I was just reading a GQ, and someone didn’t understand that multiplying decimals by each other makes them smaller! 
His teacher’s explanation of,“It just does.” wasn’t enough. That I kinda (kinda) understand. But this is a COLLEGE STUDENT who was never taught this? REALLY!
I’ve seen the same type of thing with college physics students, including those that end up getting decent grades. A lot of students learn to apply formulas and procedures to get the answer in the book or test without ever actually thinking about what they’re doing. They may know how to carry out the rituals, but they don’t have any intuitive feel for what it actually means.
I don’t remember ever being taught this. It just made sense.
multiplication in plain english is “This much of this is this” So if the first ‘this’ is 0.5 then “Half of this is this”. If the second ‘this’ is 5 then “Half of 5 is 2.5”
I’m always fascinated when I meet people who are really good at math, because I’m pretty well-rounded academically, but my weak spot is math above intermediate algebra. After talking to them for awhile though, I invariably realize that they really have no idea what they’re doing, and are just good at rote memorization. I think I fell behind in higher maths because I aspire to a deeper understanding of what things mean, and there is a dearth of people, even teachers and professors, who can convey that about any math beyond arithmetic and basic geometry and algebra.
I was too intimidated of math to major in a natural science, and ended up going with a liberal arts degree that dipped into those subjects, but I often feel like I understand physics, astronomy, and biology more completely than people who actually have degrees in those subjects.
Yes, they are that bad. Not all, of course, but too many.
It seems to me that most people treat fractions with fear and superstitious dread. They never really understood what fractions mean (except 1/2) or what decimals mean.
Lobsang-Your plain English understanding is how it SHOULD be taught.
Cisco-I’m like you math-wise, you lose me once you get to trig.
I know exactly what you mean. I have to be able to visualize things, and once we got to calculus I couldn’t visualize any more and couldn’t find* anyone to tell me how.
*Okay, didn’t find. I had already established that I was going to major in some sort of non-maths related field by then, so I didn’t really care.
The vast majority are worse than average…
Some things just aren’t intuitive to some people, especially if they’ve had bad or just poorly matched teachers in the past. With math it’s often easy to move on even if you don’t fully understand what’s happening. You don’t have to know why multiplying by a number between 0 and 1 does what it does in order to follow the rules. And so you often get students who have failed to assimilate one particular thing who end up doing more advanced work anyway, despite the hole in their knowledge.
But nice job insulting someone who’s trying to make up for their deficiencies by asking for help. I’m sure that attitude will make you lots of friends and earn the respect of your academic colleagues.
A half of a half is a quarter. Why is that so hard to understand?
Not only that, but they are worse than the median!
I see what you did there.
I teach history, but i’ve always been good at basic mathematics. I was in the top math class in my high school, and was comfortable with calculus and a whole bunch of other stuff. I’ve forgotten much of the calculus and more complicated trigonometry now, but i’m sure i could pick it up again, and my math skills are still perfectly good for everyday in-my-head calculations.
I’m amazed, though, at how many of my students can’t seem to do very basic mathematics. At the beginning of each semester, i put a breakdown of the class grading in my syllabus. It differs from class to class, depending on the assignments i set, but it often looks something like this:
Short essay: 15%
Long essay: 30%
Mid-term: 15%
Final: 30%
Participation: 10%
During the last couple of weeks of the semester, i will inevitably get a dozen emails that read as follows:
It’s incredible how many students, knowing what grades they have for three or four of the five components of the course, can’t work out how well they need to do on their remaining assignment/s in order to achieve the grade they want.
Last year, to head this off, i actually made an Excel file where students could plug in a whole bunch of grades (real or expected), and it would calculate their final grade for them. They were amazed that i was able to provide them with such a technologically sophisticated and mathematically complicated tool. :dubious:
In what sense does math require more rote memorization than other subjects…? I’ve always been drawn to math precisely because I’m lazy and could never be bothered to sit down and memorize stuff. With math I just had to understand how things work, and I could figure out how to solve the problems more or less on the fly.
The guy in GQ was asking about taking square roots of decimals, not simply multiplying them. I’d say that square roots are much less intuitive to us than simple multiplication or division is. Also, he saw the logic as soon as someone laid it out to him, so I think you’re being unnecessarily harsh on this dude.
To Meyer and Friedo: As I mentioned in thread, advanced math’s not my forte. But we’re talking about a COLLEGE student studying physics. I looked at the original thread, just to make sure it wasn’t HS remedial math. In that case, I could see the confusion. But this is a college student, who, I assume is not in Physics 101, and obviously got into college, so I was surprised he didn’t get it. Obviously giving him toomuch credit.
For a guy who thinks Wins is the most important criterion in judging the performance of a baseball pitcher, you probably shouldn’t be too hard on other people’s problems with numbers.
The hard one for people to grasp is squaring fractions or decimals. It’s counterintuitive to think if you square a number it will be smaller.
Then why when I open the baseball standings, they’re listed by # of WINS? :rolleyes: