Biggest science or math pet peeve

[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

 

[PeroK]

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

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!

 

[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:

Can you answer this?

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.

 

[fresh_42]

I actually never have learned 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.

 

[S.G. Janssens]

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.

 

[Borek]

7 - 1 x 0 + 3 ÷ 3 = ?

Or

9 - 3 ÷ 1/3 + 1 = ?

 

[Lord Anoobis]

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!

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.

 

[Beanyboy]

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:

Can you answer this?

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.

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.

 

[Beanyboy]

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!

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.

 

[fresh_42]

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.

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.]

 

[Beanyboy]

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!

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?

 

[aheight]

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

Multi-valued functions are not presented well.

 

[JaredJames]

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

 

[PeroK]

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?

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!

 

[Beanyboy]

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!

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.

 

[PeroK]

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.

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?

 

[Beanyboy]

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?

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.

 

[PeroK]

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.

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:

Can you answer this?

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!

 

[Beanyboy]

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:

Can you answer this?

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!

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.

 

[OmCheeto]

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

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.

Now the internet says a CD weighs [has a mass of] about 0.02 kg, and I had to apply an equivalent force of 2 kg to keep the CD cycling. (I'm using a fish scale to measure the forces)
That's a factor of 100.
Scaling that up to your 100 kg flywheel gives me an equivalent force of 10,000 kg. (98,000 Newtons)
One place on the internet says that a 4" diameter gasoline driven piston applies the equivalent of 2860 kg (6300 lbs) of force near the top of its stroke,

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;

 

[JaredJames]

Fish Scale;

My current favourite is when I'm asked how much force a handle will take to operate, which I give in Newtons, followed by the "and how many kg is that?" question. It's particularly amusing when I say "X N, wow, that won't be easy to shift" and get a blank look. Then have to say "it's the equivalent of lifting 50 kg" and wait for the cogs to turn...

 

[fresh_42]

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;

With this I have my trouble, too. I mean they sell me 5 kg potatoes, but use a device, that measures Newton. However, those Newtons are written by kg on it. Now, when I leave the shop, have I bought 50 N, 5 kg or did they cheat on me and sold me 5 N of potatoes?

 

[Mark44]

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

The convention is that operations are performed in order of the letters in the acronyms PEMDAS or BODMAS, with letters at the beginnings of each acronym being of higher precedence than the following letters. For example, 3 * 4 + 5 is evaluated as 12 + 5 = 17, and not 3 * 20 = 60. To indicate that the addition should be performed first is where the P (for parentheses in the first acronym) or the B (for brackets in the second acronym) come in.

Each operation in the arithmetic operation pairs, MD (or DM) and AS, has the same precedence, with these operations being performed in left-to-right order as they are found in the expression.

 

[PeroK]

The convention is that operations are performed in order of the letters in the acronyms PEMDAS or BODMAS, with letters at the beginnings of each acronym being of higher precedence than the following letters. For example, 3 * 4 + 5 is evaluated as 12 + 5 = 17, and not 3 * 20 = 60. To indicate that the addition should be performed first is where the P (for parentheses in the first acronym) or the B (for brackets in the second acronym) come in.

Each operation in the arithmetic operation pairs, MD (or DM) and AS, has the same precedence, with these operations being performed in left-to-right order as they are found in the expression.

My pet peeve is that that is all completely pointless and can only lead to confusion. It would be better if $3 * 4 + 5$ were deemed ambiguous. In a sense it always is, since I would never bet on what someone actually means by it.

It would have to be $(3*4) + 5$.

The problem gets worse when you add more and more symbols to the point where what you have obeys your wretched convention but is practically indecipherable.

Anyway, it's terribly unfair of you not to let me have my pet peeve. Everyone should be allowed to have one!

I'm well peeved now!

 

[Mark44]

My pet peeve is that that is all completely pointless and can only lead to confusion. It would be better if 3∗4+5 were deemed ambiguous. In a sense it always is, since I would never bet on what someone actually means by it.

