I Almost Failed My Rutgers University Job Interview Over a Quadratic Equation That Had No Real Zeros

I was 25 years old when I interviewed to become an adjunct professor at Rutgers University. I remember walking into that interview knowing I understood mathematics, but also knowing exactly where I was. This was Rutgers. I was young, I was interviewing to teach at the university level, and the person interviewing me was the department chair who also happened to be a former mayor of his town. Go figure.

At some point during the interview, he walked over to the chalkboard. And yes, we were still using chalkboards. LOL. He wrote a quadratic equation on the board from the top of his head and asked me to find the zeros.

Okay. Cool. I know how to solve a quadratic equation. So I started working. Except the numbers were not doing what I expected them to do.

I tried factoring it one way. Nothing. I looked at it again. Tried something else. Still nothing. And the longer I stood at that chalkboard, the more my brain started doing what brains sometimes do when somebody with authority is watching you work.

I started questioning myself.

Now, I knew there were quadratic equations that could not be factored over the real numbers. I knew that. But standing there at 25 years old in a Rutgers interview with the department chair watching me, suddenly I was wondering if I was missing something obvious. Was this a trick? Did he intentionally give me something difficult to see how I would respond? Was there some method he expected me to use that I was overlooking?

Meanwhile, internally, I am shitting bricks.

There is something very humbling about knowing mathematics and then being asked to demonstrate what you know in front of someone who has the power to decide whether you belong in the room. The mathematics you understood five minutes ago can suddenly start looking very different when your confidence gets involved.

Eventually, I stopped trying to force the equation into doing something it was not going to do. There were no real zeros.

And here's the funny part. He had written the problem off the top of his head. Neither one of us knew when he put it on that chalkboard that it wasn't going to factor nicely. I had spent all that time wondering whether he was testing me when, in reality, the mathematics was simply the mathematics.

I got the job. But I have thought about that moment many times since then, especially as my career has taken me from teaching mathematics to supervising mathematics instruction, writing curriculum, coaching educators, leading professional learning, and building my own company.

Because the part that stays with me is how quickly I questioned something I knew because I assumed the person standing across from me must know something I didn't.

Now here's the mirror. 🪞 There are educators doing some version of this every day. They know more mathematics than they give themselves credit for, but the moment they are sitting in professional development, talking with a coach, standing in front of a supervisor, or working alongside someone they perceive as more knowledgeable, their confidence changes. Suddenly, they are second-guessing reasoning they would have trusted five minutes earlier.

And I think leaders have a responsibility here too. When we enter a room with a title, credentials, years of experience, or subject matter expertise, people can automatically assign certainty to us that we may not actually have. Expertise does not mean we always know the answer. It means we have enough knowledge, experience, and intellectual honesty to stay with the mathematics when the answer is not immediately obvious.

That matters in our classrooms too.

Students are constantly reading us to determine who knows mathematics and who does not. They are also using those observations to make decisions about themselves. When one student solves something immediately and another needs more time, the student who needs more time can start telling themselves a story about what that means. When an educator moves quickly past confusion or treats uncertainty like failure, students notice. Before long, “I don't know yet” becomes “I'm not good at math.”

I was 25 years old, had studied mathematics for years, and was qualified enough to be interviewing to teach it at Rutgers University, and one stubborn quadratic equation still had me questioning whether I knew what I was doing.

Imagine being 14.

That is why I think confidence in mathematics deserves much more attention than we sometimes give it. Confidence is not pretending you know something you don't. It is being able to sit in uncertainty long enough to use what you do know. It is being willing to try a method, examine the result, change direction, ask a question, and keep thinking without interpreting every moment of confusion as evidence that you do not belong.

The same is true for educators.

I have worked with educators who are brilliant with students but become quiet around colleagues they perceive as more mathematically knowledgeable. I have seen people abandon good reasoning because somebody else sounded more certain. I have watched titles and credentials change the way people participate in conversations before anyone has even done the mathematics.

That Rutgers interview reminds me that expertise and confidence are connected, but they are not the same thing. Expertise grows through study and experience. Confidence grows through having opportunities to use that expertise, question it, strengthen it, and discover that not knowing something immediately does not erase everything you already know.

And character enters the equation when we become the person in the room who does know more.

Whether we are professors working with future educators, leaders supporting mathematics educators, or educators standing in front of students, our knowledge has an impact on the confidence of the people learning around us. We can create environments where people are afraid to expose what they don't know, or we can create environments where uncertainty becomes an invitation to think.

Looking back, I am glad that quadratic equation did not factor.

If it had been an easy problem, I probably would have solved it, finished the interview, gotten the job, and forgotten all about it. Instead, that chalkboard gave 25-year-old me an experience I can still see clearly years later. I walked into that interview knowing mathematics.

For a few uncomfortable minutes, I forgot to trust that.

DOPE MATH® in Practice

Subject matter expertise is not just about what you know when everything feels familiar. It is also about what you do when the mathematics, the environment, or even your own confidence makes you pause. If we want to become stronger mathematics educators, we have to intentionally create opportunities to strengthen both what we know and our ability to trust and use that knowledge.

Put This Into Practice

1. Do mathematics you haven't prepared for. Give yourself unfamiliar problems and work through them without an answer key sitting beside you. Pay attention to what happens when you don't immediately know what to do. Where do you begin? What do you notice? What knowledge do you pull from?

2. Start with what you know. When you're stuck, resist the urge to immediately focus on everything you don't understand. Identify the structure, properties, representations, or relationships you recognize. Give yourself somewhere mathematically familiar to begin.

3. Practice more than one approach. If you only know one pathway through a concept, an unfamiliar problem can shake your confidence quickly. After solving something, ask yourself, “How else could I approach this?”

4. Get comfortable saying, “Let me think about that.” Subject matter expertise does not require instant answers. Sometimes expertise looks like knowing how to investigate when an answer is not immediately available. Give yourself—and your students—permission to think.

5. Pay attention to what is actually making you doubt yourself. When you begin second-guessing yourself, stop and ask: Is it the mathematics? Or is something about this person, environment, or situation making me question mathematics I actually know?

There will always be more mathematics for us to learn. That's part of being a subject matter expert. But becoming a stronger mathematics educator isn't only about adding more knowledge. Sometimes the work is learning to trust, access, and use the knowledge we've already worked so hard to build.

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