“ How can curiosity for mathematics be most effectively fostered in the classroom , and how can barriers to its expression be lowered ?”
Summer Grants
Promoting Curiosity in Math
By David Lane
I f 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 ?
Last summer , I sought to better understand curiosity as it emerges in the classroom and what practices might exacerbate or reduce barriers to its expression in students . To do so , I steeped myself in peer-reviewed psychology articles on curiosity . I was delighted to find that , while this area of research is still developing , the past 20 years have seen a proliferation of results that are directly applicable to teaching practice . What I found has raised new
“ How can curiosity for mathematics be most effectively fostered in the classroom , and how can barriers to its expression be lowered ?”
In Action :
questions and shifted my perspective on how to present new mathematical concepts , frame lessons , and engage with students . It represents to me an exciting beginning to a journey of refining research-based practice in mathematics education to help more students avoid dreading math and instead attain those precious experiences of giddy delight and lasting enthusiasm .
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
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