In Paul Lockhart’s short story, the ‘Mathematician’s Lament’ we enter a dream world, one where music education has been reduced to mechanical, rote accumulation of rules and repetition. Students, frustrated by limitations set against their natural urge to play with sound, disengage, locked solely on obeying their leader’s instruction towards assessment goals and test result leaderboards.
Mathematics, like music, is an artform, Lockhart argues, and to cut creativity from math is akin to doing the same with music. It loses its essence.
David Vaccaro, a recent guest on our Math Matters Podcast, repeated the metaphor to describe how math has fallen for the same fate as Lockhart’s lament, the playful exploration of patterns and ideas lost to formulaic means.
With the natural connection of students to math severed, math’s essence is lost, and what’s left is anxiety and resistance.
Math needs more than rebranding, it needs reinventing. The fear so many see embedded within their math relationship needs to be dissected and replaced with the promise of creative pursuits and critical thinking.
Looking at the numbers shows the impact anxiety is having on our population's potential. Approximately 93% of adult US-Americans indicate that they experience some level of math anxiety, with 59% of 15- to 16-year-old students reporting feeling worried regarding math class.
The antecedent to student math anxiety has a plurality of progenitors, from parent legacy math anxiety and teacher communication to the more social anxiety from ‘competing’ with peers.
Fortunately, all these can be reversed with targeted action.
A study exploring the effects of positive and negative reinforcement by teachers showed a significant reduction in heart rate for those students positively encouraged. Additionally, multiple studies have shown mixed-ability teaching can increase confidence and develop critical thinking skills.
Removing such obstacles may allow some students to pass the threshold fearlessly and experience math again, but math needs to entice too.
Vaccaro and Lockhart agree on the solution, yet with some small caveats. Vaccaro connects his classes with relevant, real-world situations where the math in class mirrors what’s reflected outside. In one example his class input the raw World War One cemetery data into Mathematica and showed the narrative behind the numbers come to life. Breathing life into the data revealed the story of 5 million men not only showed the true world relevance of math, but revealed that math is bubbling under the surface, ready to be explored.
Vaccaro urges us to rethink our canonical math tasks, offering students big sacks of data and asking, “Now, tear it apart! Use your math skills, your emotional skills to tell the story.”
By bringing forth the story of math we bring it out of the shadows and allow its beauty to be realized. The beauty of math is exactly what Lockhart wants to rekindle, noting the ‘breathtaking depth and heartbreaking beauty of this ancient art form.’ One ‘older than any book, more profound than any poem, and more abstract than any abstract.’
Lockhart agrees that connecting math to the context of ‘real-world’ scenarios is how we counter this ‘cure for curiosity’ but warns context matters. ‘Do you think compound interest interests children?’ he asks rhetorically.
Focusing on engaging and natural problems suitable to their tastes, personalities, and level of experience, Lockhart believes, will unlock adept lovers of math.
People enjoy fantasy and that is just what mathematics can provide— a relief from daily life, an anecdote to the practical world. A safe environment where your mind can play in the sandbox of ideas and get lost to time calculating the hypotenuse.
If we fail to follow this path, we are destined to repeat the past, and as Lockhart describes, we’ll continue to complete the prescription for permanently disabling young minds. A solemn end to a seminal piece which Lockhart closes with a nod to the dialogical writing of Galileo, postulating a conversation between Simplicio and Salviati where they wrestle with the lost love of math. Concluding, Simplicio submits, ‘Alright, I’m thoroughly depressed. What now?’ ‘Well.’ Salviati holding his response, ‘I think I have an idea about a pyramid inside a cube…’
There is much to be said for Lockhart’s assessment, but something to be learned from the data too. As we know that other stakeholders in a child’s education have a profound impact on their math wellbeing, that is maybe where we should begin.