I figured out what "My Dear Miss Sally" meant, but I had to look up PEMDAS. I just never had heard these acronyms before, although I have always just known the order. Anyway, I found this: PEMDAS Rap
I agree with the answer being 12. That's what I calculated before reading any of the post below it. I didn't learn about Aunt Sally.
However, if you take the PEMDAS literally,
> 3 + 3 x 3 - 3 + 3 =
3 + 9 - 3 + 3 =
Addition comes before subtraction so adding the 3+9 and 3+3 you get...
12 - 6 =
6
Maybe it should be P,E,MD,AS
Maybe they should quit teaching about Aunt Sally and start teaching math.
James
So I take it the old Native American phrase SOH CAH TOA has been shelved?
> 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.
Funny.
The first calculator (handheld) I saw was in 1969, cost $100 and ate batteries (no alkalines then).
I knew how to use the Pythagorean Theorem before I knew what it was named and what Smoley's was. I Still have one. I was amazed how much math there was in the back of a field book. All of this while taking, in this order, Algebra I, Geometry, Algebra II(where I finally learned Algebra) and Trigonometry.
Passed a Sophomore level College Physics class with a slip stick and had ZERO basis in physics (I found a good tutor). At that time I drooled over the HP-65 available in the student union store at $795.
Fun times.
B-)
>
> Could we all use RPN to get the correct answer in this case?
The answer is yes.
I spent some time teaching high school math. Sometimes the graphing calculators didn't have a very good way of distinguishing between a negative number and a positive number proceeded by a subtraction sign. I had a student who called me over during a final, complaining that the calculator wasn't working right; she new PEMDAS and didn't believe the calculator's answer. She got a few points extra credit for knowing when to disbelieve the calculator.
I taught elementary surveying for years in community college. We spent the first weeks reviewing basic mathematics. I ended up teaching relevant algebra, geometry and trigonometry when solving for plane figures such a parcel of land. Solving for the angle using the law of cosines was a challenge for some until they learned how to break down an equation and solve using the order of operations and inserting parenthesis where necessary. It was rocket science for some, and one time the academic instructor for trigonometry came over just to watch how I used trig for real world problems in surveying.
Now, my old community college has almost quit teaching technical courses. They cut out civil engineering technology and drafting and design technology, both with a land surveying option. "Nobody is interested in those programs anymore" was what I was told. The academic people in charge decided this among themselves without going out into industry to see how their decision would affect the area construction industry!
I taught a Technical Math II class once. Most of those guys were in the class because they did not learn the first few times the opportunity presented itself and did not want to learn in this class and were being made to go to class just to stay out of jail. But there were a few in there who did not have that first opportunity. They were the gems of the class. They learned while the other college kids threw spitballs and drew dirty pictures and played on their cellphones in the back of the class. Idiots.
I liked one above post:
"The reliance on technology to replace understanding goes beyond the mathematics classroom. I'll bet that most of us have examples of that."
And another:
"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."
Agree, and I think "Readin', Ritin', and Rithmatic" should still be taught as basic education as well as Civics and American Government and U. S. History. People still need a foundation upon which to learn, and to learn how to learn.
The Trig Teacher
Almost twenty years ago I was keeping company with the "Trig" teacher from the local HS. She was a nice lady and mathematics rarely entered into our conversations. Boot scootin' and imbiberance were some of our common interests...
Anyway, I was helping her grade papers one evening and noticed almost every student had "missed" this one particular question. It was an obtuse triangle that required solving one of its sides.
I grabbed a calculator and quickly realized that a good amount of her students actually had the correct answer. It was a standardized test with standardized answers in a standardized teachers manual. I asked her to solve the problem to see if she came up with the same answer.
Now math wasn't really her major apparently. She freely admitted that to solve the problem she would have to sit down and "go through the cookbook". She did check her handbook and what I considered the wrong answer was listed for that problem. I told her she ought to at least look into it.
She gave me some bureaucratic gobbledeeguck about the folks that put the books together and how they probably knew more than me.
phhttt...
A few weeks later she showed me some correspondence between her and one of the curriculum consultants that marketed the books and program. It was almost the same thing she had told me..."every question had been looked over and checked by lots of learned folks and they had the highest regard for quality control with their material and thank you very much for your concern and we might look into it..."
I was amazed that several people had been questioned about the validity of the published answer for a rudimentary law of sines solution and NONE of them had the mental capacity to actually solve the question. I think it took me thirty seconds or less.
While I'm sure this was an insulated isodent, it gave me much doubt as to the quality of some of the local HS's material.
The Trig Teacher
Famous physicist Richard Feynman wrote in "Surely You're Joking, Mr. Feynman!" about how he once served on a textbook selection committee for the K-12 school system. He found lots of bad examples.
There was a physics book with a problem to find the time for a ball to roll down a ramp. The issue was that they neglected the rotational inertia of the ball and got an answer that was true only for an object sliding down a frictionless plane.
And an arithmetic book that had the students find the "total temperature of six stars." The fact that the sum is physically meaningless didn't faze the textbook writer, but caused Feynman to blow his stack.
Overall, he was quite frustrated by what he found. If you want to read more, just search
Feynman textbook committee
and you'll get a bunch of hits. This one reproduces his story.
http://www.textbookleague.org/103feyn.htm tm
If someone has enough courses in "education" it is presumed they are experts in school matters regardless of whether they know the subject they are teaching or writing tests for.
