Time: Squaring Math Education’s Circle

Time.

It deserves its own paragraph. Through the objective lens of physics, it is unbounded and tethered only to sometimes an equally daunting idea of space. Through the subjective lens of mortality, time is most precious — invariably fragile far too often.

Art, specifically music, must be the brought in to pay homage to why we are melancholic and wistful about how time underscores much of our lives. Whether it is Jim Croce’s Time in a Bottle, Pink Floyd’s Time or The Rolling Stones’ Time Waits For No One, there is thematic understanding that time is indifferent to our whims, wants and desires.

If there was ever a branch of knowledge that was never meant to be under the clock — to be rushed, with every topic having a preordained, arbitrary time limit — it was mathematics. It’s entire historical development and almost romantic devotion has been emphatically independent of time . The bottom-line, human narrative has been a deep understanding and respect that mathematics often takes time well beyond the lifetime of those who ponder and contemplate the impenetrable, the abstract…the dark unknown.

The results, while mathematical gold — literally — are still punctuation marks, occupying an interval of time that is dwarfed by the more ceremonious journey of reflection and inquiry. Two thousand years and more of every culture solving small and big math riddles has shown, if anything, that the shortcuts in mathematical understanding have been reserved for virtually nobody — the Euler’s and Ramanujan’s being the majestic exceptions.

Unfortunately, math education has handcuffed itself by trying domesticate the wild beast of mathematics, trying valiantly — with good intentions — to constantly shepherd every topic to finish lines. These termination points often contribute to the disconnection and anxiety that students quietly internalize. Problems are often meant to be solved within the hour of class. In high school, a somewhat humane evaluation of something like 75% of the course work over 9 months has the remaining 25% of the previously tested material compacted in a ridiculous 2 hours. Thankfully though, the discussions regarding assessment have continually been moving in the direction of less and less.

Assessment and evaluation are being debated in a healthy and holistic fashion. Content and pedagogy are now emphasizing number talks, process and dialogue. Everything in math education finally seems to be moving in a direction of meaningful and lasting change.

Except…time.

Again, time needs grammatical isolation here. Time artificially introduced into mathematical thinking makes the learning of mathematics not only predictably inorganic, it reluctantly still champions the finished product and unwittingly siphons out the natural joy and wonder of the unbounded journey. If students are not given enough time, then an artificial representation of mathematics and ability will be consistently presented.

Yet, we persist…for reasons that are both established and unexplored.

Problems that require patience and resilience demand windows of time that are measured in days and weeks — not classroom minutes. The “joyful struggle” that is often trumpeted by math educators is a great idea…that is only as great as the amount of time that we honestly and reflectively allocate to such mathematical celebration. The constant insistence on speed and execution of pedagogical pedantry will continue to yield what has been the historical experience of most students — a loveless adventure.

As Dr. Leslie Dietker of Boston University often proclaims, “students deserve to love math”. This is where the bar must be set. Anything less, and math education will struggle to honor the true spirit and joy of mathematics — leisure contemplation within the domain of simple pleasure. It’s time to acknowledge…time. If Mick Jagger was a mathematician, he would have quite easily penned “Time Waits For No Mathematical Idea”.

When David Hilbert addressed a crowd of mathematical elite at the International Congress of Mathematicians in a hot summer in Paris, 1900, he trumpeted ten of his 23 math problems that needed a time line to be solved. There was almost an impatient demand here — almost. You see, Hilbert wanted all these mathematical nuts cracked by the end of the century. Math was on the clock for literally the first time. Hilbert, as impatient as he might have been, still gave a length of time that respected and honored how mathematical diamonds are created — they take time. Mathematics was always a long-distance run — with hurdles. It has now become a sprint — with hurdles.

Let’s ask the exiting members of society how they feel about mathematics: survey says…

Only minutes to think = lifetime of confusion

While not all have negative views of mathematics, many do. Probably at least half. That’s some pretty “craptastic” quality control. The emergence of a Growth Mindset is wonderful — but, it will only be as good as the soil that this hopeful seed is planted in. That soil is time. The brain is not partitioned by any particular math curriculum or topics. It doesn’t need to always solve 19.2 problems/day. I see that is working out(See September Students below). It just needs its axons and synapses firing, and blood rushing through its hemispheres with maybe some excitement…Resilience and persistence normally don’t function terribly well with a stopwatch.

Neither does joy.

“The two most powerful warriors are patience and time”

Leo Tolstoy

Without these two needed gladiators in the mathematical arena, we are basically setting not only our children up for failure — we are setting up ourselves for failure. All the problem solving strategies that we hope to instill and have students to put in their mathematical toolbox will have shelf lives only as long as the time given to them.

Every September, students from all around North America spend the beginning of the math year on “review”. This is because we know — yes, we actually know and expect this — that most students will have forgotten anything that involves continuity/bridging. Hmmm…isn’t the definition of learning kind of not forgetting stuff? Remember those races as kids where we ran with a bowl of water that had holes in it, and we had to dump as much remaining water into some bucket? I will let your imagination work through the metaphors here.

So, if we are not addressing all of the above, then at least we should be courageous enough to ask why we are so indifferent to the detrimental effects of limiting time and caging the students of mathematics — when the discoverers were not. Are we too consumed by our mandate(s)? Are we content/helpless with a mathematical experience hamstrung by time?

Let’s ask one last question:

Perspiration vs. Inspiration: Which Mathematical Road Are We On?

Time’s up…almost.

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Author, porous educator, audiophile.

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Sunil Singh

Sunil Singh

Author, porous educator, audiophile.

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