Math Questions Grow Brains: Students Learn Through Curiosity, Not Criticism

Jamie Arreola
Jun 17
6 min read

Oh, That Middle School Math!

Middle school brings out big feelings for all of us. Parents often feel pressure for their children to succeed in school. For them, their child’s grades may represent what they perceive as their child’s effort or intelligence, or may even represent their child’s future success. For other parents, middle school may stir up memories of their own experiences, some which are not pleasant.

I have a few middle school nightmares of my own. They include humiliating memories of being dismissed by my pre-algebra teacher, when I asked for help with math. He repeatedly ignored me, saying, “Girls are better at English. Boys are better at math. Don’t worry about it.”

But I was worried as a kid. I wanted to learn and achieve in math, but I did not have the proper tools or teacher! Being pushed aside by respected math teachers during my own middle school experience stuck with me well into adulthood.

My Recent Full-Circle Middle School Math Experience

Well, I have come full circle. I recently completed a teaching job for a trimester as a middle school math instructor. The time had come to face my past, confront the pain and shame I experienced as a tween, and attempt to become the math teacher I never had.

First, let me admit that I was none too keen on teaching middle school math. It seemed akin to putting a “Kick Me” sticker on my own back. Everybody knows that nobody likes middle school math! I knew I had to challenge that assumption. I feared it would be similar to being in an extended episode of The Middle, and I would be the ever-trying, never succeeding sister, Sue Heck, never winning in the math classroom.

As I began to preview the curriculum, I was filled with nervousness, remembering the challenges that middle school math gave me, and also, how the teachers made me feel stupid, incapable and unworthy as a student. I had to shake that feeling first, before I could effectively teach. First I had to relearn everything from the viewpoint of curiosity.

Math is Fun !%$*

You won’t believe it, but math on my own terms has actually become such fun! All of the pressure I felt as a child has vanished. I had to first adopt a new attitude, which was something like, “ I am bright and capable. I can learn this so well that I will be able to teach it!” Please add here a visual of me making all of the rock star hand gestures, facial expressions and head nodding to go with my 1980s kid experience. And that is what I did! I got into math and conquered it. Actually math has not been wholly conquered, but I am a few steps ahead of the kids, which all teachers, parents and coaches know is the ticket! It all came back to me once my stress level was lowered. This is key for all learners. When we lower our stress filter, and boost our curiosity, we learn better!

I was determined to break that stereotype of, “You either get it or you don’t”, and to help all of my new students reach for their personal best in math and in life.

My Math System

Once I got the hang of teaching math, I put a system in place that all students could follow, and any math teacher or tutor could understand. In my math class, we use three main steps to solving any math problem.

First, there is the math problem itself. Math requires reading words and symbols, and taking notes: Problem. Here is where students interpret the question and take notes.

Next comes the computation: Solve. Students show their work and write down the answer pieces as they go.

Last, is the final answer with labels: Solution Key. My students label their steps, show what they are thinking and how they did each step, and they box their final result in the Solution Key.

This three step process, with many substeps at each level, allows for a record of what the student did to solve, and leads to a robust discussion about HOW each student is thinking about the problem and what they are trying in order to arrive at a solution. Best of all, this process allows me to reteach at the exact point of error, and give partial credit for correct steps within the process. It requires that I examine classwork, review homework, and grade tests promptly, so feedback happens in real time as much as possible.

This trimester, I was able to talk my students into showing their work, and explain why showing their work matters. When a student shows me their work, I can see through the student’s eyes. I can see what they were thinking, where they got confused, and what part of the process needs support.

Instead of saying, "That’s wrong. You need to redo it, I may say, "Show me how you got there."

Showing Work Builds Confidence

The invitation for students to show me HOW they got to their solution, (or how they got stuck), is changed everyone’s attitude; mine and the students I taught. It moved students from shame to becoming problem-solvers. I started by saying,” Let’s go over this quiz. Take notes, ask questions, and pay attention.” Then after growing my students' math skills on the subject I asked,” Who would be willing to take this quiz again and try to do even better?” Almost every hand started shooting up, and smiles crossed the faces of even my struggling students. Repeat after me, “Failure is not an end. It’s a checkpoint!”

When students, parents and teachers only care about the final answer, students are tempted to copy answers from a reliable friend, guess, or hide their confusion. But because I decided to value their thinking process, students began to learn that their steps matter. A math mistake is not a character flaw. It is just information. When we (teacher and student) can see the misstep, we can find a way back to the path.

Guide, Don’t Shame

A critical teacher shames their pupil with, "Why didn’t you know this?" or, "everyone else understands." And the ever-popular, "You’re not paying attention." This makes students feel embarrassed and defensive. By middle school, as 11-13 year children, some students have already stopped trying. Others have become good at copying, (I never say cheating), just to avoid being judged. (By the way, I have observed that most kids don’t copy answers because they are lazy. They copy to please their parents and teachers, and to save face around their peers. They don’t want to let us down. They are copying to cope, because they don’t know how to arrive at the correct answers YET.)

A growth-focused teacher will get curious, and ask, "What did you do first?" and, "which step feels confusing?" or, "what could you try next?" These questions help students self-correct.

The Goal Is More Than a Correct Answer

In math, the final answer matters, but the process matters even more. When students learn to show their work, explain their reasoning, and review their steps, they become stronger thinkers. They learn that they can find and correct mistakes, improve their procedure, relearn, try again, And that they don’t have to be perfect to learn.This builds resilience, honesty, and independence.

Encouragement Creates Effort

For teachers, encouragement is not pretending everything is correct. It is giving credit for partial learning, and keeps the students following the path towards improvement and mastery. Encouragement sometimes sounds like, "You had the right first step." and "you organized your work well,”or, "you caught your own mistake." Students especially like when I include an invitation to continue such as, "Would you like to look at the next step together?" Students need adults who can highlight what is working while gently guiding what needs correction.

From Copying to Thinking

When students feel judged, they may look for shortcuts. They may copy the answer because they think the goal is to look right. But when students feel safe, they are more willing to show unfinished work, ask questions, and learn from mistakes. That is where real learning happens. If you are a teacher, a parent, a tutor, a coach, or anyone working with students towards improvement, I give you a challenge. This week, try asking a student, "Can you show me your thinking?" Then listen carefully. Their work may show you exactly where to begin.

The Lessons Still Apply

Although you may not be a math teacher, the lessons here may still apply, including, ”Show your work. Get curious. Grow your brain. Show your children, employees, friends and loved ones that it is human to make mistakes, and to learn from them. Keep trying. It is okay if you don’t know how, YET.”