EPTIs Algebra Necessary? - Page 25
| Forum Index > General Forum |
|
Silvanel
Poland4733 Posts
| ||
|
ain
Germany786 Posts
Everyone who believes algebra is not necessary to be taught clearly needs to be stripped of any opportunity to educate children. There is just no questioning the importance of mathematics. If you don't get it, fine, but spare other people (and especially children) your misinformed opinion. | ||
|
Squigly
United Kingdom629 Posts
On July 30 2012 01:27 paralleluniverse wrote: I don't want to go over this again. So let this me a final summary on the issue. The order: 1. exponentiation. 2. multiplication/division 3. addition/subtraction is an arbitrary convention that people have agreed to. There is no reason that it can't instead be: 1. addition/subtraction 2. exponentiation. 3. multiplication/division. You're argument that it has to be the first way because multiplication is repeated addition is irrelevant. Multiplication can still be repeated addition (for integers) even if the convention was changed. E.g. If we interpret 2+3*3 to mean that (2+3)*3 because addition is first, then multiplication is still repeated addition because the expression is equal to (2+3)+(2+3)+(2+3). And this is a different concept to 2+(3*3), which is why they aren't equal. But once you've agreed on a convention and translated everything to using your invented order of operation convention, everything in math that is currently true is still true. BIDMAS is not a theorem. It's a convention. The idea that multiplication is repeated addition is something that is taught in primary school, but it's not generally true, how is pi*e, the sum of pi, repeated e times? If you want to give a rigorous definition of pi*e, it should not be the sum of pi, repeated e times. It should be: let {x_n} be a sequence that converges to pi, and {y_n} be a sequence that converges to e, we know these sequences exist because the real field is a complete metric space, then {x_n*y_n} is a Cauchy sequence because {x_n} and {y_n} are, so it's limit also exists in the real field, call this limit pi*e. Yes this is a lot more complicated and highly technical, that's why it's not taught outside of university level calculus. It's also less intuitive, unless you know a lot of math. But thinking of multiplication as repeated addition is not a good way to think about higher mathematics. This is also a good post: http://www.teamliquid.net/forum/viewmessage.php?topic_id=356624¤tpage=8#152 You are literally having an argument about notation.....its just convention, nothing more. Yea it could be different, but its not. | ||
|
jakeyizle
15 Posts
On July 30 2012 01:30 Silvanel wrote: Since math in Poland isnt teached that way (we have classes in math in general) i dont really know what we are taking about. Anyone care to explain? What is level of mathematical knowledge that is required from a high shool gradute? A link to exampalary test or something would be nice. In Florida, students graduating in 2014 or later are required to have 4 years of math. 1 year which must be Algebra I or equivalent (such as a year in Algebra 1A and a year in Algebra 1B) and 1 year which must be geometry or higher (pre-calc, alg 2, calc, maybe probability & stats). Edit: students entering high school in 2012-2014 are required to pass Algebra 2 as well. Edit 2: this is a practice Algebra EoC exam (end of course exam, passing it is required to get credit) http://www.flvs.net/areas/studentservices/EOC/Documents/Practice Test for flvs_net_Final.pdf | ||
|
Colour
Canada68 Posts
| ||
|
Muirhead
United States556 Posts
On July 30 2012 01:27 paralleluniverse wrote: If you want to give a rigorous definition of pi*e, it should not be the sum of pi, repeated e times. It should be: let {x_n} be a sequence that converges to pi, and {y_n} be a sequence that converges to e, we know these sequences exist because the real field is a complete metric space, then {x_n*y_n} is a Cauchy sequence because {x_n} and {y_n} are, so it's limit also exists in the real field, call this limit pi*e. Yes this is a lot more complicated and highly technical, that's why it's not taught outside of university level calculus. It's also less intuitive, unless you know a lot of math. But thinking of multiplication as repeated addition is not a good way to think about higher mathematics. One can define pi*e as the area of a rectangle with lengths pi and e, without involving any Cauchy sequences. This interpretation makes it easy to see the commutativity of multiplication etc. Do not insist that everything be symbolized and Cauchyfied: Hilbert perfectly rigorized Euclidean geometry without any such crutches. | ||
|
-_-Quails
Australia796 Posts
On July 30 2012 01:37 jakeyizle wrote: In Florida, students graduating in 2014 or later are required to have 4 years of math. 1 year which must be Algebra I or equivalent (such as a year in Algebra 1A and a year in Algebra 1B) and 1 year which must be geometry or higher (pre-calc, alg 2, calc, maybe probability & stats). Edit: students entering high school in 2012-2014 are required to pass Algebra 2 as well. For the non-Americans, it would be helpful if you gave a few examples of what each of those courses covers. Most other countries have a single unified mathematics course which is taught over several years and the concept of semester-long courses exists in few places. If you explain what sort of things are in the syllabus for each course, people can compare to their own system. | ||
|
Silvanel
Poland4733 Posts
Example: http://www.algebra.com/algebra/homework/playground/lessons/Basic-Algebra-Exam-1A-and-B-with-Solutions-by-Rapalje.lesson | ||
|
jakeyizle
15 Posts