When I took 9th grade algebra (in the late 50s) the acronym was MDAS, which we remembered with the help of the mnemonic device "My dear Aunt Sally." Without some sort of convention such as MDAS, PEMDAS, or BODMAS, the expression 3 * 4 + 5 is ambiguous. I agree with you that often people posting here are ignorant of the convention that y - b / x - a means $y - \frac b x - a$, and not as they probably intended, as $\frac {y - b}{x - a}$.

There are similar conventions on the order of operations in most programming languages. However, since there are a lot more operations that are covered, there aren't any handy acronyms to help you remember them.

Since this thread is about pet peeves, one of mine (pretty picayune) is calling all of the enclosing symbols "brackets."

As I learned them, and this could be an American thing, they all have different names.
Parentheses - ( ) -- Each one is a parenthesis
Brackets - [ ] -- sometimes called "square brackets," seemingly redundant to me, akin to a "round circle" or "straight line"
Braces - { } - AKA "curly brackets"
Angle brackets - < >

 

[fresh_42]

TIL

As I learned them, and this could be an American thing, they all have different names.
Parentheses - ( ) -- Each one is a parenthesis
Brackets - [ ] -- sometimes called "square brackets," seemingly redundant to me, akin to a "round circle" or "straight line"
Braces - { } - AKA "curly brackets"
Angle brackets - < >

Thanks. This reminds me on the notation $[a,b]$ for closed and $(a,b)$ for open intervals. I find this a little bit disturbing, since parentheses are used in too many places. I learned $]a,b[$ to denote open intervals, which I find much more telling.

 

[OCR]

Lol... Windows 10 Calculator - STANDARD...

Windows 10 Calculator - SCIENTIFIC...

Who'da thunk it... ? [COLOR=#black]..[/COLOR] [COLOR=#black]..[/COLOR]

 

[fresh_42]

W7 - same results

 

[Beanyboy]

The convention is that operations are performed in order of the letters in the acronyms PEMDAS or BODMAS, with letters at the beginnings of each acronym being of higher precedence than the following letters. For example, 3 * 4 + 5 is evaluated as 12 + 5 = 17, and not 3 * 20 = 60. To indicate that the addition should be performed first is where the P (for parentheses in the first acronym) or the B (for brackets in the second acronym) come in.

Each operation in the arithmetic operation pairs, MD (or DM) and AS, has the same precedence, with these operations being performed in left-to-right order as they are found in the expression.

Thanks. Personally, I didn't have a problem with it. Seemed pretty straightforward to me. Appreciate the explanation though.

 

[Chestermiller]

So far, all I see are math pet peeves. Doesn't anyone have any science pet peeves? I know that I have a slew of these. But, I want to wait and see what other people say.

 

[Mark44]

Lol... Windows 10 Calculator - STANDARD...
View attachment 106206
Who'da thunk it... ? .. ..

In standard mode, the calculator appears to be evaluating all operations left to right. If you calculate 7 - 2 * 3, you get 15.

 

[OCR]

In standard mode, the calculator appears to be evaluating all operations left to right. If you calculate 7 - 2 * 3, you get 15.

Yeah, it is...

In the scientific mode you get 1...

 

[Bystander]

Doesn't anyone have any science pet peeves?

"Over unity/PMMs."

 

[OCR]

W7 - same results

Yeah, I think they both have the same functions ...

https://en.wikipedia.org/wiki/Calculator_(Windows)#Windows_7

 

[Student100]

Maybe it's just me, but does anyone else think significant figures as explained in a number of textbooks are a bit ambiguous? Something like, $2.000(11.23 - 10.53)$ could be interpreted as $22.46-21.06$ or $2.000(.70).$ Even beyond what I see as ambiguity, significant figures based on multiplication/subtraction/etc. are kind of annoying. It seems just as easy to teach propagation of uncertainty and get students use to seeing a number with it's accompanying error bounds. Although I can see the appeal to the quick and dirty method (it's quick).