Why Are Basic Math Skills Lacking in Aspiring University Students?

[ProfuselyQuarky]

I’m a student and, of course, and I make a whole lot of too many mistakes, but while occasionally helping my fellow peers, I’ve seen really--it hurts to say it--awful mistakes that shouldn’t even be mistakes. Like, a 16-year-old not knowing how to use FOIL, or being unable to graph a parabola or circle. One time, I even saw this: $(5\log)x=5(\log x)$ … what does that even mean?? What makes it worse is that it’s not coming from students who plan to just get out of school as soon as possible--these mistakes come from people saying they want to go to a good university and pursue all these highly credited careers. I find it really sad. So I was wondering, for all you teachers/professors/academics … is that really how it is everywhere? Or am I just stuck with a “special” batch of people? If the former, do you just get frustrated and upset and let the student know? Do you ignore the mistakes and just not care?

Being a teacher of a higher level class only to discover that those you are teaching can't even do basic work sounds extremely disheartening.

 

[fresh_42]

I’m a student and, of course, and I make a whole lot of too many mistakes, but while occasionally helping my fellow peers, I’ve seen really--it hurts to say it--awful mistakes that shouldn’t even be mistakes. Like, a 16-year-old not knowing how to use FOIL, or being unable to graph a parabola or circle. One time, I even saw this: $(5\log)x=5(\log x)$ … what does that even mean?? What makes it worse is that it’s not coming from students who plan to just get out of school as soon as possible--these mistakes come from people saying they want to go to a good university and pursue all these highly credited careers. I find it really sad. So I was wondering, for all you teachers/professors/academics … is that really how it is everywhere? Or am I just stuck with a “special” batch of people? If the former, do you just get frustrated and upset and let the student know? Do you ignore the mistakes and just not care?

Being a teacher of a higher level class only to discover that those you are teaching can't even do basic work sounds extremely disheartening.

The very first phrase of our constitution is: The dignity of man is untouchable. (We have a gender neutral word for man, though.)
One of my favorite bumper stickers I ever saw was: The stupidity of man is untouchable.

It's a truth and as you see right now on every news channel: stupidity doesn't prevent people from getting famous, successful or rich.
The first year at our universities is usually the toughest one because the difference to school is quite big. There has been a favorite path for students: signed up in macroeconomic → found too much math → changed to microeconomic → still math, ... → finally registered to study laws.

However, you may not forget that even good students have bad days or just make mistakes on carelessness or due to time pressure. There are some mentors here I really admire for their patience with my mistakes or those of others. I guess one has to get more experienced than a 16 year old can be to handle it with calm. For now: get a laugh at (by yourself, not to others). This way they are at least good for something.

 

[ProfuselyQuarky]

There has been a favorite path for students: signed up in macroeconomic → found too much math → changed to microeconomic → still math ... → finally registered to study laws.

That's a comic

(in a ... really sad way ...)

However, you may not forget that even good students have bad days or just make mistakes on carelessness or due to time pressure.

Oh, of course, I’m not denying that! Just the other day I found myself plotting a graph of lab data with the independent variable on the y-axis … and then I started analyzing the daft-looking data and completing the report (explaining all the possible errors affecting the conclusion) without the slightest idea on where I went wrong.

For now: get a laugh at (by yourself, not to others). This way they are at least good for something.

*sigh* I don’t find funny. Forgetting how to find the slope of a line in 11th grade is not funny. Sure, I can playfully tease and you get a laugh from the others, but it’s still sad

 

[micromass]

Once I taught a refresher course in math for prospective science students. I stressed a million times that $(x+y)^2 = x^2 + 2xy + y^2$. So they really got that.

So when the time of the test came, sure enough, a lot of them solved $(x+2)^2 = x^2 + 4x + 4$ correctly. I was happy. But then most of them also said $(x+y)^3= x^3 + y^3$. Sigh

 

[ProfuselyQuarky]

So when the time of the test came, sure enough, a lot of them solved $(x+2)2=x2+4x+4(x+2)^2 = x^2 + 4x + 4$ correctly. I was happy. But then most of them also said $(x+y)3=x3+y3(x+y)^3= x^3 + y^3$. Sigh

Do you find it depressing or do you simply ignore it? Are you one of those teachers who will yell in front of class telling everyone how disappointed you are or do you smile and make fun of it?

