When I taught high school math, I wish I spent more time creating the conditions that help students be more curious about math. I’m reminded of this every time I ask adults whether they remember math class being a place where their curiosity was nurtured. Ninety-nine percent of the time, their answer is “No.” And if you’re curious about what the last 1% say, it’s usually that they felt an intrinsic curiosity in math rather than being in math classrooms that regularly made them more curious.

Fortunately, nurturing curiosity in math class isn’t teaching pre-school*. There are simple tactics that can easily be used in any grade level, course, or topic in math. You may be familiar with popular techniques such as “Notice and Wonder,” “Creating Intellectual Need,” and “Three-Act Tasks.” These approaches fall under the umbrella of “creating conditions for curiosity,” and here are two key principles these techniques leverage along with additional ideas that any teacher could use in math class tomorrow.

Beg the Question

A well-known example of the first principle – begging the question – is in Dan Meyer’s viral TED Talk where he showed students a video of a water hose slowly filling a tank which made them ask, “How long will it take to fill up?!” There are many online interactives available that beg irresistible mathematical questions. But you don’t need multimedia to beg a question. The title of this article is maybe the simplest way to beg a question – claiming that something is the “second-best” instantly makes an audience wonder, “What’s the best?” In math, there’s rarely a “best” method or technique for proofs or computations but positioning any claim as a comparison or competition generates even more curiosity about what makes something “the best.” It also creates an opportunity to have a rich dialogue about how we choose criteria and rationale for judging things.

Number strings and patterns are also simple, effective techniques for begging the question in math, and especially when teaching elementary and middle school computation. For example, many of us were taught that “subtracting a negative number is the same as adding those two numbers,” but unfortunately that meant it was just a rule to be followed rather than a logical truth of mathematics to be understood. A simple, more effective way to ensure students understand this idea is to create a number string that begs a question:

7 – 3 = 4

7 – 2 = 5

7 – 1 = 6

When we give students these three equations they usually wonder on their own, “What’s the next equation in the pattern?” They’ll know easily that it’s 7 – 0 = 7, and they might even call it the “fourth” equation. If we call it the “fourth” equation, we create the conditions for students to naturally wonder what the “fifth” equation is. At that point, students will almost certainly jump right to it and see that if the pattern continues, it means 7 – (-1) = 8. Using this technique of begging the question, students have both experienced and understood logically why subtracting a negative is like adding the two numbers together. And it’s not because we’ve given them a confusing rule to follow that removes thought and kills curiosity; rather we’ve leveraged their innate curiosity by begging a question they were able to answer themselves.

Leverage Motivating Contexts

Too often, we over-simplistically think that the best way to cultivate students' curiosity is to apply math in the “real world.” However, we need to remember that different things are “real” to students, and the logical reasoning they learn in math won’t always an immediate or tangible application to their life. For example, there were no “real-world application” problems in the number string above; we can all clearly understand that 7 – (-1) = 8 without having to invent a confusing context like a bank refunding a fee they mistakenly charged. While some adults might subtract negative numbers on a regular basis, curiosity can be nurtured without trying to force every math topic into a real-world or career application. Similarly, while the “filling the bucket” video described earlier is a “real world” thing that happens, students weren’t curious because they believed timing the filling of a bucket is relevant to their adult lives or future careers.

The truth is that for many math concepts – especially at the high school level – real-world applications don’t effectively motivate students to ask questions because the applications of something like cubic functions are too abstract and removed from students’ lived worlds. But when put into a game where students direct robots to complete missions on alien planets, the motivating context begs questions about how cubic functions can help complete the mission by intersecting with key points on a graph. It’s important to remember that video games like Super Mario and Angry Birds aren’t “real world” applications, but they are highly engaging and motivating for students because they present a meaningful, motivating context. Because every context won’t motivate every student, math teachers are continually working to find engaging, easy-to-use, and effective resources for their classroom that include situations and circumstances that will motivate their students to ask more questions. For some students, baseball might be a motivating context that they’re curious about, while for others a number puzzle might captivate their curiosity for days.

Just as different contexts motivate different learners, there are also different types of curiosity that students exhibit within these contexts. In his book, Why? What Makes Us Curious, Mario Livio defined different types of curiosity that can be helpful for math teachers seeking to better understand their students and improve their lessons. One type is *perceptual curiosity*, which seeks resolution because the mind can’t sit still until the question is answered. For math teachers, the motto “create the headache for which math is the aspirin” supports perceptual curiosity. Importantly, perceptual curiosity will often be context dependent for each student as discussed earlier. Another type Livio defines is *epistemic curiosity*, which is the anticipation of finding out how things resolve. Any time teachers are begging a question in math, we’re creating the conditions for students to exhibit epistemic curiosity. And like a good movie or TV show, teachers should look for opportunities to leverage contexts that create a cliffhanger to ensure students are wondering how a situation used in the lesson will end.

If you’ve read this far, you might still be wondering what the best article about curiosity in math of 2024 is. Right now, that’s unknown because it’s still early in 2024. Given how much everyone values curiosity in students and how easy it is to use small tactics for cultivating students’ curiosity in math, I’m hopeful that there are many others developing and sharing great strategies for igniting student curiosity in math. If you find such an article, send it my way. I’d be thrilled if by the end of 2024 this is the tenth-best article about nurturing curiosity in math.

*I used this asterisk as another example of a simple way to beg the question to inspire curiosity: By design, asterisks stand out visually and connote some type of exception. Because they don’t belong, they literally beg readers to ask the question, “I wonder why that’s there” and motivate readers to go find out what it means. It’s different than a footnote numbering, which often denotes just a citation or expansion – not an exception. If you’re not sure whether asterisks are motivating, imagine how frustrating it would be if my article had the asterisk, but didn’t have this asterisk explanation. Asterisks create intellectual need, which is one characteristic of curiosity. Another question begged in this sentence that many readers may have is wondering why I mentioned teaching pre-school. Instead of using the typical analogy, “it’s not rocket science,” I chose to use the alternative “teaching pre-school.” By some measures, it’s more difficult to teach pre-school than it is to do rocket science. Because of mathematics, we can be confident rockets will go where we tell them to. But preschoolers… not so much.

About the author

Dr. Tim Hudson serves as Chief Learning Officer at Discovery Education, where he supports partner districts and internal teams as they develop and implement research-based, innovative, and effective learning resources for teachers and students. Prior to joining Discovery Education, Dr. Hudson spent over 10 years in public education as a teacher and district administrator.