Republic of Mathematics blog

I responded that maybe teaching them something about writing secret codes and trying to crack them might work. I had worked with my colleague Nigel Smith who taught mathematics to grades 5 through 7 at Twyford School in Hampshire, UK. When Nigel and I planned a sequence of lessons on codes his students were very keen to form teams, writing secret messages and trying to crack those of the other teams.

Just before Christmas break we set the kids the task of writing a reasonably long coded message, long enough so that the other teams would have a chance of cracking them. I explained to the students that in practice, most coded messages were not cracked by intelligence, but rather bu a failure to observe protocol, or by coercion. One of the boys asked me about coercion, and when I explained, he asked Nigel with some enthusiasm: “Sir, can we torture the other teams?”

Maybe code writing and breaking will not work as well for Ben’s year 4 as it did for Nigel’s years 6 and 7. Yet the first steps in coding are simple and fun, and require little more than an ability to count, make educated guesses, and analyze data carefully. With that in mind, here is a first step in coding for kids.

Algebra has been a big concern of mathematics educators for many decades. My late colleague and friend Jim Kaput, famous for his work on algebra learning, essentially moved away from traditional algebra to simulation and modeling as routes for students to learn about change in mathematics. Jim was a visionary, and the cognitive difficulty of algebra sent him exploring many routes to help all students obtain mathematical competency.

Discussions about the utility, or otherwise, of algebra surface regularly. Recently an Education Week article “Is There an Algebra Overkill” tackled this question again.

The author, John W. Myres, comments:

“Most people add, subtract, multiply, and divide, using whole numbers, fractions, decimals, and percentages. They purchase food and clothing, balance checkbooks, create budgets, verify credit card charges, measure the size of rooms, fulfill recipe requirements, and even understand baseball batting averages or horse-racing odds. These activities don’t require a real knowledge of algebra.”

I feel the implication here is that it is not the “average” person that John Myres wishes to refer to, but the “typical” person. The implication, to me, is that it is a relatively rare bird who would find a need for algebra in their lives, or am I misreading Mr. Myres? To be fair, he does write: “These activities don’t require a real knowledge of algebra.” Yet the tone of the article is that “most” people do not need to use algebra on a daily basis.

Is Mr. Myres right? I know my wife does not use algebra in her job as a university administrator, though she does use arithmetic in her job and at home to balance budgets. I am am a mathematician and I rarely use algebra except when I am teaching it! or when I am teaching other parts of mathematics. Then I use it a lot. So, who else apart from mathematics professors like me, and other mathematics teachers, uses algebra on a regular basis as part of their job? If we can scarcely find anyone then Mr. Myres is right and we have to ask why we are inflicting on school and college students what is known to be a fairly painful experience, one at which many students are likely to fail miserably.

Here’s a comment on the blog Intrinsically Knotted:

“Efrique I use algebra every day, typically seven days a week. I use it a lot in my job (I work for a software company). A day I don’t use algebra to solve a problem in my work is likely a day where I haven’t achieved a whole lot. I use it to do research. I use it in my hobbies. I use it when I go shopping.  Mostly, I just use it to think.”

So here’s someone in a software company – we don’t know what sort of job – who claims to use algebra daily. Maybe lots of software jobs call for people to use algebra regularly. But are such people “typical”.

At Yahoo! answers wooliebear07 writes:

“I use it all the time in cooking. I often have to make recipes smaller because I only cook for two. Also, I am a campaign manager and use algebra all the time for determining my targeting. In high school or college I never thought I would need algebra for my job. It’s surprisingly useful in many different careers.”

We don’t know what wollibear07 does for a living, but if Mr. Myres is right, wolliebear07 is not typical.

Pisces ♥ Math writes that engineers, astronomers, statisticians and accountants use algebra in their everyday jobs. Supposing she is right, and also Mr. Myres is right, then people working in these professions are not “typical”.

Now to me it is beginning to sound suspiciously like Mr. Myres means that in certain aspects of our daily life – such as those he describes – we do not need or use algebra: this is, in fact, whet he writes. With that I agree. However, even a cursory examination suggests that in many numerate professions people do use algebra regularly. And in an highly educated society more and more people work in these sots of professions: they cannot be simply dismissed as atypical.

A huge educational problem is that school and college students do not see what happens in the daily work like of professionals. Shouldn’t that be part of a student’s education? Shouldn’t real life professionals be invited to school to say to students and teachers what skills they use daily? Shouldn’t that be part of a student’s education?

Postscript

Chancellor740 posted a interesting question about algebra on reddit.com: “Why does algebra make me want to kill myself?”
The question and comments are worth reading.