Reigniting Math: Connections Over Corrections and the Embrace of Wonderment

by Ben Koch

Easily, the most successful course I’ve developed over the last few years is one called Mathacadabra: The Magic of Math*. In it, students trace the mythological magic square from ancient China to Ben Franklin, use Fibonacci and the Golden Ratio to see if they’d have cut it as an Olympian supermodel in ancient Greece, test their common-sense view of reality with topology and the Moebius strip, and learn all order of mental math agilities, including an exploration of the “memory palace” method espoused by both Sherlock Holmes and U.S. memory champion Ron White. Bear with me…this post is not a bragfest on my curriculum writing skills. Rather, I’m hoping my passion and enthusiasm for this Math-based content is coming across clearly, because I need to contrast it with its stark opposite: my past self.

Were there a magic thread I could trace back through time, perhaps I could identify that moment, or at least a cascade of micro-moments, when I broke from Math and began to identify it–at least subconsciously–in the same life category as “Novocaine shots into my gums” and “soggy green beans.” As a young boy with the “gifted” label and some of the learning opportunities that entailed, I had consistent opportunities to embrace Math, to see beyond its facade of empty numerals and operations. But somewhere along the way, I’d failed to connect Math to my already voracious curiosity about things like the composition of the rings of Saturn, the concept of infinity, the physics of black holes, or even my obsession with LEGO construction and fascination with breaking new speed records on my Big Wheel.

“I’m not a math person.” As Mindset author Carol Dweck has highlighted, this phrasing and self-conceptualization can become a misguided badge of honor. But it isn’t only struggling students who create such a shield to protect themselves from the perceived slings and arrows of the most taken-for-granted of our core subjects. Over the years, I’ve seen that our brightest students are just as likely to see math as the dark cloud of their school day, to be endured like a perfectly timed and predictable bout of bad weather.

For me, that disconnect persisted well into adulthood, driving me as deep into the refuge of the humanities as possible, where I pleaded for sanctuary from the cold, heartless reach of Math at the feet of Keats, and Steinbeck and an entire lineage of poets and philosophers who seemed to share my seething resentment for the dark art of repetition and red-marked worksheets. Instead of seeing Math as a layer to my understanding of the world, I’d come to associate it with a tedious attention to a circular system of numerals and symbols with no real connection to things beyond its oppressive logic. I wish I could say that revolutions in Math education have identified, diagnosed and bridged this chasm, but I’m afraid this Math disconnect is prevalent and will continue for many otherwise highly curious and bright young students. The problem, in essence, is that rather than embracing the origin of curiosity in the arts and humanities, most Math curriculum takes the pretentious stand that it legitimately exists in isolation of the arts, as a final and authoritative anchor of STEM. If you don’t want to lose more students like me to the S.S.M.H.E.M (Secret Society of Math-Hating English Majors), here’s what we must do: broaden our conceptualization of “Math” to include, and in fact begin from, the intersection of the world and our sense of wonderment about it.

This approach to Math, which I call “Connections Over Corrections” for its ability to incite curiosity and deepen our appreciation of an interconnected universe of beings, objects, and ideas, has a couple simple premises:

Allow Math to arise organically in an environment of open, passion-based inquiry, not in isolation:
Drill and kill approaches to math create a false, insular understanding that mastering math for math’s sake is some kind of academic achievement. Math mastery is an achievement only when used as a tool for more holistic goals: solving an engineering problem, coordinating angles and lines in a wall-sized mural, calculating imperceptible light shifts in the hunt for exoplanets. Don’t worry, no one is denying there’s a basic foundation of math concepts and skills to be grasped and even mastered–heck, there’s even a place for flash cards! But when the next skill to be learned and mastered arises organically out of the problem at hand, CONNECTION is inevitable, and a long-term grasp of why that skill is important is encouraged.

Emphasize Math as yet another LANGUAGE with which to understand phenomena, not a “pure” reductionist explanation stipped of all mystery:
The Math of my childhood classroom, especially in secondary school, came across as the antithesis to my unnatural passion for poetry. If someone had shown me the interaction between Math and Poetry (“Hey, let’s try a Fibonacci sonnet!”), perhaps that would have provided an opening just wide enough to let Math back in.

While developing a growth mindset can play a huge role in encouraging and re-engaging “lost” or reluctant mathematicians, I argue there is a more powerful (and much more challenging) approach. Let’s leave space in our curriculum for organic connections to reinforce curiosity and drive problem solving, and allow wonderment – raw, childlike amazement with the universe – be the fuel that energizes, and ultimately reignites, our learning of math.


We are proud this post is part of the March Math Blog Hop on Hoagies’ Gifted Education Page!


Blog Hop graphic by Pamela S Ryan – click above for more Blog Hop posts!


*Mathacadabra: The Magic of Math course title and syllabus are the intellectual property of NuMinds Enrichment.


3 Reasons to Take Your Kid to The Martian

by Ben Koch

In an era of cinema when reboots, remakes, and endless “-ilogies” have come to dominate the multiplexes, I don’t blame you, parent, for being skeptical about whether films of any deep educational value still grace the silver screen. Sure, you indulge the kids now and then with a superficial superhero flick because, let’s face it, even YOU are looking for that spark of inspiration, perhaps that Rosebud-like secret from your own childhood love affair with movies that ignited something special. When previews for the newly minted box office hit The Martian began appearing, I feared yet another high-budget dud. I saw just enough hope glinting off Matt Damon’s astronaut visor to compel me, however, to surrender yet again to the big screen experience.