On July 30 2012 01:43 -_-Quails wrote: For the non-Americans, it would be helpful if you gave a few examples of what each of those courses covers. Most other countries have a single unified mathematics course which is taught over several years and the concept of semester-long courses exists in few places. If you explain what sort of things are in the syllabus for each course, people can compare to their own system. Well, it kinda varies state by state. Algebra 1 involves graphing/solving linear equations, polynomials, factoring, radicals, some statistics and probability, quadratics, and inequalities. Not necessarily in that order, and there may be fewer or more topics covered. Geometry involves shapes, introduction to logic, proofs, some trig, a shit ton of circles and triangles. Algebra 2 includes properties of functions, the algebra of functions, matrices, and systems of equations. Linear, quadratic, exponential, logarithmic, polynomial and rational functions as well. | ||
|
paralleluniverse
4065 Posts
On July 30 2012 01:40 Muirhead wrote: One can define pi*e as the area of a rectangle with lengths pi and e, without involving any Cauchy sequences. This interpretation makes it easy to see the commutativity of multiplication etc. Do not insist that everything be symbolized and Cauchyfied: Hilbert perfectly rigorized Euclidean geometry without any such crutches. Yes you can define it that way. But then it's still not repeated addition. | ||
|
mRpolite
189 Posts
you can teach algebra to a monkey User was warned for this post | ||
|
Lightwip
United States5497 Posts
On July 30 2012 01:47 Silvanel wrote: THe thing is i dont know what for example Algebra 1 or 2 or pre-calc means. YEsh i googled it but i dont really know how relevant those things are. Algebra 1: basic use of variables (add/sub/mult variable expressions), linear/quadratic functions, goes up to about the quadratic formula Algebra 2: third degree variable expressions, more complex manipulations (synthetic division, imaginary solutions, logarithms, trig expressions, matrix math), more complicated functions, often pretty much encompasses trigonometry Pre-Calc: Basically, Algebra 2 and some trigonometry. It's pretty much unnecessary for good students that can just go algebra 2-> calculus. On July 30 2012 01:58 paralleluniverse wrote: Yes you can define it that way. But then it's still not repeated addition. There is merit in teaching methods that are simplified and that only encompass a small part of the problem. We teach Newtonian gravity even though general relativity is more correct simply because there's merit in simplicity where it applies. When you're teaching grade school, the special case of repeated addition applies. | ||
|
TheToaster
United States280 Posts
The point is that algebra has always been part of a high school curriculum because it doesn't just teach you math, but other important mental exercises as well. Just because kids these days are completely slacking and dropping out doesn't mean the curriculum needs to be changed, it means the kids have to change. If we lower the standards of education, even more kids will start to drop out and it won't solve the problem. | ||
|
Vorgrim
Korea (North)1601 Posts
Barring people from non technical college courses because they aren't wired that way is ofc not optimal, but if it was really a problem colleges would have picked up on it by now, if they haven't already, and lowered their requirements to keep courses full of students who are genuinely interested and capable in the subject being taught, rather than simply being vaguely intelligent. | ||
|
Arghmyliver
United States1077 Posts
On July 29 2012 16:40 UrsusRex wrote: Not one person has given a compelling reason how making algebra mandatory improves critical thinking skills. All of you supporting and condeming it are missing the basic problem. The entire world teaches algebra to their students but nowhere has it ever been shown to improve the quality of the people who learn it. All of you talking about tools and learning skills and resonating knowledge do not one shred of evidence for your position beyond asserting it as fact repeatedly. Show me any data than doesn't even imply, just correlate thats all I ask, any data that would link studying algebra to improving learning skills, because if it doesn't do that, we are teaching an irrelevant subject to millions of people. It's not like educationalists everywhere were like "hey lets teach some arbitrary bullshit thats completely useless." The reason Algebra is taught so universally is that it's widely considered to be an incredibly useful and versatile tool applicable to many different fields of study. | ||
|
Adonminus
Israel543 Posts
| ||
|
mRpolite
189 Posts
its f***ing unbelievable o m g not teaching algebra... | ||
|
Monochromatic
United States998 Posts
Algebra is important, for life in general. If so many people fail it, then they should get help, because it is clearly needed. Why not remove all school since people can fail school? | ||
|
corpuscle
United States1967 Posts
It doesn't surprise me in the least, by the way, that the author of the article is in the social sciences. edit: I should clarify. With the way your typical math class is taught, it's very much understandable and expected to have a lot of kids failing. Math is hard for a lot of people, and there needs to be more support and individual attention in math and science classes (and education as a whole), but that's an issue of lack of resources, and is in no way an excuse to make algebra an elective. | ||
|
RvB
Netherlands6256 Posts
On July 30 2012 01:37 jakeyizle wrote: In Florida, students graduating in 2014 or later are required to have 4 years of math. 1 year which must be Algebra I or equivalent (such as a year in Algebra 1A and a year in Algebra 1B) and 1 year which must be geometry or higher (pre-calc, alg 2, calc, maybe probability & stats). Edit: students entering high school in 2012-2014 are required to pass Algebra 2 as well. Edit 2: this is a practice Algebra EoC exam (end of course exam, passing it is required to get credit) http://www.flvs.net/areas/studentservices/EOC/Documents/Practice Test for flvs_net_Final.pdf That's not difficult. I wasn't good at maths but everyone with average intelligence has to be able to pass a test like that. I'm sure there are people who can't pass it but those are usually not very bright persons and wont use it later in their jobs either. | ||
| ||
