All My Students Are Smart: Competency in the Math Classroom

In my content seminar, we have been talking a lot about mathematical competency. This was inspired by Ilana Seidel Horn's book, Motivated, where she talks about various ways to make math class fun and engaging for every student. We started talking about this by asking: What competencies are valued in your math classroom? This led to my guiding question: When you look at your class roster, can you identify at least one way that makes each of your students mathematically smart? 

Teachers Value Correctness Over Critical Thinking 

In my own educational experience, both as a student and in observation, teachers have cared much more about if students obtain the "right" answer than if they ask good questions relating to the topic at hand. A question that could yield a "wrong answer" or something other than what the teacher has planned for the lesson is often met with "No....." or "Well, I don't think....". Why are we so quick to redirect students when they ask good questions? Is this aspect of critical thinking not a fundamental part of mathematics? 

When a student asks a good question about the content, it is worth discussing. For example, if a student finds an alternative method to solving an equation, then instead of shutting down the student's ideas, it is worth exploring the student's method of thinking. Other students may benefit from seeing a different way of thinking, while the teacher's exploration of different ideas will encourage students to share their thinking more often. 

When we look at our students, we are often met with frustration due to their lack of "understanding" of a topic. However, we define understanding of mathematics in a completely different way: of course we will have understanding of the topic, we have a degree in mathematics! What if, instead, we looked at our students in their potential to ask questions? Instead of judging our students for their lack of mathematical fluency and ability to produce the correct answer immediately after a lesson, we should be focusing on their ideas and the questions they produce to guide our own teaching. 

What Classifies Students as "Smart?" 

Typical Definitions 

I often find myself falling into the trap of labeling students as "smart" due to their procedural fluency rather than their ability to think and reason mathematically. This is the same way most teachers define their "smart" students: If a student quickly understands the material, if they are always answering questions, if they are helping other students, then they are automatically labeled as "smart." Of course, these students are intelligent and they should be applauded, but what teachers often do is maintain faith in these students and compare them to their other students, which leads to frustration. Teachers may be thinking to themselves, "_____ understands the material. Why can't my other students?" 

The danger, then, in defining our students as "smart" or "struggling" is putting them into a box. Of course, we must identify students' misconceptions in order to best help them. However, if we always label a student as "struggling," we will lose confidence in them, causing them to lose confidence in themselves. Conversely, if one of our "smart" students is struggling, we may pay less attention due to their understanding of other topics. Either way, we risk not helping our students to the best of our abilities due to pre-defining them. 

All my Students are Smart 

I admit, it is incredibly difficult for me to get myself out of the trap of putting these labels on my students. I find myself relying on one of my students in my fourth hour to answer questions, since he is "smart" and is even going to be in the honors section of mathematics next year. Conversely, I have found myself losing confidence in other students, since they haven't previously had procedural fluency in doing problems. 

However, it is important to continuously challenge myself in seeing the strengths in ALL my students, and seeing how smart they all are mathematically, even if they do need extra support in their understanding. For example, I have a student in second hour who has very little motivation and some days outright refuses to do his work. He is also a "problem student," and he has been suspended multiple times for various infractions. It's very easy to lose hope in this student, and to tell myself, "Oh, he'll never get it, so why even try?" But, how can I begin to see how this student is mathematically smart? He is great at visual reasoning, as I have noticed when he is working with other students. Additionally, he has a lot of social prowess, and if he gained scaffolding in explaining his work, perhaps he could learn to help others with their work. While I'm no expert in this student's life and I would have to learn more about him in order to determine how to boost his morale, this brief glimpse into who he is and what makes him intelligent is a good way for me to gain confidence in him. 

As another example, I have one student in my fourth hour who, grade-wise, could be labeled as "struggling." However, when I listen to him reason about mathematics, he has great critical thinking skills and amazing visual reasoning in math problems. I asked him one day why he didn't complete the homework, and he said, "Well, I can do it in my head, so why would I write everything on paper?" This was a great insight into what makes him intelligent: While he doesn't do his homework and wouldn't be considered as "smart" by most teachers due to his academic progress, I can see his strengths and thus this has helped my confidence in him. 

When we start viewing all of our students as people with potential and the ability to critically think about mathematics, rather than as in a box of "smart" or "struggling," we are able to gain insight into how they are as students, and how we can help them. We cannot give up on our students, and we must focus on helping everyone! Realizing that all of our students are smart and bring a strength to the classroom is a good way to begin doing that.