Making Mathematics Tactile and Visual
In
this article in The Atlantic, Jo
Boaler and Lang Chen (Stanford University) say that children counting out math
problems with their fingers, which is frequently discouraged in classrooms, is
“far from being babyish.” They cite a branch of neuroscience that has mapped a
specific area of the brain that connects to our fingers to support cognitive
understanding. “Remarkably,” say Boaler and Chen, “brain researchers know that
we ‘see’ a representation of our fingers in our brains, even when we do not use
fingers in a calculation.” Brain imaging showed this area “lighting up” when
8-13-year-olds were given complex subtraction problems and didn’t use their
fingers.
Other researchers have found
that the more purposefully students used their fingers in first grade, the
better they did at comparing numbers and estimation in second grade. In fact,
six-year-olds’ facility with finger representation was a better predictor of
future math test performance than their scores on tests of cognitive
processing. One researcher went so far as to say that if students aren’t
learning about numbers by thinking about their fingers, numbers “will never
have a normal representation in the brain.” This is a strong argument for
teaching children “finger perception” – that is, telling one finger from
another by touch – something that isn’t included in standard math curriculum
programs that the authors reviewed.
In short, say Boaler and Chen,
“Teachers should celebrate and encourage finger use among younger learners and
enable learners of any age to strengthen this brain capacity through finger
counting and use.” Some possible school and home activities:
-
Giving
children colored dots on their fingers and asking them to touch the
corresponding piano key.
-
Giving
children colored dots on their fingers and asking them to follow the lines on
increasingly difficult mazes.
-
Using
number lines to teach math concepts
“Number-line representation of number
quantity has been shown to be particularly important for the development of
numerical knowledge,” they say, “and students’ learning of number lines is
believed to be a precursor of children’s academic success.”
“To
engage students in productive visual thinking,” conclude Boaler and Chen, “they
should be asked, at regular intervals, how they see mathematical ideas, and to draw what they see.” With this
approach, math can be “an open and beautiful subject, rather than a fixed,
closed, and impenetrable subject.” They believe schools should beef up this
kind of instruction to prepare students for the new high-tech workplace, which
increasingly draws upon visualization in business, technology, art, and
science.
“Why Kids Should Use
Their Fingers in Math Class” by Jo Boaler and Lang Chen in The Atlantic, April 13, 2016, https://bit.ly/2vULNZQ;
Boaler is at JOBOALER@stanford.edu.