There was once this person who was trying to solve a system of equations and he was supposed to use Gaussian elimination. I told him to make an augmented matrix to derive something in row-echelon form and then … he asked what a matrix was.

Doesn’t something like that bother you?

 

[Astronuc]

So when the time of the test came, sure enough, a lot of them solved (x+2)2=x2+4x+4(x+2)2=x2+4x+4(x+2)^2 = x^2 + 4x + 4 correctly. I was happy. But then most of them also said (x+y)3=x3+y3(x+y)3=x3+y3(x+y)^3= x^3 + y^3. Sigh

Perhaps you mean or perhaps less concussively

It didn't occur so some that $(x+y)^3 = (x+y)^2(x+y)$

 

[axmls]

Unfortunately, I feel like a lot of this results from people treating math like they treat, say, history. They often think "well, we've had our test on the FOIL method, now I can forget that and learn the next topic."

As an old professor of mine used to say, if you're in a history class and you didn't do well in the 1500s, you can still do well in the 1600s. That's not the case with math, though. Students need to have it stressed that, yes, they do need to remember all this stuff. It's not something you can forget right after the test, because math is cumulative.

A lot of it, I think, occurs because many teachers teach math as a set of arbitrary rules for manipulating formulas into particular forms that look completely uninteresting to the layman. And, don't get me wrong, we do need to have those rules drilled into our heads until we get it right. But oh, how much more beautifully math could be taught.

 

[blue_leaf77]

During one mathematical physics class, a friend of mine was asked by the lecturer to go in front of the class to work out certain differentiation problem $$\frac{d\,f(x)}{dx}$$, I don't remember the particular form of $f(x)$. Then she nonchalantly stroke out the $d$'s in the numerator and denominator as if it acts like a multiplication, and ended up with a meme-type equation
$$\frac{d\,f(x)}{dx} = \frac{f(x)}{x}$$
Strangely though, she demonstrated that unintended joke in front of the class but only a (very) few of us noticed that that was laughable. The majority of the class seemed to either agree with her work or didn't know themself what to be done with that problem. I thought if she had been given other non-trivial mathematical expressions and was asked to simplify it, she might set up a new trend of math meme.
Such people are basically lacking in the information needed to properly tackle the problem they are given, at the same time they use "intuition" based on what they already have learned - a misuse of concept.

 

[Mondayman]

I took a University math prep class last September - equivalent to grade 12 mathematics, essentially precalculus. During our trigonometry unit test, one of my classmates was solving sin(14° + 46°). This is trivial to any who has taken trigonometry and was meant to be a gimme, but unfortunately one of my classmates took the degree symbol to be a zero exponent, and sin(2) was her answer..



She nearly cried when informed of her mistake a few days later.

 

[micromass]

I took a University math prep class last September - equivalent to grade 12 mathematics, essentially precalculus. During our trigonometry unit test, one of my classmates was solving sin(14° + 46°). This is trivial to any who has taken trigonometry and was meant to be a gimme, but unfortunately one of my classmates took the degree symbol to be a zero exponent, and sin(2) was her answer..



She nearly cried when informed of her mistake a few days later.

To be fair, degrees are stupid.

 

[cnh1995]

I don't remember the particular form of f(x)f(x)f(x). Then she nonchalantly stroke out the ddd's in the numerator and denominator as if it acts like a multiplication, and ended up with a meme-type equation

My maths professor once carelessly stroke out variables and messed up the entire solution. While simplifying an expression, he stroke out the x's in log(x)/(x) and wrote it as log(x)/x=log(1)=0. Coincidently, the expected final answer was also 0, so he didn't realize his mistake until one of us brought it to his notice. He still does such things. He's famous among the students for doing such silly things and has earned a nickname too!

 

[micromass]

Some student actually turned this in on an exam, and expected partial credit because he had the right answer:

$$\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0$$

From: http://www.math.vanderbilt.edu/~schectex/commerrs/

 

[collinsmark]

Some student actually turned this in on an exam, and expected partial credit because he had the right answer:

$$\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0$$

What in the... .. That's just <loss for words>. I don't even know where to begin.

