Math Education 2020: The Dawn of Reckoning, Reawakening, and Rebirth.
Change will never be this slow again…and yet, we must stop.
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My general personality is definitely on the extroverted side. I crave human connection, and the first 40 years of my life, music was the go-to medium to have soulful, shared experiences. However, as my ideas of mathematics changed over the years, so did my belief in its final, resting purpose — friendship. The belief was strong enough to be the last chapter of the book I co-wrote with my friend, Chris Brownell.
So, in the spirit of friendship, I am writing this article. To inspire honesty, engender trust, and promote health and well-being in math education. However, I think the first thing that math education must do, as well as anyone who is responsible for managing and discussing its direction, is to just flat out stop.
This past week I was in the Mayan Riviera. My father, who came to Canada 50 years ago with only a hope for a better life for his kids, took his entire 14-member family of kids and grand kids for one last vacation of this magnitude.
One of the mornings I got up early and walked to the beach to catch the sunrise. Feeling the cool sand between ones toes has an instant calming effect. I looked around, and there wasn’t really anyone else on the beach. The earth was under my feet. The ocean water was within a stone’s throw. And the air, always around us, seemed naturally sweeter. The only missing element was “fire”. The confluence of all of this created a natural stop. I wasn’t thinking anything deep or profound. I was just in the rare moment of time that offered a cleansing and purifying stop.
2019 had three critical milestones for me that confirmed the vector that I need to stay on for the new decade. Publishing a math book about play, indirectly calling for the emancipation of mathematics from unhealthy subscription to 20th century ideologies. Being invited to be part of the NCTM Regional Baltimore Planning Committee for 2021, and collectively sketching out the theme of (Re)Humanizing Mathematics and helping write one of the strands. And, being asked by Vicki Abeles, director of Race to Nowhere and Beyond Measure, to be interviewed for her film, Gatekeeper: Math Crisis in America.
Stop.
As a former math and physics teacher, the way that math education is approaching change — specifically changing direction in its principles and aspirations — runs metaphorically counter to how change occurs in physics and calculus. If you are moving in a certain direction, and you want to change direction, you need to slow down and stop. You can’t keep moving in the same direction and thinking/wanting you can go in another. That is why we don’t have continuity in math education goals — we have competing unconscious, subconscious, and conscious narratives.
Distilling down all the chatter — especially on social media — we have three basic camps in math education. Those that are/want to enable the current infrastructure of testing/performance, those that want to work within the system to manufacture change, and those that want to blow it all up and start again.
From a strictly mathematical point of view, the only one that involves a critical point of stop is the last one. The first one is cancerous. The second one is the most heavily populated and has the best intentions, but in my opinion, will not get to the root toxicity of math education — alienation, anxiety, and depression. These markers are directly linked to the mental health epidemic among young children and teenagers.
In calculus, the point of inflection — which has both its change and the “change of its change” linked to zero — is a critical point that marks the change in concavity. Sure, humans and agreement/cooperation are a tad messier, but the closer we can get to symbolically aligning ourselves to this mathematical idea of stop/change, the better our chances will be of achieving our lofty goals of rehumanizing math education.
If I could borrow a leaf from Brene Brown, then all our communication in math education should at least follow the following.
WE all need to be clear with our intentions with each other. If you agree, be clear. If you disagree, be clear.
Math education is made up of two components, mathematics and education. From my vantage, the quality in both parts are severely lacking. The K to 12 mathematics curriculum lacks coherence, vision, imagination, and joy. It is a hodgepodge of disconnectedness with its primary objective to be a servant to assessment/standards. Thinking one can extract joy and love from the same curriculum that causes over 90% of Americans some form of anxiety is to be squarely dishonest.
The last decade was heavily rooted in the micro, painstaking care of how to teach every topic with steely precision and focus. The problem was, that as teachers, our energies our finite, and very little was left in the tank to bring actual joy to mathematics. It was all task oriented, with benchmarks, milestones, and suffocating pedagogy along with way. It’s what made me leave the classroom in 2013. It is also what makes both my kids now hate mathematics.
