# Featured Biggest science or math pet peeve

1. Sep 16, 2016

### Greg Bernhardt

Could be a common wrong definition or an ineffient way to solve a certain equation. I don't know, what in science and math bugs you? Educators should fill this thread! :D

2. Sep 16, 2016

### PeroK

Without a doubt anything and everything to do with BODMAS and PEMDAS. If it's not obvious, use brackets. Everything else is ambiguous and not worth discussing.

In particular, teaching order of operations instead of some "real" maths!

3. Sep 16, 2016

### PeroK

An an illustration, from http://www.thecalculatorsite.com/articles/units/pemdas-bodmas-order-of-operations.php

In 2012, Dr Peter Price, co-founder of the Classroom Professor website, posted a mathematical question on his Facebook page. This is what he asked:

7 - 1 x 0 + 3 ÷ 3 = ?

The post quickly spread around Facebook, with over 70,000 people seeing the post and 6,000 people leaving answers and comments. After 2 weeks, Peter pulled together the results - results that surprised him. Only 26% of respondents gave the correct answer (the correct answer is 8).

What a load of baloney! As if that mathematical mess has a "correct" answer.

4. Sep 16, 2016

### Staff: Mentor

I actually never have learnt or even heard about this abbreviation, until here on PF. It's kind of the type: How to create a problem where there hasn't been one before. However, what I've read in "modern" schoolbooks here isn't much better. E.g. the distinction between integers and quotients in the sense that integers aren't quotients. And no, it had nothing to do with equivalence classes in which case I would have had some sympathies.

5. Sep 16, 2016

### Krylov

Thank you for teaching me the expression "pet peeve". It sounds sweet.

I know others may disagree (and that is fine, but only this time ), however: A long-cherished "pet peeve" of mine is the tendency that I perceive in higher mathematics education here to present pure and applied mathematics as two separate institutions without any common ground. This creates an artificial kind of competition and animosity that does not do justice to research practice and, so is my conviction, will ultimately be detrimental to both.

6. Sep 16, 2016

### Staff: Mentor

Or

7. Sep 17, 2016

### Lord Anoobis

Something else I noticed. The convention that $\sqrt{4}$, for example, indicates the positive square root of 4, not both the positive and negative roots seems to fall by the wayside among many students.

8. Sep 17, 2016

### Beanyboy

Forgive my ignorance. I'm an adult learner, studying Physics and having to study calculus to have a better understanding. Much of pre-calculus is algebra, and coincidentally, I'm doing some work on "order of operations" at the moment. Would you mind indicating why it's a "mathematical mess"? Much appreciated.

9. Sep 17, 2016

### Beanyboy

Funny that, I'm trying to learn Pre-Calculus at the moment so I can later "play with the big boys, and girls". Currently, reviewing "order of operations". Would you mind being a bit more specific, perhaps with an example? Much appreciated.

10. Sep 17, 2016

### Staff: Mentor

One of the statements has been: When in doubt, use brackets! This means brackets group things and all calculations within brackets have to be done before we can drop them. So brackets define what comes first. If multiple of them are nested, then it has to be inside out.
E.g. $(5 + ( 3 \cdot (7 - 2))) = (5 + ( 3 \cdot (5)))=(5 + ( 3 \cdot 5))=(5 + ( 15 ))= (5+15)=(20)=20$ because the grouping is inside out.

The example above $9 - 3 \div 1/3 + 1$ is ambiguous because it is not clear, whether $9 - (3 \div (\frac{1}{3})) + 1 = 1$ is meant or $9 - ((3 \div 1) \div 3) + 1 = 9$. Associativity is the word for the rule $a\,\cdot\,(b\,\cdot\,c)=(a\,\cdot\,b)\,\cdot\,c \;$ or $\; a\,+\,(b\,+\,c)=(a\,+\,b)\,+\,c \;$. Our notation of division is not associativ! Thus there are actually brackets needed. They wouldn't be necessary, if we wrote $3^{-1}$ instead of $\frac{1}{3}$, because there is no division anymore, just a minus sign. The same minus that we use at subtraction to indicate inverse addition; only in the exponent as it is an inverse multiplication. So the need to talk about division is only due to our sloppy notation.

For the order of usual operations, take an example. You need blanks to cover a room which one part is a square of $4m^2$ and a second of $5m$ by $3m$. How much wood is it?
You'll certainly multiply $5m \, \cdot \, 3m$ before you add them to the $4m^2$. Since taking the meters to the power $2$ is actually a multilpication, one doesn't have to mention that it comes first. This becomes somehow necessary if we deal with something like $2 \,\cdot\, 2^\frac{1}{2}$ but only because we have no other way to write $2^\frac{1}{2}=\sqrt{2}$. It is the diagonal of a square of length $1$. So nobody would assume the doubled diagonal to be $2\sqrt{2} = 2 \,\cdot\, 2^\frac{1}{2} = 4^\frac{1}{2}=\sqrt{4}=2$. In this sense, the demand to calculate powers before multiplications is nonsense and only due to a lack of understanding what $2^\frac{1}{2}$ means. If we had to calculate $5\,\cdot\,3^2$ then it is $5\,\cdot\,3\,\cdot\,3$ and it doesn't matter whether we calculate $5\,\cdot\,9$ or $15\,\cdot\,3$.
The rule that the power comes before multiplication is nonsense, since it is a multiplication and these are associative. If one correctly understands what $3^2$ or $m^2$ is, the question doesn't come up. $5\,\cdot\,3^2 = 15^2$ would only show, that someone hasn't the slightest idea what $m^2$ really means. Therefore the demand: teach them proper math instead of dull rules.