Believe it or not, The Martian delivered. From a science point of view, the film has even successfully traversed the tricky crucible of culturally savvy, movie-loving astrophysicist Neil Degrasse Tyson, whose only “critique” seems to be a very early tweet about the movie’s over-optimistic depiction of high-powered stakeholders actually taking science, serious science, into full consideration when making policy decisions. It’s a depiction he suggests is the most fantastical element of the entire film.

But he then went on to praise it on several levels.

I don’t come to you with the scientific chops of an astrophysicist, but as a teacher, and as an advocate for revolutionizing education to prepare students for a future perhaps not unlike the one depicted in The Martian. This is not a review or a synopsis, but rather a plea to parents and teachers to not yet abandon the big screen as a source of insight, inspiration, and educational fodder.

Here are, in my opinion, 3 reasons to take your kid (or heck, teachers, your whole class!) to see The Martian:

One – Diversity in Representation of STEM

This film immediately caught my attention as an exception to the tired formula of a secondary token minority represented among a gaggle of scientists and engineers. Minorities and women are represented in key, influential STEM roles. And here’s the clincher: it doesn’t feel contrived, or that it’s done with any self-conscious preciousness. It feels natural in the universe of the movie. It could be argued, in fact, that the real hero of the movie is the awkward, brilliant African American physicist Rich Purnell (played by Donald Glover) who cracks the real conundrum with some hard-core lateral thinking (more on that below) that facilitates the rescue of stranded astronaut Mark Watney (Matt Damon). Passionate, driven project manager Vincent Kapoor (played by Chiwetel Ejiofor) is portrayed as an African American whose “father is a Hindu” and “mother is a Baptist.” If you based it on screen time, he’s essentially the main protagonist for the Earth-based action. And this is a mainstream flick!

Infographic copyright Lee and Low Books (click image to visit original article)
Infographic copyright Lee and Low Books (click image to visit original article)

In addition, females play prominent stakeholder roles across the cast, including mission captain Melissa Lewis (played by Jessica Chastain), who leads the international crew of the mission with gusto, assertiveness, AND compassion. Minority females, however, are not well represented. In fact, the film has recently come under harsh criticism by the Media Action Network for “whitewashing” certain Asian roles with both white and black actors (including the character of Vincent Kapoor, mentioned above).

Two – A Model of Grit in Action

Mindset, the philosophical shift in thinking proposed by Carol Dweck, is a wave that has swept and reshaped our beliefs about the power of attitude in success, but it’s quickly approaching the dangerous status of becoming a series of concise platitudes (“Just add ‘yet’ after every ‘I can’t’ statement!”). Often equated with the term “grit,” a growth mindset allows us to persist in the face of setbacks and failures, and in fact grow from those experiences. In The Martian, both astronaut Mark Watney and his colleagues on Earth are the embodiment of grit, stubbornly EMBRACING setbacks as the keys to unlock the NEXT solution. “I woke up alone on Mars, left for dead, with a piece of shrapnel through my gut? Guess I’ll go perform some self-surgery, stitch it up, then assess my food rations!” Now that’s a growth mindset in action.

Three – Divergent Thinking, Not Multiple Choice

One of my favorite activities for developing flexible, divergent thinking in students is a game called “morphing” in which we must re-imagine everyday objects by mentally transforming them into new objects based on one or more transferable attributes. This helps counter functional fixedness and encourages students to apply lateral thinking to the problem solving process. When astronaut Mark Watney is alone on Mars, he must use all the “stuff” left behind to survive for what he knows could be 4 years. 

This quickly becomes a massive exercise in divergent thinking. What do some giant tarps, astronaut poop, and burning hydrogen have to do with growing crops on Mars? How do you modify a rover intended for limited daytime trips into a long-distance vehicle able to survive frigid Martian nights, recharge itself, and stock enough survival supplies? There was no room for dogma or reliance on stock answers for any of the problem-solving required, and that’s beautiful.

Deep into an era in which high-stakes testing has driven us to think of the world in terms of multiple choices, the realities of survival depicted in The Martian reflect the spontaneous, divergent nature of real innovative problem solving.

The Flaw: A Missed Opportunity

For as much passion as I have for STEM and the excitement that innovative thinking brings to my visioning of the future, in my heart of hearts I confess I’m a humanities guy. For this reason, I almost never address STEM on its own, and instead embrace STEAM, an approach which couches STEM in a human cultural and philosophical context (The “A” represents “Arts”, thus expanding the acronym to “Science, Technology, Engineering, Arts, and Math).

As razzle-dazzled as I was by how Mark Watney kept his BODY alive through ingenious problem-solving, inventiveness, and grit, I would be much more intrigued by how he kept his MIND intact through what would be the most isolating situation a human has ever experienced: being alone on a PLANET.

Whether you have spiritual leanings or not, the philosophical questions provoked by Watney’s circumstances would have made excellent fodder for deeper psychological ponderings by the film. Granted, watching him have an existential break over a left-behind copy of the Tao Te Ching would not have made for a riveting two hours, but the film seems to skim this spiritual/psychological question too lightly. We get tastes of our lonely astronaut’s evolution via the video diary he keeps throughout the film, but other than transforming into a gruff, skinny, bearded Leonardo Di Caprio-esque figure by the end, he seems to have come through it all relatively easily.

Alas, a movie is still a movie, and it has to entertain. After all, we do have the BOOK to deepen the narrative. Remember, the book? We can get Mark Watney back from Mars, but can we find time to read? Now that’s a problem worth chewing on. In the meantime, DO take your kid to see the movie. It just might plant some positive seeds of wonder, and might begin to prepare them for a future in which we really do tackle complex problems like an international mission into the outer reaches of our solar system.

“The Martian film poster” by Source. Licensed under Fair use via Wikipedia –