Let’s be clear. Math education functions with high dysfunction, some of it unchecked and unattended to.
And, when it comes to actual education, math education is running behind some of the most contemporary and challenging ideas that are being offered. When I was at SXSW EDU 2019 in Austin, very little of what I saw was being promoted in math education. Not that any of that surprised me, as math education has been a conservative beast for the most part over the last 100 years. In fact, it doesn’t even mine ideas of progressive education from its own people! Alfred North Whitehead was one of the preeminent mathematicians of the 20th century. But, he also wrote one of the most important books about education.
9 editions and 90 years later, almost all of it has been ignored by math education. The echo chamber has a radius that is only growing.
Mathematics education is not just one big gate. There many smaller gates embedded in the system. From curriculum gatekeepers of fractions and algebra to ones of voice/leadership. Which brings me to equity. Thankfully, the discussions around have grown exponentially over the last few years. Unfortunately, I am beginning to see some asymptotic behavior in its discussions. Namely, that the conversations don’t seem very inclusive to bringing in a larger historical narrative to math education, offering only trite recognition.
If equity, in the end, only means giving all kids access to the same stressed out dysfunction of math education, then we will have fallen short. Equity needs to mean giving all kids access to the same joyful and purposeful journey.
Generally speaking, math education, trying hard to move forward, is not doing a good job of looking backwards. Not sure why that is? Is it because we see leadership as having strength of knowledge, and not understanding/knowing the history of mathematics would dislodge us from our podiums? Well, then our leadership model deserves some improvement.
Expertise is exhausting. Learning not so much. A lifetime of learning will lead to wisdom. It’s also humbling.
In the world of mathematics, the words of Anthony Bourdain are tattooed to me, reminding me constantly that I have many, many miles to go…
We need to go back, way back, right to the beginning, and see where the missteps and blind spots are.
Zero has been a thematic part of this article, with the constant referencing to the idea of stop. Also, zero, as in zeroing the scale, refers to resetting scale because of accumulation of debris, preventing an accurate reading. So, the idea of the mathematical idea of zero is actually a critical part, symbolic perhaps, of how things need to be fixed.
The transmission of zero from India to the West was not done correctly. It only left India as a placeholder. The deeper and more substantial ideas of it being related to the laws of addition and subtraction did not. At this point, I am deeply indebted to the knowledge of Jonathan Crabtree, an Elementary Mathematics Historian from Melbourne, Australia, and his illumination of Brahmagupta’s entire vision of zero.
Integers in North American math education are introduced after fractions, in middle school. That idea is the direct consequence of misunderstanding the whole complete idea of zero. So, now that we have this information, what are we going to do with it? Will it be a polite nod and smile, or will something of substance be added to our discussions on equity?
The salient point here is that we need to have more math history in our K to 12 curriculum. We need to have more stories of discovery and enchantment in our K to 12 curriculum. And, they cannot be token topics of extension or stamp size bios filling in pages of worksheet problems.
Mathematics and how it has been learned, explored, and enjoyed is braided with stories, compelling and symbolic of the human spirit and curiosity.
In this decade, math education, the one based on the performance culture of success and measurement, will hopefully die. However, the rebirth of mathematics will coincide with this needed passing. In fact, the signs are already there for this.
While I was humbled to have my book as part of this group, I need to direct your attention at the two books in the upper left corner. For me, Francis Su’s Mathematics for Human Flourishing and Jo Boaler’s Limitless Mind, represent the path to the needed macro journey of mathematical boundlessness that is inclusive of everyone and the richest/most human objectives of why mathematics is important in our lives.
We need to lift and support each other in ensuring that future of math education embarks on this wide and colorful trail. Not just for this decade, but the decades to come. I will leave you with one of my favorite quotes from one of my favorite authors.
Let’s hoist our sails and reach that point…
