“All the Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime” by Keith Devlin in The Huffington Post, January 1, 2017,

What 21 st -Century Students Need to Know in Mathematics

In this Huffington Post article, Keith Devlin (Stanford University) says that when he

graduated from a prestigious university in 1968 with a bachelor’s degree in mathematics, he

had a set of skills that “guaranteed full employment, wherever I chose to go, for the then-

foreseeable future – a state of affairs that had been in existence ever since modern mathematics

began some three thousand years earlier.” But by the year 2000, he says, his computational

ability was “essentially worthless, having been very effectively outsourced to machines that did

it faster and more reliably… In a single lifetime, I experienced first-hand a dramatic change in

the nature of mathematics and how it played a role in society.” Calculators took over the

ancient art of mental arithmetic, and computers and cloud-based systems executed pretty much

any mathematical procedure – accurately and in less than a second.

So what mathematics, if any, do students need to master in the 21 st century? Devlin has

a very clear answer: “Whereas it used to be the case that humans had to master the

computational skills required to carry out various mathematical procedures (adding and

multiplying numbers, inverting matrices, solving polynomial equations, differentiating analytic

functions, solving differential equations), what is required today is a sufficiently deep

understanding of all those procedures, and the underlying concepts they are built on, in order

to know when, and how, to use those digitally-implemented tools effectively, productively, and

safely… The human brain compares miserably with the digital computer when it comes to

performing rule-based procedures. But that human mind can bring something that computers

cannot begin to do, and maybe never will: understanding. Desktop-computers and cloud-based

mathematics systems provide useful tools to solve the mathematical aspects of real-world

problems. But without a human in the driving seat, those tools are totally useless.”

The most basic contemporary mathematics life skill, Devlin believes, is number sense.

This has been defined as “fluidity and flexibility with numbers, a sense of what numbers mean,

and an ability to use mental mathematics to negotiate the world and make comparisons.”

Specifically, according to Marilyn Burns, number sense is the ability to:

- Think and reason flexibly with numbers;

- Use numbers to solve problems;

- Spot unreasonable answers;

- Understand how numbers can be taken apart and put together in different ways;

- See connections among operations;

- Figure mentally;

- Make reasonable estimates.

All this may seem “fuzzy and imprecise,” says Devlin, but students who don’t master these

aspects of number sense quite early in their education “struggle throughout their entire

subsequent school and college years, and generally find themselves cut off from any career that

requires some mathematical ability.” With a clear conceptual understanding of number sense,

any skill in the K-12 curriculum can be mastered quickly and easily. Students still have to work

at math, but the work will be relatively straightforward. And this is exactly the orientation of

the Common Core standards.