The Fields Institute Turns Twenty-Five 170725 Final book with covers | Page 174

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George Gadanidis
ways in which computers can change learning. He had
pursued mathematical research at Cambridge University and
then worked with Jean Piaget at the University of Geneva,
and these combining influences led him to consider using
mathematics and computers in the service of understanding
how children learn and think. As Papert once remarked, “I
was really looking at computers as a way to understand the
mind. But at MIT, my mind was blown by having a whole
computer to myself for as long as I liked. I felt a surge
of intellectual power through access to this computer, and
I started thinking about what this could mean for kids and
the way they learn. That’s when we developed the computer
programming language for kids, Logo.”
Papert designed Logo to have a low floor (where kids
can engage with minimal prerequisite knowledge) and a
high ceiling (where they are free to investigate complex
relationships and representations). Over the last dozen years,
along with my research collaborators and graduate students
in Canada and in Brazil, we have taken up this idea seriously
and have been working to develop low floor/high ceiling
(LF/HC) access to important math ideas such as infinity and
limit, circular functions, linear functions, binomial theorem,
non-Euclidean geometry, and group theory, for as young as
grade one.
We also stretched LF/HC perspective by interviewing
mathematicians on these themes. We asked mathematicians
to engage in the same sorts of activities as kids did in
classrooms, and then we had the mathematicians discuss
these ideas further. The idea for interviewing mathematicians
in this way grew from my work on the Fields Institute’s
“Windows into Elementary Mathematics Project,” whereby
prominent mathematicians were invited to discuss topics
from elementary mathematics—for instance, Ken Davidson
(Waterloo) discussed insights into mathematical proof;