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Engaging math instruction


Photo by Yan Krukau

Almost a decade ago, I became fixated with the concept of student engagement. Stemming from my personal experiences as a teacher and principal, I wanted to know why some students engaged in learning while others in the same class didn’t. More importantly, I wanted a framework to explain student engagement so it could be more easily analyzed and implemented.


Fast forward to 2017 and, after much research and labor, I wrote my first book on the subject titled Solving Student Engagement: Designing Instruction to Motivate Every Student. In the book I share a framework for student engagement using the acronym CRAVE:


  • Competence: Students are motivated to learn when they have a sense of self-efficacy and feedback that shows them the path toward mastery. They ask, Can I do this?

  • Relationships: Learning is a highly-social activity and students who are connected to their teacher and their peers are better equipped to engage. They ask, Does this connect me?

  • Autonomy: The need for voice and choice is hard-wired into every human’s psyche, and learning activities that provide autonomy are inherently motivating. They ask, Do I have to?

  • Value: When learning tasks are relevant or align with a goal that the student is striving for, students are more engaged and have increased persistence. They ask, Does this matter?

  • Emotions: The gatekeeper to all memory and cognition is our emotional state, so learning that engenders positive emotions is highly beneficial. They ask, How do I feel about this?

While I have continued to study and write about student engagement and how to apply the CRAVE model when designing instruction, I’ve also leaned heavily into my love for mathematics. Since 2020, I’ve developed this website and a YouTube channel with well over 1,500 math instructional videos from grade 1 through Algebra 1. For the longest time, these two parts of my life developed separately, but I’d like to take a moment to explore the intersection of student engagement and math instruction.


Social identity


The point of engaging math instruction is two-fold. First and foremost, engaged students have higher achievement. Ultimately, if an instructional practice doesn’t impact student performance, it would be wise to evaluate if it’s worth the effort needed to implement it. Secondly, however, engaged math students develop a more robust math identity. While the concept of social identity has been studied in the realm of psychology and sociology for some time, its application in the field of education is less defined.


People tend to behave in accordance with the social norms of the identity that is most salient at the moment. I, like everyone reading this article, have a multitude of social identities. I am a father, a son, a brother, a husband, a runner, an educator, a supervisor, a Texan, a Baptist, a conservative, a disc golfer, and Dallas Mavericks fan, amongst others. When I’m at home, my relational identities are most active (e.g., father, husband) but when I’m at work my work identities (e.g., educator, supervisor) are more prevalent. In each context, I regulate my behavior to match the norms of my active identity.


When students are engaged in math and feel like they are competent in it, they begin to develop a math identity. This identity can be accompanied by a host of values and norms, such as:

  • Mathematicians show their work and take care to avoid errors

  • Mathematicians can prove their answers using a variety of methods

  • Mathematicians explain their reasoning using academic vocabulary

  • Mathematicians persist when they don’t immediately see a solution

  • Mathematicians are open to feedback and seek to continuously learn

While the list can go on and on, hopefully you read the previous statements with something approaching envy. Wouldn’t it be wonderful if your math students believed these things while in your class? That’s the power of a strong math identity, and engaging instruction is a great way to develop it.


Corner Confidence


While there are no shortcuts or quick fixes for designing and delivering engaging math instruction, I’ll share a few thoughts on how I’d get started if I were beginning a new math class tomorrow with one of my favorite teaching strategies, Corner Confidence.


Whether students believe they can, or believe they can’t, they’re right! More important that always being right is the belief that they can succeed in math. This belief requires more than simply hanging a few motivational posters around the room. For some students, math is already out of reach because of a host of previous experiences.


In the room, I label each corner with a number from 1 (I don’t know much) to 4 (I know everything). I then show a problem on the board/Smart TV and ask students to move to the corner that best aligns with their level of confidence to solve the problem at the moment. At their corners, students discuss what they know of the problem and work together to pool their cognitive resources. If, while talking with others, they gain greater insight, they can move up a number or two.


Teachers aren’t idle but instead asking probing questions of various corners, usually starting with corner 1. They can ask, “What do you know?” or, “What is one question that I can answer that would help you better solve this problem?” This allows the students a chance to better discriminate what they know and don’t know as well as provides real-time feedback to the teacher.


One of the best features of this strategy is that it is low-/no-stakes. Students aren’t asked to solve the problem, just move to a corner that aligns with their level of confidence. If they have no idea where to start, they move to corner 1. The amazing thing is, however, is that they won’t be alone. Knowing that other students also struggle with the concept is a relief because oftentimes so many students think they are the only one that doesn’t get it.


Additionally, the teacher can have students from corner 4 partner up with students from corner 1 to explain how to solve it. For a class debrief, the teacher can have a volunteer from each corner (starting with corner 1) share one thing they know about the problem and how to solve it, even if it’s just naming a quantity from the problem description.


Most importantly, celebrate movement! As students get more confident in their ability to solve the problem and move up, call them out and have them share what they learned. Let students know it’s okay not to know because, with the help of their classmates, they’ll always figure it out.


Student motivation


How does this strategy exemplify the CRAVE model of student engagement and develop a math identity?


Competence: Corner Confidence allows students to literally see their self-efficacy grow as they move corners. They will leap at the chance to use this strategy because they know that they will have various levels of support when solving a problem rather than being handed a worksheet and told to get to work.


Relationships: Students work together in each corner, learning from each other and improving relationships in the context of mathematical content. This directly affects the development of their math identity.


Autonomy: While not as visible as the facets of competence and relationships, there is some embedded choice in this strategy. Students aren’t placed in a corner by the teacher but get to choose which one most closely aligns with their level of confidence. They also have the ability to move corners as their confidence increases.


Value: This motivational facet is not directly addressed, as few teaching strategies will directly align with all five. Students might find the task inherently valuable based on the type of problems being solved, such as a review for an upcoming test.


Emotions: This strategy is FUN! It gets students up and out of their seats, talking with their friends. Any type of movement in the classroom gives a small boost to attention, heart rate, and positive emotions. And, when the answer is finally revealed after the class discussion, students get a hit of dopamine as they revel in their intellectual prowess.


This is just one math instructional strategy, though I do admit it is my favorite. As you consider engagement strategies in your classroom, think about these two questions:

  • How can I design instruction so that all students CRAVE learning?

  • How will I develop my students’ math identity?




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