Ok- let me put out there WHY we learn math the way we do. No- the average adult will never factor polynomials again in their life. But factoring causes multi-level logic processes. You have to find the answer and need to manipulate the problem within a set of constraints/rules. Linear progressions. Geometry develops spatial awareness and has students develop the idea of proof- yes it's true, why is it true? It causes the student to question the world around them. I could go on and on about the philosophies of math (and yes, even Common Core math which is a good idea it's just applied terribly wrong in the United States. I have a math degrees and don't believe we should be teaching advanced number theory to kids before they are neurologically unable to handle it)..,
@SchroedingerPussPuss, a most splendid rant, have an upvote
@SchroedingerPussPuss, I consider myself a bit of a math wiz, and good at solving things, until I saw the Common Core stuff. I literally stared at it for a good 5 minutes thinking, 'what in the hell is this?' If it ain't broke, don't fix it.
@SchroedingerPussPuss, depends also on the field you plan on working in, if you're gonna be working as a computer researcher, electrical engineer, chemical, physics, or any other field of the sort, you're gonna need multivariable calculus, differential equations, Laplace transformations, and so on. At lower levels, you are correct, it does help develop cognitive thinking as well.
@TheKen42, except, it was broken. In my graduate-level teacher education program, at first we were struggling with understanding upper elem/middle school concepts because we were taught "move this over there" and "cross-multiply" without the logical underpinnings of why that was the rule. We couldn't use math logic to figure out which strategy to apply when because we were never taught why the strategies work. We had no reference point. CCSS do three things that I like. A) They require students to at least attempt to understand mathematical concepts rather than just plugging in numbers. B) They offer students multiple strategies for solving a problem, so that everyone can find at least one thing that works for them. C) They start as heavily based in manipulatives in the early grades before phasing them out as children become better at abstract concepts.
@Ruupasya, We went to the moon with the old system and pencil/paper. Hence I see no reason why we should change it.
@TheKen42, because we're one of the lowest first world countries in math proficiency?
@Ruupasya, I doubt that has much to do with the methods of 'mathing.' I also don't agree with the common core in that a student's correct answer would be marked wrong simply because he did it the old way. Stuff like that really ruffles my jimmies, so to speak.
@Ruupasya, uh...no. Common core doesn't do anything like what you just said.
Look up who made common core math. There was only one person who had a math degree, he was also the only person who had ever taught students (although he taught college). Nobody else had any experience with teaching, or with math.
The only mathematician/only teacher voted against the whole curriculum, but it passed without his approval. Since then he has traveled the country giving testimony in cases and to legislators on why they shouldn't take common core math.
There is zero research showing that common core does anything. There isn't a single study that showed common core math works as a teaching method. The worst is Geometry curriculum, which is based on a theory that was only tried once. In the 1970s, in Russia, and it was so horrible that parents actually protested...in Soviet Russia, and the curriculum was removed after just 2 years.
@Ruupasya, I saw updated Texas TEKS implementing CCS. So -5 + 8 = (-5 + 5) + 3 = (0) + 3. That's higher level number theory and I'll explain why- it's expecting the student to recognize that you are taking a part of a larger number to fill a "perceived void" (negative values are NOT voids of lack of, they are simply a negative direction, so the idea of replacing a missing value already pisses me off). You fill the void and look at the remaining value. That's awesome! But that's something that should be analyzed HIGHER than elementary. The concept of filling a void is abstract when using numbers as the child is still in concrete learning stages. THAT'S where the problem is. Using negatives as voids instead of directions also screws up students in Algebra... i.e. -4x slope is SMALLER than 2x slope because "-4" is a SMALL number... When all the negative does is tell you it's traveling in a different direction, so the -4x slope is actually larger
@talmet, it's supposed to teach higher level thought processes, but people WITHOUT higher level math are teaching it. To kids who can't neurologically process it at the stages they are being handed it. So yeah, I could see one guy with a math degree working with a bunch of education doctorates who knew nothing of what was going and wearing ugly teacher vests. Thanks for the info- I'll look it up! I have Texas TEKS which aren't great, but certainly aren't Common Core
@TheKen42, there's nothing in Common Core that states what you just said. That's a choice on the part on individual teachers. With my students, I'll mark it partially wrong in that case, but only because that means that they didn't read the directions, which is something they need practice with.
