The math mystique
Americans have a mythical fear of math. It is considered the provenance of the brainy. Math teachers – people who triumphed in the field against the odds inherent in a deficient system – perhaps unwittingly convey to students that math is hard.
Well, it’s not.
It simply viewed wrong, and by extension, taught wrong.
The folly starts in elementary school, with things like mindless timed drills that fail to put mathematical ideas in context.
As they teach younger children to add, subtract, divide, and multiply, even the best-intentioned, most successful teachers appear to stop at things like mindless, mnemonic, tricks.
Some children may never realize that the basic operations – or ratios, fractions, and percentages, for that matter – are many faces of the same coin; beautifully interrelated; weaving wonderful patterns.
Application – even in its simplest form, word problems – is minimal and sporadic.
The folly goes on through the grades. Disjointed sub-strands of mathematics – algebra, geometry, etc. – are taught, while not at complete random, at the very least not concurrently enough to build context and see a coherent whole.
The pure drudgery and disjointedness of it never ceases to astound and depress me.
The system, I think, kills the beauty of math.
Yes, I do get stares often, when I mention that alien concept.
In an article called “Down With Algebra II!”, author Dana Goldstein makes part of my point (as well as many other interesting points) by recounting one of her conversations:
“I called Daniel Willingham, a cognitive psychologist at the University of Virginia who studies how students learn,” writes Goldstein. “He is worried about any call to make math-or any other subject-less abstract. I told him that even though I once passed a calculus class, my husband had to explain to me what a derivative was, as opposed to how to find it using an equation. Willingham replied, ‘This is very common. There are three legs on which math rests: math fact, math algorithm, and conceptual understanding. American kids are OK on facts, OK on algorithm, and near zero on conceptual understanding. It goes back to preschool. And this is what countries like Singapore do so well. They start with the conceptual business very, very early.’
“Willingham believes substituting statistics for algebra II might not solve the problem of high school math as a stumbling block,” continues Goldstein. “After all, basic statistical concepts-such as effect size or causality-also require conceptual understanding.”
“Of course, if math teachers are to help students understand how abstract concepts function in the real world, they will have to understand those abstractions themselves,” continues Goldstein. “So it’s not reassuring that American teachers are a product of the same sub-par math education system they work in, or that we hire 100,000 to 200,000 new teachers each year at a time when less than 20,000 people are majoring in math annually,” writes Goldstein.
In contrast, successful systems, such as the one in Singapore quoted above, see basic mathematical operations as a means to an end, not an end in and of itself, in math instruction; a secondary tool in solving deceptively “complex” problems.
Word problems that would baffle an American student are the meat of instruction, with solution alternatives creatively modeled. They are categorized, and step-by-step solution mechanisms systematically taught, rather than left to only the brightest to randomly discover. The information contained in problems is represented through a variety of models – think approaches such as model drawings, manipulating parts, wholes, ratios, and fractions in visualizations, re-stating and diagramming information…
Beyond basic ability to do it, the speed of calculation is immaterial; timed drills, a silly waste of time.
Math is less about numbers and more about logic, seeing patterns, evaluating information, thinking.
Having practiced the application of common approaches to ostensibly stand-alone areas of mathematics, students develop conceptual understanding. They gain the ability to categorize problems, see the commonalities across, say, algebra, geometry, and statistics, and indeed, between mathematics and other fields of knowledge.
Ordinary children, taught to see the interrelatedness of it all, begin to look like geniuses to the American eye. Mathematical, as well as any other kind of, intuition, after all, is only experience in disguise.
So what can be done?
Jump off the high horse of American superiority in all things and learn from others.
Stop bashing what you don’t understand, as the world laughs.
It’s not as if American minds are deficient.
The sporadic school districts in the United States that have adopted the Singapore approach – or a similarly sensible system – report that, while it was initially hard to retrain the adults in a system, the payoff was substantial for its youth.
Goldstein’s “Down With Algebra II!” can be read here: www.slate.com/articles/life/education/2016/03/algebra_ii_has_to_go.html
Kremena Spengler is a former academic and journalist with the BTA, the Bulgarian national news agency, and Reuters. After a bit of world travel, she moved to live a quiet life and raise children in New Ulm, joining The Journal in 1997. She likes to think her views are not that unusual for a naturalized American.