And that multiplication comes before addition is obvious, too. Otherwise $2m+3m$ couldn't even be performed.
[$2m+3m=2\,\cdot\,m \,+\, 3\,\cdot\,m = 5\,\cdot\,m = 5m$ and $(2m+3)m$ is absolutely senseless.]

11. Sep 18, 2016

### Beanyboy

Would you care to comment on Sal Khan's transcript of Khan Academy, on the subject of Arithmetic Properties: " I want you to pay close attention, because EVERYTHING else that you are going to do in Math is going to be based on your having a solid grounding in,order of operations." He's making the point that we have conventions for interpreting algebraic statements. Forgive me, but is there a problem with agreed upon conventions?

12. Sep 18, 2016

### aheight

Multi-valued functions are not presented well.

13. Sep 18, 2016

### JaredJames

Interchanging mass and weight. Or more to the point, people not recognising there is a difference.

14. Sep 18, 2016

### PeroK

The convention that you need is "if there is any risk of confusion, then brackets must be used". No mathematician would write:

$a + b \times c \div d$

And expect everyone else to know what they mean. First, $\div$ is not actually recognised as a mathematical symbol in the ISO (International Standard) for Mathematical Symbols.

Any good mathematician would write, for example:

$(a+b)c/d$

or $\frac{(a+b)c}{d}$

There is then no ambiguity.

Let's take an example of completing the square for a full quadratic expression:

$ax^2 + bx + c = a(x^2 + \frac{b}{a}x + \frac{c}{a}) = a([x+ \frac{b}{2a}]^2 - [\frac{b}{2a}]^2 + \frac{c}{a})$

$= a([x+ \frac{b}{2a}]^2 - \frac{b^2 - 4ac}{4a^2})$

What rules of order of operations do you need to memorise to understand that? And what would Dr Peter Price think of that? So many unnecessary brackets!

15. Sep 18, 2016

### Beanyboy

Thanks for clarifying. If I've understood you correctly then, your problem is with his notation, which you argue is ambiguous and doesn't comply with ISO - which I'm inclined to agree with you. He, as a "Math Professor", ought to know better, you argue. Hence the peeve. Presumably though, you do agree that, given appropriate notation, we should all proceed using the same convention, inelegantly phrased as PEMDAS.

16. Sep 18, 2016

### PeroK

No, because PEMDAS implies that we can leave out the brackets and everyone can decipher what we mean. I don't care what PEMDAS has to say about:

$a + b \times c \div d$

To me it's nonsense, whatever PEMDAS says. And, any mathematical argument about what is the "correct" answer is of no consequence.

And, in fact, homework posters on this forum often leave out brackets. What do the homework helpers do?

a) Assume we are all using PEMDAS and answer the question as implied by the PEMDAS rules?

or

b) Ask the poster to clarify precisely and unambiguously - by inserting brackets - what expression they intended?

17. Sep 18, 2016

### Beanyboy

I can imagine it must be frustrating trying to help when people are being ambiguous. However, if your preference is for (b), insert brackets, are you not then requiring the learner to comply with the first rule of PEMDAS - parentheses first? As a learner I'm being informed that the order of operations has nothing to do with what is "correct", but rather that a convention has been established, and to avoid confusion, we all follow the same convention.

18. Sep 18, 2016

### PeroK

If you have a convention, why use brackets? That's the whole point of PEMDAS and what Dr Peter Price is saying. What he is saying is that:

In 2012, Dr Peter Price, co-founder of the Classroom Professor website, posted a mathematical question on his Facebook page. This is what he asked:

7 - 1 x 0 + 3 ÷ 3 = ?

What Dr Peter Price is saying is: that expression makes perfect sense if you follow his convention; that all mathemticians should follow his convention and get the same answer; and that someone who says that expression is ambiguous is wrong!

What I'm saying is that that expression is garbage. There is no right answer or wrong answer. It's meaningless and of no interest within mathematics.

And, part of my peeve, is that this stuff is taught instead of real mathematics!

19. Sep 18, 2016

### Beanyboy

I can assure you I'm not trying to be obtuse, but, you've said: "If you have a convention, then why use brackets". My understanding was, the usage of the brackets IS the convention, and that it is not the convention of Dr. Price, but rather the convention of the global Math community. I have no idea who this man is, and it matters not. So, are you arguing that he's making up his own conventions? Sorry to be a pest. Feel free to just "let this go". I understand.

20. Sep 18, 2016

### OmCheeto

Ah! Hahahaha!
I had the most dreadful time trying to post something the other day because of this, without sounding like more of a fool than I already am.

In retrospect, I'm pretty sure I just got disgusted, and went with my 18th revision.

ps. I'm still blaming it on my fish scale.

Om; "Fish Scale, why do you measure in both force and mass"?
Fish Scale; "Because American's are a bit slow, but have lots of money, but the international market is heating up".
Om; "Why don't you then offer buttons for slugs and newtons"?
Fish Scale; "Because there would be too many 'Om is a fat slug' jokes".
Om; "Ok. That makes sense".
Fish Scale; "ps. And you really haven't figured out how the two buttons work yet, have you".
Om; "Not really. And I can appreciate what you are saying. If you'd had two more options, you'd have been in the trash on the first day".
Fish Scale; "You got it".
Om; "Thank you, Fish Scale. I <3 you".
Fish Scale; "I know".
Fish Scale; "Oh. And Om, you should try and figure out if "LB" stands for "LBF" or "LBM".
Om; "I hate you, Fish Scale........"
Fish Scale;