As a math coach, my work with my fellow educators involves providing support with developing conceptual understanding in students. As we work to develop this conceptual understanding, the teacher gains a deeper understanding of effective mathematics pedagogy. One day, a teacher I was working closely with commented on students’ lack of willingness to engage: “How do you get kids to engage? It’s not realistic to constantly prompt them. How do I help my students feel like they’re capable of learning math? Some don’t engage and some get discouraged easily. How do I empower them to keep trying?”

I recognized the challenge my colleague was facing. Perhaps you have encountered it in your classroom too. It’s called productive struggle. When students are not taught explicitly about productive struggle, it is very challenging for them to manage the emotions they experience when learning new content. If the frustration becomes too great, the proverbial ‘shutdown’ occurs. Of course, no new learning happens during the shutdown. This can be the beginning of a vicious cycle. Students may begin to see themselves as incapable of learning math. As such, engagement may wane and less-than-optimal learning occurs. Over time, this affects students’ identities. Hence the phrase, “I’m not a math person.” 

To break down that cycle, we need to build up our students’ confidence about math. The following mini-lesson was designed to promote a positive math identity for our students and show them that they are capable of learning math:

1. First, I invited our students to draw pictures of a ‘reader.’ They all started drawing quickly and confidently. Many drew themselves, which was exciting because we want our students to see themselves as readers! Next, I asked them to draw a picture of a ‘mathematician.’ There was a stark contrast –  students hesitated. They didn’t draw themselves. They questioned what mathematicians do. I responded to their questions by asking, “What is a reader?” Without hesitation, they responded, “A reader is someone who reads.” I asked, “Then what is a mathematician?” But they were unable to answer. They needed some time and a shift in perspective before they could land on the idea that a mathematician is simply someone who does math.
2. Next, we watched a quick video from math educator Jo Boaler titled, “Boosting Messages From ‘How To Learn Math for Students.’” The video briefly explains four important research findings: 1) everyone can learn math, 2) self-belief is important to learning math, 3) struggling and mistake-making are necessary parts of learning math and 4) speed is not important to learning math. As we debriefed the video, students began to identify behaviors that mathematicians use while engaging with mathematics, such as thinking deeply, reasoning, predicting and making connections. We discussed the ways that the students used many of those same behaviors to read (making connections, predicting, asking questions, etc.), and then we got ready to examine their behaviors in math class.
3. I asked the students to reflect on their recent experiences at the math station set up in the classroom. Together, we listed the actions they took at each of the four stations: Math with the Teacher, At Your Desk, Teamwork Math and Hands-On Math. As students discussed the tasks at each station, they began to recognize that the steps they had taken – such as thinking deeply, reasoning, predicting and making connections – matched the behaviors of mathematicians. This led them to conclude that they were, in fact, mathematicians!

This mini-lesson is a great first step in making our students feel empowered to learn math. However, we need to help students develop their mathematical identities all year. That’s why I recommend these two additional strategies for encouraging students to see themselves as mathematicians. These can be used at any given point in time – from exploring new concepts to demonstrating mastery.

Exploring new concepts:

Focusing on engagement rather than concept attainment is key, particularly when new concepts are introduced. New concepts may seem daunting to some students, so it’s critical for them to explore these problems without worrying about whether they get ‘the right answer.’ I suggest starting with questions that have no right or wrong answer, such as “What do you notice?  What looks new? What seems confusing?”

When a student shares, it’s absolutely critical to validate their thinking. Offer feedback that affirms the behaviors of a mathematician: “You’ve found a relationship between those numbers, and that’s something mathematicians look for.” When another student chimes in, you might say, “I love how you’re seeing this in a different way because mathematicians find so many different ways to reach solutions.” Listen carefully each time a student speaks because, as you do, you’re receiving more information about how they’re processing the new concept. Essentially, this is a formative assessment. Each time you speak, you’re using that information to guide them toward a deeper understanding. Not only are you engaging in responsiveness, but you’re also validating their ability to know, do and understand math; you’re co-constructing their identity as learners.

Assessing understanding: 

Historically, math education is primarily product-driven, not process-driven. However, a hyper-focus on answers may cause students to lose touch with their mathematical identities. Simply noting whether an answer is ‘right’ or ‘wrong’ makes it extremely challenging for students to go back to their process and figure out where their thinking went awry. 

This is why it’s essential to offer feedback during the formative assessment process to promote learning. The combination of students reflecting upon their own learning coupled with feedback allows students to learn from their own thinking rather than simply being instructed on a series of steps or procedures to follow. I often ask students to represent their thinking in many ways (numbers, visuals, manipulatives) and to accompany those representations with an oral explanation. Then, I ask questions that promote and validate thinking: “It looks like you used your estimating skills. Explain to me how you did that.” “I got lost in your process here. Did you make an assumption or did you use some math logic that you can walk me through?” I am always looking for opportunities to validate students’ thinking because validating their thinking ultimately leads to the creation of positive learning identities.

As you’re reflecting upon your own math pedagogy and contemplating your practice for this fall, I hope you’ll consider building this mini-lesson into your plans and encourage students to see themselves as mathematicians right from the very first day of school. I genuinely hope the questioning strategies shared here support your work from day to day – in developing your students’ math identities, boosting their confidence and inspiring their growth!