 

[fresh_42]

$$\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0$$

I can't help but admire the artistic creativity. I love modern art.
I mean, NASA once crashed a Mars probe because Lockheed and them used different systems of unities ...

 

[axmls]

Reminds me of the old $$\require{cancel} \frac{64}{16} = \frac{\cancel{6}4}{1\cancel{6}} = \frac{4}{1} = 4$$ That's why the process is just as important as the answer!

 

[fresh_42]

Reminds me of the old $$\require{cancel} \frac{64}{16} = \frac{\cancel{6}4}{1\cancel{6}} = \frac{4}{1} = 4$$ That's why the process is just as important as the answer!

... or why multiplication points not always should be omitted, resp. conventions about notation has to be clearly defined.

 

[ProfuselyQuarky]

Reminds me of the old $$\require{cancel} \frac{64}{16} = \frac{\cancel{6}4}{1\cancel{6}} = \frac{4}{1} = 4$$ That's why the process is just as important as the answer!

It's hard to believe that that is a real mistake some one made ...

To be fair, degrees are stupid.

To be fair, the use of radians in daily measurements is stupid.

 

[axmls]

It's hard to believe that that is a real mistake some one made ...

I don't know that anyone's ever actually done that (though you never know...) but it's more of an example of how just because a method gives the correct result does not mean that method will always work.

 

[fresh_42]

It's hard to believe that that is a real mistake someone made ...

Why? $\require{cancel} \frac{64}{16} = \frac{6 \cdot 4}{1 \cdot 6} = \frac{\cancel{6} \cdot 4}{1 \cdot \cancel{6}} = \frac{4}{1} = 4$

 

[micromass]

To be fair, the use of radians in daily measurements is stupid.

Burn the heretic!

 

[ProfuselyQuarky]

Why? $\require{cancel} \frac{64}{16} = \frac{6 \cdot 4}{1 \cdot 6} = \frac{\cancel{6} \cdot 4}{1 \cdot \cancel{6}} = \frac{4}{1} = 4$

Haha. Let's see ...

$\frac {63}{9}=\frac {6\cdot3}{3\cdot3}=\frac {\cancel{3}\cdot\cancel{3}\cdot2}{\cancel {3}\cdot\cancel{3}}=2$

Ah, accuracy.

Burn the heretic!

I'm willing to die a martyr for what I believe

 

[fresh_42]

Burn the heretic!

Exactly. Don't mess with Leonhard!

 

[fresh_42]

Haha. Let's see ...

$\frac {63}{9}=\frac {6\cdot3}{3\cdot3}=\frac {\cancel{3}\cdot\cancel{3}\cdot2}{\cancel {3}\cdot\cancel{3}}=2$

Ah, accuracy.

$\frac{63}{9} ≡ \frac{3}{4} ≡ 3 \cdot 4 ≡ 12 ≡ 2 \mod 5$ - Only a matter of perspective

 

[vela]

Some student actually turned this in on an exam, and expected partial credit because he had the right answer:

$$\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0$$

From: http://www.math.vanderbilt.edu/~schectex/commerrs/

I can believe the part of the student wanting partial credit. I find it hard to believe anyone would actually turn that in! How did they end up in a calculus class?

 

[DrGreg]

This wasn't a "sad mistake" but a deliberate abuse of notation (as a joke) from my maths teacher when I was 15.

To solve: $$
\frac{dy}{dx} = y
$$Integrate:$$
y = \int y + C
$$Rearrange:$$
y - \int y = C
$$Factorise:$$
\left(1 - \int \right) y = C
$$Divide:$$
y = \frac{C}{1 - \int}
$$Expand the geometric series:$$
\begin{align*}
y &= C + \int C + \int^2 C + \int^3 C + \dots \\
&= C + \int C + \iint C + \iiint C + \dots \\
&= C + Cx + \frac{Cx^2}{2} + \frac{Cx^3}{3!} + \dots \\
&= Ce^x
\end{align*}
$$which is the correct answer.

Of course the method is nonsense for a 15-year old, but years later when I studied functional analysis and operator theory, I realized the method is essentially correct (if you rewrite it with more appropriate symbols, terminology and apply the correct terms and conditions). I don't know if my maths teacher had known this or not.

 

[Tobias Funke]

It's refreshing to not see any posts about how people were so much better at math in the old days, or how every Chinese toddler can get a 750 on the math SAT. Isn't it comforting to know that people have been making these mistakes for centuries?

