Math Test

Answer: B

I'll admit I had to look up the order of operations.

20 years ago fresh out of the classroom I knew it cold. Skills not exercised get rusty. One of the downsides to the blessings that we call Data collectors and Computers.

Boundary surveyors answer = Well, if both of you thought it was "a" for the last 10 years, then "a" it will be on the map. After all, it's only "b" because a bunch of people before our time agreed on the rules that it would be that way. Another rule is not wrong (if you can get everyone to agree on it), it's just different.

These problems always generated the "why" question from my best students. Made for great discussion. Those that took my advice and did them by hand, writing down the steps, tended to remember on the exams. Those that insisted on using the calculator exclusively tended to get "a" on the exams.

Yep, still a daily problem in any mathematics classroom. They're supposed to teach order of operations in pre-algebra, if not sooner, but half or more of students don't get it The first department head I taught under at community college said, "You can't turn a weak math student ino a good one by giving him a calculator." Technology does dumb down work, sometimes with unintended consequences.

We use algebraic calculators exclusively in my school, but I used RPN in industry, and RPN seems to be the favorite among surveyors. So, let me ask a question.

Could we all use RPN to get the correct answer in this case?

50 years ago a math teacher told me to remember "My Dear Aunt Sally"

Don't forget the Please, the parentheses that interrupt the order. Nowadays, I hear PEMDAS, Aunt Sally apparently being sexist or offensive to someone in some other way.

That gets you through 99% or better of what you encounter. The thing that's left out is that division and multiplication are completed in the order that they occur in the expression to be evaluated. Usually it doesn't matter, but sometimes it does.

Mathematics is indeed a language with it's on words and syntax. You have to read it in order to do it.

Sorry. That should be "its own."

"Could we all use RPN to get the correct answer in this case?"

I don't see why not. We can all get the correct answer with either type. RPN is better for learning I think. My students came from differing majors and had all different types of calculators, mostly algebraic. Most of the algebraic will do everything automatically for the student as long as they enter the string correctly, however, many would still get the wrong answer (didn't know how to enter as a string or calculator didn't support that). In fact many of the students would buy a better calculator after seeing others with the capability, rather than try to learn the order of operations. Probably RPN can do the same thing, but I never did things that way myself.

Where the problems surface is in later courses where one is required to put together an equation from data and then solve it (problem solving without software; imagine). The calculator will not do that for you, and you have to know the order of operations. Were it up to me I would not allow calculators that allowed students to avoid learning in the basic algebra courses. And then there's smart phones to try and keep out these days.

Maybe the biggest hurdle for many of my students was the typical idea that for their particular major there was no reason to know "this stuff". Barriers to learning at Community College are mostly self imposed and dependent on life experience before entering. Technology is a double edged sword; it can either help or hinder breaking down those barriers, depending on how it's used.

Do your courses require one certain calculator? I always thought that would be the way to go but was not allowed to implement policy such as that.

Agreed. After a while those skill sets fade away...every once in a while I inverse two points by hand, or reduce field notes by hand..just so I remember how to do it.

That's what I was taught.

In a sense, we do. The county school system buys Texas Instruments calculators from the TI 83/84 family.

My colleagues and I share your feelings about calculators sometimes lessening understanding. That's likely to get worse as calculators embody more and more elements of Computer Algebra Systems.

I asked the question about RPN because using it to evaluate the example expression requires user-knowledge of order of operations. An algebraic system would evaluate it correctly if the expression were entered as one continuous entry. Personally, I don't consider that to be an advantage and students still find ways to screw it up.

The reliance on technology to replace understanding goes beyond the mathematics classroom. I'll bet that most of us have examples of that.

I think math should be taught from scratch. A person should add, subtract, divide and multiply with no calculator at first. (test...no calculators allowed). You get simple math tests and learn the orders of operation, then move up to calculators and computer programs. How many can check simple math without a calculator these days?

When I check things like a legal description or a drafted subdivision or sketch, I always pull out the calculator and plug in several parts to curves and check the missing parts. I might catch a bust before I even run the perimeter if there is one. It's just good to know what the big software is doing and know enough to do it yourself.

Of course posting here is probably preaching to the choir.

Please Excuse My Dear Aunt Sally...

The answer is B...

It amazes me that the concepts of basic math are lost among a lot of the youth today. They don't teach the same way we were taught and it's kind of scary. The schools local to where I am don't even teach cursive anymore.

It's good preaching regardless. One of the huge roadblocks to correcting such deficiencies among high school students is protests from parents. Another is the lack of time for remedial work granted by today's curricula and testing environment. More than one parent believes that math isn't important and my Math III curriculum seems to assume that every student mastered every item in every preceding course.

I appreciate the comments here. Coming from professionals who rely on math every day, they are valuable. I may share them with my colleagues who sometimes think that nobody cares.

Math Teacher,
I went to a survey technical school. The first x-amount of time we did exactly what I was talking about. We had adding, subtracting, multiplication, and division tests - no calculators. We used sine-tables, and the whole nine yards. One thing that you find out for sure was how easy it is to not carry a 1, or have one small easy to make mistake. I buzzed through the first exam in no-time flat...and after I got marks on all I missed, I learned to buzz through them all and go back and redo them as a double-check. (on a similar note, we also learned how to read transits, "throw chains", and how to use all the older equipment before moving to modern equipment. I never forgot how to read a transit or an internal vernier either.)

When you least expect it, a piece of that old knowledge will come in handy.

The first Algebra/Trig course I ever taught, I introduced the numerical values of the trig functions with a table. We explored how sine and tangent increase as the angle increases while the cosine decreases. I was amazed to discover that students believed the table but questioned the calculator. I have no idea where that came from, but those young'uns believed paper over a screen. On test day, they asked if they could use the table rather than the calculator. Go figure that.

When I took Algebra we had to show all our work, or at least turn in our scratch paper, And we didn't have the multiple choice option.
One of the greatest teachers I can remember; he explained once that math problems were a lot like shooting free-throw shots, the more you practiced, the better you got.

Now it is PEMDAS (Parenthesis, Exponents, Multiply, Divide, Add and lastly Subtract)

That question reminds me of a discussion I had with the elementary school a Ross the street. They were teaching the kids PEMDAS, but not the parts with equal footing. The written lesson plans were grotesquely incorrect. The bad part was they had been that way for years. Scary stuff...

Honestly as much as I hate to say it, for the majority of students they are probably right. Outside of the engineering fields, it just makes someone seem dumb not to know basic math, but it's a bit like deciding that it makes someone seem uncultured to not have basic art knowledge for all the relevance it actually has in their lives. I know a lot of people who get by just fine with less math then I knew in 5th grade.

Hell, I know one finishing up her doctoral thesis.