“A” is for Algebra, “E” is for Elementary; (E)(A)=The State of Current Research…

Linear algebra was always my mathematical strong suit—heavily relied upon, as it barely shrouded my thin quantitative undershirt. This surprised my artist mother somewhat. She had always assumed —visuospatial as I was—that I would be better matched to the more ‘creative’ study of geometry or even abstract algebra. But to me, linear algebra WAS creative, in a predictably pretty sort of way—its mastery relied on using elegant variables to represent the unknown—and each composition (equation) relied on the perfect visual balance between constants and variables.

When I did embark on the ‘creative’ territory of abstract algebra, I was confronted with polynomials, matrices, and an increasing amount of variables as compared to a dwindling amount of numbers. Suddenly, even my grasp of linear algebra became muddled and mired like a bad painting. ‘Creativity’ must have its bounds, because I still don’t particularly understand abstract algebra…or abstract art, really…

Rubik’s Cube group structure (abstract algebra) + Piet Mondrian’s abstract paintings=my confusion CUBED! Image courtesy of: bit.ly/MGdFT1

Truth be told, algebra was also my mathematical weak suit—full of holes at the seams. I had struggled with math throughout elementary school and middle school, relying on iterative reasoning and memorization to get me by where true number sense failed me—and I was an “A” student. Fortunately, researchers are now investigating how early algebra can be introduced to (and understood by) elementary students to prepare them for ‘big A’-Algebra.

Exploring Children’s Understanding of Functions (CUF) is one such initiative. CUF is a research collaboration between TERC and Tufts University exploring how children in grades K-2 understand functions as a context for early algebra. Project researchers have pilot tested teaching experiments among young elementary students, and have observed that K-2 graders are an optimal audience for grasping early algebra.

That’s right—5-7 year olds. So what is it about these tykes that make them so good at algebraic thinking?

It may be that K-2 graders don’t have a lot of mathematical baggage—that is, they don’t solve problems by relying on recursive relationships like many of their upper-elementary brethren (or, ahem, I) do. Early research observations suggest that they do not have strong aversions to or misconceptions about using variables—and seem to be equally at ease using symbolic notation (variables) and natural language to talk about math problems. And project researchers noted that the K-2nd graders in their sample were more likely to represent a function rule as an equation (e.g. R + R=V) rather than an expression using syncopated language. Wow!

So perhaps 5-7 year olds can be harnessed as truly ‘creative’ algebraic thinkers in newly-pressed (but maybe slightly oversized) mathematical strong suits. That sounds like a lot fewer holes for the budding mathematicians of tomorrow!

To learn more about Exploring Children’s Understanding of Functions, check out: http://www.terc.edu/work/1665.html

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