The question is: the Purpose for Learning math is it necessarily Concrete?

Sunil Singh

Jun 2, 2021

Think of the moment when kids understand that fingers — not just their fingers — is a way to count.  The common refrain in math education is "when are students going to stop using their fingers for counting?"

My response is "hopefully never", meaning that there is something unresolved with students that needs attention and time to.

The pandemic proved that education has no interest/idea in shifting the historic purpose of mathematics — practice, perform, and practicality — into something more aligned to the abstract origins and beauty of the subject.

It is no coincidence that many of the great mathematicians in history were great philosophers, fully acknowledging and honoring the deepest ideas/secrets of mathematics lay in a philosophical matrix.

I understand the power of mathematics to unveil all the wonderful practical applications and science phenomena in the world. It's endless.

You could spend several lifetimes here and still not observe a fraction of the physical illumination of our universe.

I had a long chat with a father of student I taught this past year with my remote "Math Recess" class.

I told him I would like to design a course for young children that intertwines mathematics, history, and philosophy — and gets shared as storytelling. He was a little more than intrigued:)

Just reflect on our emotions, equally abstract. Love, anger, sadness, joy, confusion, frustration, hope, etc. They all dance with mathematics.

While some of the ones mentioned are perhaps negative emotions, they still need to sit with mathematics in our journey with mathematics.

For if they don't, another emotion, far more damaging and almost irreversible will begin to calcify in the mind of a student — alienation.

The drifting away of the core of our being/identity with mathematics is a spiritual death — which we never recognize it as such.

We only recognize it when it manifests itself into something concrete to communicate that anxiety. Facial expressions. Incomplete work. Failed tests.

We live by the concrete and we die by the concrete.

Our restrictive domain of how/why mathematics intersects our lives is an exhausting journey of external functioning for teachers, parents, and society.

There is nothing inward.

There is complete malnourishment of our souls. The insidious journey of being unwell with mathematics is a sad, paradoxical journey that begins almost immediately with all our students.

A few escape the soul-crushing defeat that lies at the end. Most yield to the weight of its concrete purpose and expectations, and just suffer in silence — thinking the problem is with them.

The problem is with our specific harvesting of math's practicality, eating the body and neglecting its soul.

The gift of mathematics lies in the dreamy allusions of the abstract machinery of our universe.

We have tended to mostly look outward, and not inward. We have tended to look mostly at the ground, and not towards the boundless sky above. The metaphors for our ailing health in mathematics are numerous.

The abstractions of mathematics might be far more elusive, but we don't even have to fully understand them.

We just have to chase them…

Note: Like what is a Group theory?

Let's consider a set X with an arbitrary binary operation * (just an asterisk) that can be applied to any pair of elements in X. If

  1. for any two elements in X, the composition of these elements belongs to X,
  2. for any three elements x, y, z in X (x * y) * z = x * (y * z)
  3. there exists a neutral element (or identity element) and for any element x in X the composition of x with the neutral element gives x,
  4. for any element x in X, there is an element in X that is complementary for x to the neutral element,

then X is a group. Consider a Square and rotate it 90, 180, 270, 360 degrees

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