bcplimpton Loc: Southern New Jersey

Actually, IMHO, the title of this discussion should be Old Math vs. Misunderstood Math. Mathematical notation states to avoid such confusion when a denominator contains and expression it MUST be placed under a horizontal line which acts as implied parentheses. We need to understand both the rules of mathematical notation and order of operation to get the right answer. If you try to enter the subject expression into a calculator it will require you to enter a multiplication operator between the 2 and the (.

This is perhaps the clearest definition of PEMDAS I have see recently.
"You can remember the correct order of operations rules by the mnemonic PEMDAS, which says to compute anything inside Parentheses first, then compute Exponential expressions (powers) next, then compute Multiplications and Divisions from left to right, and finally compute Additions and Subtractions from left to right. The highest priority for parentheses means that you should follow the remaining rules for anything inside the parentheses to arrive at a result for that part of the calculation."

This definition at least groups multiplication and its inverse division as well as addition and subtraction but does not mention the inverse of exponents which is roots. They did however use a root in one of their examples.
See https://www.mathmistakes.info/facts/AlgebraFacts/learn/ctm/arith.html for the source of the quote.

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We are introducing expressions and algebraic concepts earlier in the educational process each year. It is now in the elementary (grade school) level in my town and is being taught by teachers some of whom chose elementary education because they were weak in math. I have long felt that we in the US have the wrong approach to education. We regularly assign the best teachers to the brightest students and to the most advanced courses. I believe that we should put our best teachers in the early grades have them use a variety of teaching methods because some students learn differently than others. The students should be encouraged and told that they CAN learn this. I have seen students in community college that have to take a remedial algebra and come into the class believing that they cannot do math having heard that from teachers since grade school. By telling them "You CAN do math and I will help you." combined with new ways of presenting the concepts the students are able to do very well in the remedial algebra course which covers most of high school Algebra I and II.
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Longshadow Loc: Audubon, PA, United States

Agreed. Algebraic equations are not new.

"New Math" in the early 60's was the introduction of various number based systems, primarily binary.

"New Math" today seems to be a bastardization of the old mathematical operational methods...

MrBob Loc: lookout Mtn. NE Alabama

Brings back memories of thinking in Hexadecimal..... Oh, so long ago. Assembly language when it was an honor to write the smallest and most efficient code... Now processing power is fast and memory is cheap.

jerryc41 Loc: Catskill Mts of NY

That's what so nice about math and science. They are so flexible that they can fit anyone's opinion.

Longshadow Loc: Audubon, PA, United States

At work I had two semiconductor test systems that were HEX based and two that were Octal based.
That was fun when I had to load the bootstraps into the machines... Even with the maintenance panels color coded for the respective number base.

I know one guy that worked with Octal so much he accidentally did a bank deposit slip in Octal one time. The teller looked at him REAL funny...

For one class I had to create an assembly language rudimentary word processor with word wrap for a 6502 based computer. When the instructor gave me my graded (A+) papers back, he asked if I did it all myself. I replied yes. It was only four, maybe five pages long. I dislike verbose code.
Now it seems that there's no interest in "small efficient" programs. Of course everything we wrote back then had to fit in less than 64K.

Longshadow Loc: Audubon, PA, United States

And one can prove anything with statistics.

Zooman 1

Never heard of PEMDAS. Guess that is showing my age.

Day.Old.Pizza Loc: Maple Grove, MN

Good thing we’re Photographers and not planning Elon Musk’s manned trip to Mars. His rocket would hit the Sun.

Dean37 Loc: Fresno, CA

Long shadow, AND it had to allow space within the 64k for the program to work.

Longshadow Loc: Audubon, PA, United States

I was going to say something about not planning any interstellar travel.

Longshadow Loc: Audubon, PA, United States

Yup. Couldn't use ALL of the 64K either, the OS resided in that space too.

Longshadow Loc: Audubon, PA, United States

I didn't remember "PEMDAS" either, I just remembered the rules.

Dannj

Scroll back. You’ll find a few explanations.

boberic Loc: Quiet Corner, Connecticut. Ex long Islander

Since the 2 and (2+2) are both under the / they are 1 expression. And (2+2) is 4. and2 is multiplied by the expression within the parenthesis 2X4=8. So 8/8=1 So the correct answer is one. That's the way I learned it over 60 years ago, sounds like old math. It's a standard "trick" algebra question. The trick is the slash. If the expression was written with a line underneath the 8 as it usually is instead of that / the equation would be very easy to solve.

Longshadow Loc: Audubon, PA, United States

That's an assumption.
You have to pick one, either is or not. Pick based on the rules.
If it was written 8/(2(2+2)) it would leave no room for doubt.