## The Real Basic Skills in Math and Arithmetic

Long story short: The writer of a Letter to the Editor recently took me to task over a recent column. She strongly disagreed with my opinion that arithmetic skills are no longer** as** important as they used to be, and the view that math and arithmetic are not identical.

Part of the problem seems to be that I was a math educator. (Don’t tell my mom. She still thinks I was a saloon bartender). Apparently, this means I am unprofessional, don’t use math in the real world, and disqualifies me from any meaningful discussions about basic skills and how students learn them.

Aside from the Letter’s tone, I really have no quarrel with the writer. She’s entitled to her opinion after all, and a couple of her views aren’t terribly unusual. But I do think some observations about her points are in order:

- This always-present objection about cashiers who can’t calculate change quickly is simply NOT a technology problem. (Nor is being late, phone alarm or not). Some of us can remember such cashiers (and late arrivers) well before calculators were invented!
- I will gladly agree
*that the ability to tackle and solve real world problems is the goal of mathematics!!!*It is partly why I believe we need to spend MORE time on that skill these days, and LESS on ‘adding and subtracting large numbers’. - I would quickly agree that math anxiety can start when students fall behind in arithmetic skills. Part of my point exactly! (Especially
*timed arithmetic practice!!*Students begin to think they’re ‘dumb’, when they aren’t, simply because they can’t do something quickly. ) - The writer seems highly enamored with engineers. I would ask her to show me an engineering firm that still calculates with paper and pencil, or ‘long multiplication and division’.

Digging deeper, I believe the subtle crux of the disagreements here lies in the terms ‘basic skills’ and ‘fluency’. The writer makes a big deal that basic skills are needed for ‘higher math’ and problem solving. It sounds reasonable, and I partially agree. SO, let’s stop and ask: “Just what are basic skills in 2017? What were they *ever*?”

Consider Student A who can easily and accurately divide 396 by 52 using long division, but who is stumped by the question “If John donates $396 to a cause in one year, what is his average weekly donation?” Which would we prefer Student A be able to do? Which is the ‘basic skill’?! Would we say Student A is fluent in division? Moreover, if Student B knows that division is called for here, does it really matter *how* he/she gets that answer – mentally, abacus, pencil, or calculator?

**This has been our confusion for decades – even before technology.** Basic skills involve knowing

*when*an operation is called for, knowing

*how*to apply that operation (with technique of choice), and then knowing how to

*interpret*the answer in the real world. Being able to learn and flawlessly perform some rote technique to get ‘an answer’ isn’t a

*necessary*basic skill any longer. It used to be our only route to getting those answers, but no more. If we are in trouble, then it is because we have mistakenly focused (even before calculators!) on

*techniques*rather than

*recognition and application of skills*(part of problem solving).

We ALL want our students to be able to efficiently tackle and solve ‘real world’ problems, using whatever tools/techniques are at their disposal. We should continue to focus on that common goal. And in the process, using a calculator to get past the tedious calculations does not hurt – indeed, helps with – the *real* basic skills.