Saint David's prioritizes faculty development through research-informed programming. Our teachers are supported to continually learn and grow in their professions, allowing us to stay abreast of and advance best practices in teaching and learning for boys. During the last school year, we awarded 53 research grants, and this summer alone 20 faculty members enrolled in one or more of our new professional development opportunities.
Below, from our current issue of Saint David's Magazine, Upper School Mathematics Teacher David Lane shares what he learned from his 2023 summer study grant about harnessing curiosity for learning as it emerges in the mathematics classroom.
If you add an infinite number of positive numbers together, will the sum always be infinitely large? Is the number 0.999… (repeating) less than 1? Can all numbers be organized from least to greatest?
To the surprise, confusion, and fascination of many of my students, the answer to these three questions is no! I love questions like these. When I was a student, such provocative answers to seemingly straightforward questions challenged my assumptions and laid bare the limitations of my own understanding. They suggested to me that reality is richer and more intriguing than I could have imagined. They ignited my curiosity.
To state the obvious, not all students find giddy delight in being shown that their instincts are wrong in math class. For many people, math is more closely associated with negative emotions such as anxiety or frustration than excitement or curiosity. A central question emerged to me last year in light of student interactions with math: How can curiosity for mathematics be most effectively fostered in the classroom, and how can barriers to its expression be lowered?
The description of curiosity used by modern studies was first published in 1994 by George Loewenstein. He describes curiosity as arising from an information gap, a recognition that one’s knowledge differs from what he or she wants to or should know. This is, he says, a fundamentally unsatisfying state that humans are driven to avoid by closing the gap – that is, by learning more to match that desired or expected level of knowledge. Curiosity, then, is the instinct we have to close these gaps. For example, when I tell my fourth-grade students that you can add numbers infinitely without the sum being infinitely large, that can come as a surprise, resulting in a gap between what they understand about numbers and what they feel like they should be able to understand. Their inquisitive response is curiosity, generated by their desire to reconcile this unexpected result.
So, curiosity requires the student to be aware that their knowledge is insufficient. This alone provides a valuable (if common sense) starting point for educators to generate curiosity: Frame lessons around the unexpected, the unintuitive! However, the moment a student recognizes an information gap is a moment of vulnerability. A feeling of lack of control, failed attempts, or discomfort here can lead to experiences of frustration or confusion rather than curiosity. Accordingly, comfort with uncertainty and confidence that they will be able to close the gap successfully are essential for students to view these moments as positive.
Our role as teachers, then, is to help students develop a perception of control amid uncertainty and to model and reinforce positive reactions to it. In math class, one valuable strategy posited by researchers for helping students learn to successfully navigate uncertainty is to encourage question generation and alternative approaches rather than emphasizing a single means of thinking about a problem. This prompts students to reflect on what they do and do not know and experiment with their knowledge to draw conclusions. It centers uncertainty as a natural part of the learning process, helps students identify what they know, and acclimates them to the process of leveraging their knowledge to draw new conclusions. Normalizing mistake-making as a natural part of learning is likewise essential to help students develop comfort taking risks in their problem-solving and thereby become more willing to engage with problems that expose their information gaps.
One study of high-achieving college students found that students motivated by grades are less likely to explore the unknown, embrace novelty, and accept uncertainty. For these students, uncertainty endangers their academic goals. Accordingly, it has been shown that helping students move away from grade motivation and towards a more intrinsic desire for mastery results in more curious behavior. Numerous studies have shown that praising students for their process or effort are effective ways to guide them towards this mindset.
As I learned more about the role that comfort with uncertainty plays in student learning, I began to see curiosity less as an end goal and more as one indicator of a more fundamental outcome: helping students become comfortable with uncertainty. Larger information gaps (greater uncertainty) arise in contexts where more perseverance and creativity are required in problem-solving; they are the hallmarks of challenging problems. Thus, in addition to its effect on student curiosity, comfort with uncertainty reinforces positive experiences with challenge. For both struggling and high-achieving students, this begets greater engagement and investment in longer, more meaningful problems essential to developing nuance and rigor in problem-solving.
While much research on curiosity is still young, I find it empowering and serendipitous to know that barriers to curiosity can be addressed with the same methods that might help prepare students to flourish in mathematics. By taking steps such as giving students time to explore, emphasizing student process, and scaffolding information-seeking, we as educators can simultaneously help students reach a state of mind in which they can find more joy in their education and prime them to meet challenge and uncertainty with poise and confidence.