward one correct answer. It is a way of reasoning with others.
Sarina’s critique of mathematical definitions helped me identify another source of my earlier confusion. Words such as simplify, reduce, factor, solve, and evaluate had sometimes seemed interchangeable in school. In university mathematics, I discovered that definitions were not minor pieces of vocabulary. They were anchors for reasoning. Students cannot effectively monitor their understanding when the language surrounding a concept remains unstable.
From personal experience to research questions
My own learning experiences strongly influence my interest in mathematics education research. They lead me toward questions about students who can follow a procedure without understanding why it works, students whose performance hides what they know, and students who interpret confusion as evidence that they do not belong. At the same time, research helps me move beyond treating my experience as universal. My experiences give me questions; research gives me ways to investigate them more carefully.
CTL1120 helped me reinterpret my mathematical history. I no longer see my earlier struggles as evidence that I lacked mathematical ability. I see how intuition, self-regulation, identity, language, and classroom culture developed unevenly across my education.
This is what continues to draw me toward mathematics education research. I want to understand how we can create learning environments in which students do more than produce answers. They should learn how to notice what they understand, identify where their reasoning breaks down, and revise their thinking without experiencing confusion as failure.
In other words, I am interested in how we can teach students to debug their mathematical thinking while still seeing themselves as capable mathematicians.