 

[Drakkith]

Math is hard. Who knew?

I took a University math prep class last September - equivalent to grade 12 mathematics, essentially precalculus. During our trigonometry unit test, one of my classmates was solving sin(14° + 46°). This is trivial to any who has taken trigonometry and was meant to be a gimme, but unfortunately one of my classmates took the degree symbol to be a zero exponent, and sin(2) was her answer..

Let's see... sin(14 degrees + 46 degrees) = sin(60 degrees) = sin(a slightly chilly day) ≈ -sin(boiling hot) = -212 degrees - sin() ≤ liquid nitrogen. Did I math correctly?

 

[Lord Anoobis]

Math is hard. Who knew?
Let's see... sin(14 degrees + 46 degrees) = sin(60 degrees) = sin(a slightly chilly day) ≈ -sin(boiling hot) = -212 degrees - sin() ≤ liquid nitrogen. Did I math correctly?

Nay, thou hast erred. sin(a slightly chilly day) ≈ -sin(boiling hot) implies that boiling hot is a small(ish) negative radian value and a slightly chilly day is the absolute value thereof. Which reeks of sorcery. Of course, my caffeine overdose has not kicked in yet so I may wrong.

 

[Mark44]

During one mathematical physics class, a friend of mine was asked by the lecturer to go in front of the class to work out certain differentiation problem $$\frac{d\,f(x)}{dx}$$, I don't remember the particular form of $f(x)$. Then she nonchalantly stroke out the $d$'s in the numerator and denominator as if it acts like a multiplication, and ended up with a meme-type equation
$$\frac{d\,f(x)}{dx} = \frac{f(x)}{x}$$

This is obviously wrong, She should have continued cancelling.
$$\frac{d\,f(x)}{dx} = \frac{f(x)}{x} = f$$

 

[anorlunda]

From Anguished English by Richard Ledere

The inhabitants of Egypt were called mummies. They lived in the Sarah Dessert and traveled by Camelot. The climate of the Sarah is such that the inhabitants have to live elsewhere, so certain areas of the dessert are cultivated by irritation. The Egyptians built the Pyramids in the shape of a huge triangular cube. The Pramids are a range of mountains between France and Spain.

The Bible is full of interesting caricatures. In the first book of the Bible, Guinesses, Adam and Eve were created from an apple tree. One of their children, Cain, asked "Am I my brother's son?" God asked Abraham to sacrifice Issac on Mount Montezuma. Jacob, son of Issac, stole his brother's birthmark. Jacob was a partiarch who brought up his twelve sons to be partiarchs, but they did not take to it. One of Jacob's sons, Joseph, gave refuse to the Israelites.

Pharaoh forced the Hebrew slaves to make bread without straw. Moses led them to the Red Sea, where they made unleavened bread, which is bread made without any ingredients. Afterwards, Moses went up on Mount Cyanide to get the ten commandments. David was a Hebrew king skilled at playing the liar. He fought with the Philatelists, a race of people who lived in Biblical times. Solomon, one of David's sons, had 500 wives and 500 porcupines.

 

[ProfuselyQuarky]

Nay, thou hast erred. sin(a slightly chilly day) ≈ -sin(boiling hot) implies that boiling hot is a small(ish) negative radian value and a slightly chilly day is the absolute value thereof. Which reeks of sorcery.

I have no idea what that is, but that is just ... Lord Anoobis, if you can turn a math problem into sorcery ... then I really need to know what math you've learned.

Of course, my caffeine overdose has not kicked in yet so I may wrong.

Nah, the problem's probably correct. I punched the problem into a ye olden vintage calculator and it gave me a laughing wizard as a the answer.

 

[OrangeDog]

Sometimes I think much faster than I write, and my information generation, transfer,and recording waves become out of phase. My calc professor told me (in a japanse sensai accent) "You are like my old computer, It crash, I did not know why. I work on it. It running too fast, Justlike you! It overheat and crash. You must slloowww down so you don't crash!"

 

[Lord Anoobis]

I have no idea what that is, but that is just ... Lord Anoobis, if you can turn a math problem into sorcery ... then I really need to know what math you've learned.

Such knowledge may not be passed to muggles.