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.

We’re suffering from lack of fluency in basic math

The case of mistaken identity with math isn’t between arithmetic and mathematics, it’s between math educators and professionals who actually use mathematics in the world outside of the K-12 classroom.

In a previously published Local Voice, Dr. Campbell asks, “Do we really want to spend time anymore on learning times-tables and other purely arithmetic procedures? When was the last time those were used in the workplace, especially where time is money?”

Apparently, Dr. Campbell hasn’t observed the inability of young cashiers who can’t calculate change in real time when the computerized cash register becomes useless during a power outage. Or perhaps he’s never waited for a job candidate who showed up because the candidate’s phone calculator couldn’t identify the correct time for setting the alarm.

But inconvenience in the workplace isn’t the worst of what 21st-century thinking has brought America’s developing children. Serious problems include:

Lost opportunity for optimal brain development and logical problem solving. Humans are not born with the ability to solve problems. Brain imaging research on young children indicates that learning arithmetic changes the human brain in a way has a positive effect on solving problems by looking for logical solutions. The human brain needs to be conditioned by the raw sensation of basic computation so that later, children can derive understanding and solve more complex problems.

Poor foundation for higher order mathematics. A lack of fluency in basic math fact recall significantly hinders a child’s subsequent progress with algebra and higher-order math concepts. It’s very difficult to get to graduate-level mathematics if you can’t hack calculus because you couldn’t hack algebra because you couldn’t hack middle-school math because you couldn’t hack arithmetic.

Increased math anxiety and confusion. Just as letters are components of words and words are components of sentences, arithmetic facts are the foundation blocks for learning the next level of math. Math anxiety starts when children fall behind in learning the basic building blocks of arithmetic and can’t keep up.

Skills such as adding and subtracting larger numbers, telling time, counting money, measurement, long multiplication and division are just a few of the concepts that a child will encounter fairly early in her math career. If she has mastered her arithmetic, these concepts will be significantly easier and she will be better equipped to solve them more quickly. If she is spending a lot of time doing the basic facts, she is more likely to be confused with the process and get lost in her calculations.

Educators’ emphasis on 21st-century learning combined with common core aligned high school math and science curricula are a scandal and leave our children unprepared for independent thinking and our state without the technical expertise it needs at the post-high school and college level. We need engineers, scientists and mathematicians to design and evaluate our state’s arithmetic to mathematics course sequence; not math educators extolling the virtues of calculators at the expense of our children’s neurologic, academic and emotional development.