Whenever I meet someone new, and they ask me what I do for work, and I reluctantly (because I know what's about to come) tell them that I'm a math teacher, I am undoubtedly met with their story of math trauma and everything they dislike about our profession. It's usually followed by, "Why don't you teach people how to do their taxes?" To which I normally answer, "Do you ask art teachers to teach children to cut corners when painting a wall, or English teachers to skip the classics or grammar and get down to how to send a fun but professional work email?" It does, however, raise a deeper question: these people all saw the math they were being taught not only as boring and unengaging but also as pointless. Ultimately, what is our job? Is it to make kids good at algebra or to open the world to critical and curious thinkers? When we start to view our job as the latter and see the curriculum as a tool to unlock that potential, we see more engaged, excited, and happy learners.
People often think of practical and engaging as the same thing, which leads us to ask questions like this:
In Natasha's candy shop, chocolate, which sell for $4 a kilogram, is mixed with nuts, which are sold for $2.50 a kilogram. Chocolate and nuts are combined to form a chocolate-nut candy, which sell for $3.50 a kilogram. How much of each are used to make 30 kilograms of the mixture?
The natural response to this question is, "$2.50 a kg for nuts?! In this economy, I need to get her supplier." Alternatively, questioning Natasha's business sense: is she just randomly allocating sale prices and working backward to figure out her margins? What is this candy shop that deals in chocolate by the kilo? Notice that none of these thoughts that immediately spring to mind are “ahh yes, better set up a system of equations”—unless you're a math teacher, that is.
How Can We Foster Engagement?
Encourage Students to Feel Safe Taking Risks
Many students carry trauma into a math classroom, be it the high academic weight that the course holds, past failures imprinted on their memories, or the mathematical fear they've heard in the zeitgeist. Use these strategies to support your students' mental health in the mathematics classroom:
- Establish Classroom Routines - Knowing what's coming and daily predictability can help students be more relaxed in a space and move them out of fight or flight.
- Take an interest in your students - Build welcomes and farewells into your classroom routine. Talk to your students about their interests. What clubs are they a part of? Do they play sports? Watch TV? You don't need to know what they're talking about or try to shoehorn in a connection to your life; just showing you’re interested is enough. Remember, every day is a new day; hold no grudges.
Try this technique!
Empower Students to Take Risks - When providing students with math questions, give them the opportunity to self-select the difficulty of the problem (fig 1). I split my questions for that day’s concepts into three, sometimes four levels of difficulty. I ensure the labels of the levels don't resemble grades in any way, so level 1, 2, 3, 4 are out, as are ‘easy, average, and hard’. I opt for levels of spice: Mild, Medium, Spicy, and Extra Hot. I then ask the students to select where they think they are at today. This not only gives students choice, empowering them in their own learning but also promotes safety as the students will know there will never be a day in math class where they can't be successful in some way as they work toward grade-level standards. The knock-on effect is that when the students feel safe, they take more risks with their selections and challenge themselves routinely.
Encourage Students to Collaborate to Help Address Gaps in Knowledge
Collaboration embodies the Swiss cheese model, where each student is likened to a slice of Swiss cheese with knowledge gaps represented as holes. As these slices are stacked atop one another through collaboration, these gaps are gradually filled. By encouraging meaningful sharing, not only does the group collectively solve problems, but each student's individual knowledge gaps also shrinks and fluency increases. Explore these methods to create a community within your classroom:
- Randomize Groups - I start every one of my classes by randomly allocating students to seats. It's important these groups aren't pseudorandom, as this will not build trust in the classroom; the randomness is fair, and students soon adjust to working with all people in the space. Here's a Google sheet that will do it all for you! Make a copy and make it your own.
- Co-construct a list of classroom norms - When students create these, the entire classroom (including you) is held accountable. When a kid steps away from these norms, this document can be used to redirect the student.
- Encourage Sharing - When the students are working on a set of problems, and the goal is learning, not summative assessment, encourage them to share knowledge with each other. Scaffold for them what it looks like to support a student in understanding versus giving them the answer.
Fill in the Gaps - Specific practices involving group work and sharing can assist students in addressing gaps in their math knowledge and fluency.
Try these techniques!
Sharing the Pen - Limiting each group to only one writing implement that way, students are compelled to communicate effectively. A crucial aspect of this approach is that the student holding the pen cannot contribute ideas. This ensures that students who may be struggling with a problem are actively guided through every level of understanding.
Share Back - After individually solving a problem, prompt students to share their solution within small groups and explain the process they used. The goal is any group member should be able to talk through the solution. When serving as a facilitator walking the room, adopt the role of a toddler, constantly asking "why." Challenging mathematical assumptions held by some students and requiring them to explain promotes a deeper understanding and helps others fill in their knowledge gaps. Additionally, having students share their solutions can unveil new perspectives on problem-solving for the entire class.
One of my most hated clauses in the English language is, “I like math because it's right or wrong.” This statement shows a gross understanding of math. When we support students in their reflection of their math, we promote deeper thinking and engagement.
Replace Grades with Feedback (when possible): Whenever possible, remove grades from work and replace them with comments. Comments force students to look back on their work and actively reflect on how they could approach the problem next time. The general structure of these comments is: you are here, this is where you can be, this is how we get there. I've experimented with grades and feedback, proficiency and feedback, even checkmarks and feedback, but I've found that as soon as you put any kind of quantitative data on work, a student stops engaging in the rich qualitative feedback, and learning stops. If you are required to grade quantitatively, you can try to release them the following day or class to further encourage student engagement.
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Deeper Reflection - At the end of the class, challenge students to reflect on their work. This needs to be scaffolded as looking inward is challenging for teenagers, and they'll often come back with rich thoughts like “I got question 6 right.” The purpose of the reflection is to get them to inform their future learning. Share guiding questions such as:
- How did the challenge feel to you?
- How do you think you could have collaborated better?
- What barriers did you face? (I.e. Did you feel too tired to learn? If so, why, and how do we change that for the next class?)
Implementing Universal Design for Learning (UDL) in math classrooms can be challenging. The tiered nature of the subject means that if too many pieces of the Jenga tower are missing, it all comes down. As teachers, we feel pressured to ensure we aren't setting up our students for failure in future years. This pressure can lead us to power through the same way that, potentially, we learned. However, I chose the strategies outlined above because they can be implemented incrementally and have been shown to increase understanding and retention in all students. Remembering how we learned math can blind us to seeing that UDL is essential for some students to learn math and is beneficial for all.
Continue Your Learning:
- UDL for Middle School Mathematics
- UDL for Elementary Mathematics
- Universally Designed Mathematics Lessons
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Blake Mahovic is a mathematics and inclusive education specialist in British Columbia, Canada. His approach and commitment to UDL are framed by personal experiences as a student with learning disabilities. Despite leaving high school math at 16, Blake achieved a First-Class Honours degree in mathematics. Now, he advocates for equitable opportunities and empowers students and educators alike to see the beauty, versatility, and multifaceted nature of mathematics.