…in horseshoes. I remember that from my youth. It’s a silly expression that today’s youth will probably never appreciate because the horseshoe pit is mostly a memory reserved for old people. When I was younger though, it was a staple in just about every campground that I can remember.

It was a phrase that I used a great deal teaching computer science as the talk would inevitably get around to being one of precision and having your computer program generate the best possible answer. It was closely related to the talk about Garbage In, Garbage Out. GIGO. They were cute phrases that, at best, made me feel good as the teacher and, at worst, reinforced the age difference between teacher and student.

But precision is an important concept and something that should be checked and rechecked with every program written. Just because the computer says the answer is this doesn’t necessarily mean that it’s right. Computer science teachers will immediately recognize the look of success that comes once syntax errors have been swatted and the computer actually gives an answer. Making sure it’s the right answer is another thing…

Yesterday, I ran across this old problem that I’m sure that you’ve seen many times. “‘Simple’ maths problem stumps Boltonians – can you solve it?

Give the article a read.

Then, head over to Quiz World and see their treatment of the same problem. There are some great mathematics in the comments.

Depending upon your understanding of basic mathematics, you could get a number of different answers. I liked the discussion on the original article including how you can get the wrong answer by using a computer.

I’m sure that you’ve seen the articles “10 Things You Didn’t Know Google Could Do”. One of them is how it can act as a calculator when you enter an expression. I just had to put it to the test. How would Google fare?

All right! Google knows its order of operations.

How about Bing?

You can’t fool the programmers at Microsoft. Yahoo!?

Winner! Winner! Chicken dinner. I’m starting to tire but let’s check DuckDuckGo

There’s not an incorrect answer in sight. And, I’m tired of checking but I am impressed. It looks like they’re all honouring order of operations and not just solving from left to right. I did find a couple of seldom used search engines that didn’t do the calculations. Interesting.

It was also interesting to note how the search engines displayed their results. DuckDuckGo just gave the answer. Yahoo! displayed the question and answer in an online calculator. Google and Bing both provided the answer, a calculator, and put parentheses into place so that you could visualize the order of operations. That’s a nice touch.

Is it a concession to the fact that everyone uses an algebraic calculator?

I seldom do.

It was Statistics at university and a quiet conversation with Dr. Gentleman who gave me a demonstration of the difference between an algebraic calculator and a reverse polish notation calculator. I was sold with how many fewer keystrokes that an RPN calculator requires. I went out and bought myself a Hewlett-Packard RPN calculator and never looked back. That calculator has long since expired (well the battery anyway) but I have an app installed on any device that I own or there are many online like this one.

Since you’re pushing and popping numbers onto a stack, the concept of a parenthesis key isn’t necessary. You just need to know your order of operations and away you go. Today’s sophisticated calculator feature every bit of scientific functionality and graphing that any student could ever possibly need so that bit of mental fun isn’t always there!

Have we lost the need for parentheses?

Certainly not in the computer programming world where you absolutely want to know that the answer you get will be the right one. And, in the mental problem solving world, if you don’t understand PEDMAS, you’re in for a world of hurt. Mathematics, Computer Science and Science have made the tools for expressions at least interesting, if not challenging. Do you know the differences between parentheses, brackets, and braces? If not, here’s a refresher.

There’s a great deal of thought that goes into being precise but it’s worth it. Hopefully, our students aren’t satisfied with just being close.

I never got used to RPN, but I see its utility. I code in Java, and when casting values you write the cast type first, in parentheses:

myString = (String)someObject;

No big deal, unless you’re trying to do something with it:

myString = ((String)someObject).toUpper();

If the casting was written afterwards we could have had:

myString = someObject(String).toUpper();

I find the choice of language/tool fascinating. I’m still trying to decide how/whether a formula calculator or immediate execution calculator affects a student’s learning of algebra…

Good stuff, Doug!

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