Building Students’ Confidence and Understanding in Math

The phrase I hear most often in my secondary mathematics classroom is not “This is hard.” Instead, I hear a lot of students say, “I’m just not a math person.”

Sometimes students say it before we have solved a single problem. Often, they are repeating a belief they have carried for years.

After more than 15 years of teaching mathematics across middle and high school, I have learned that some of my most important lessons are not found in a textbook. They emerge when students work through an equation they don’t understand yet, revise an incorrect graph, defend a solution strategy, or finally make a connection between a mathematical idea and the world around them.

5 LESSONS MY MATH CLASSES HAVE TAUGHT ME ABOUT LEARNING

I’ve learned so much in my time as a math teacher, but the following five lessons have changed the way I view learning in the classroom.

1. Mathematical confidence can be built in small moments. While there are definitely some students who are naturally more confident in math, those who aren’t can build their confidence over time. In my own classroom, I’ve worked to help my students build confidence by giving them opportunities to experience success in the process of problem-solving.

For example, if a student isn’t sure how to approach a word problem or graph, rather than immediately stepping in to tell them where to begin, I ask questions like “What does this equation tell us?” or “What does the intersection represent?” or “Which part of this problem looks familiar?”

Usually, students can at least begin to answer one of these more straightforward questions, giving them the confidence to continue working. By breaking down a complicated problem into smaller pieces, you can help students learn to trust themselves to begin, even if they aren’t sure of every answer.

2. Productive struggle helps students build their understanding. As teachers, we know that when students more actively uncover new information and connections, they are more likely to understand and remember it. That is why allowing students to engage in productive struggle is so important: If we always tell them what strategy to use, they may not understand what makes it useful.

In my classroom, I like to give students a problem that they can partially solve using their previous knowledge, but let them uncover for themselves that they need a new strategy or tool to get to an answer. From there, I can introduce new concepts, and students actually understand why the new information matters.

3. Identify foundational gaps. As a secondary math teacher, you can’t ignore the importance of foundational skills: A student struggling with Algebra II functions may need support with fractions, or a student struggling with exponential equations may need to revisit the laws of exponents.

When I notice a student repeatedly making the same kind of error, I try to trace it back and find the foundational skill that they may be missing. I ask myself what prerequisite concept the given problem is building upon, and from there I can review or reteach the necessary skill with an individual, a small group, or the whole class.

I’ve found that this is often more effective than just giving students more of the same problem to work on. If they are missing a foundational skill, reteaching that skill can unlock their ability to access grade-level material in a way that more of the same practice may not.

4. Encourage students to ask “why.” Across all my classes, my students are constantly asking why: Why does multiplying two negatives produce a positive? Why does the quadratic formula work? Why is the slope of a vertical line undefined? Why does changing an exponential function’s coefficient affect its graph?

These are not interruptions to mathematics. They are mathematics. I not only allow my students to ask these kinds of questions, but actively encourage them to think about the why behind what we are learning. In each of my units, I choose one formula or procedure and ask students to explain why it works. They can use graphs, numerical examples, visual models, or algebraic arguments to justify their thinking.

Because students have to explain the concepts in their own way, they build a much stronger understanding and are more likely to remember the rule they are justifying.

5. Give students precise praise. The kind of praise we as teachers give our students can impact how they see themselves. For example, if a student is struggling and they hear me tell another student that they are “good at math,” the struggling student might feel resigned that they will just never be good at this subject.

Instead, if a struggling student hears me give another student praise like “Drawing a model is a great first step to get started” or “You really persevered through that challenging content,” the struggling student might think that they are capable of doing those things too.

By intentionally replacing generic praise with specific, behavior-based praise, I can help show my students that they are all capable of earning praise and improving. You can try this out in your classroom by praising a student’s strategy, representation, question, explanation, or persistence.

Ultimately, I don’t want students to leave my classroom remembering only how to solve a quadratic equation or find the derivative of a function. I want them to remember what they learned while solving it: that unfamiliar problems can be approached one step at a time, that not knowing the answer yet doesn’t mean they can’t learn it, and that they can change how they see themselves as mathematicians.