Jo Boaler in the Atlantic

This is from Marshal Memo 80.  I shared it with our math department chair and a department member whose wife is an area math DC.

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.