@talmet, Well, I know that SC voted against adopting the CCSS standards and instead, a bunch of teachers worked together to create the SCSS, and they made them nearly identical to the CCSS, because, in the informal words of one of the teachers on the committee, "the Common Core standards are quality standards, so we basically just did the same thing."
@SchroedingerPussPuss, I have NEVER seen anything like that in Common Core. Maybe it's a middle school thing, idk. I just know elementary. What I do know is, for example, this:
Students learn the following methods of solving a division problem in third grade:
- Repeated subtraction
- Using counters to divide into equal groups
- Using inverse operations
- Using a multiplication chart or an array
- Counting backwards on a number line
And prob more that I can't remember off of the top of my head. It's showing students that there's more that one way to solve a problem. Some of my kids like the counters method. Some use inverse operations because they have a lot of multiplication facts memorised. Some like to use repeated subtraction. There's something for everyone.
@SchroedingerPussPuss, ...ok, you have some education but a lot of what you said is just plain wrong.
I have a PhD in Particle physics, and a masters in Applied Mathematics....negatives are not "voids"
-4 is less than 2. It isn't a void...it is less than.
Negative slopes are directions only when you (the person) say so. It's a convention. In some cases they are the opposite direction, in other cases, they are interference...
Teaching students that -5+8=(-5+5)+3=0+3 is just stupid and long. -5+8=8+-5=3, just teach the commutative property. That is actually useful...thinking about negative numbers as voids, or directions, or whatever is just an interpretation that only applies in certain cases.
The commutative property works in any case other than with infinite series. Therefore, teach it, not just some interpretation which only applies in a small number of cases.
commutative and distributive are what should be taught.
-5-8=-(5+8)=-13 done, no void, no directions, just the answer
@SchroedingerPussPuss, in case you were wondering. The commutative property fails with infinite series because there are an infinite amount of each number.
I.e. -1+1+1-1....has an infinite number of -1 and an infinite number of +1. If you can reorder the terms, you can make that series equal any number you want.
I.e. Take 90 +1's and put them in front. And then reorder the rest of the series so it still alternates back and forth. If the associative property is used, then group every pair after the first 90 +1's. The series now equals 90.
Using associative and/or commutative property, you can get most infinite series to equal anything you want if you are clever. Which is why we say that those two properties do not apply to infinite series.
@Ruupasya, that's all good and everything, but are they ready for that depth of knowledge? That's my biggest issue. They can't master a skill of they are presented with 4 different solving methods at once. Master one and then move on. That, and elementary standards need to stop using "x" as multiply. That causes all sorts of hell for students at the secondary level.
@talmet, truth. Infinite series are fun. Also, the mind blowing moment when you tell a 14 year old that there an infinite amount of points between 0 and 1....and my students can't touch infinity no matter how much weed they smoke. Btw- I had two kids smoke so much that they a) missed three days of school and b) said they touched infinity.
@SchroedingerPussPuss, lol, the thing that gets most students is statements like:
-there are an infinite number of numbers between any two numbers, not just whole numbers but like 0.000000000000000000001 and 0.000000000000000000002 or any number regardless of how close the two numbers are to each other.
-if you draw a line, and then remove a point. The length hasn't changed. If you remove an infinite number of points, the length still hasn't changed.
-a googolplex and 1, are both exactly the same distance from infinity.
@SchroedingerPussPuss, well...x as multiply is nice for when you get to cross products....to show that it is a product, just a different type. But, it could be another sign...
Using the x for normal multiplication is just odd, and it makes no sense why they do it in elementary school.
@SchroedingerPussPuss, yes, they are ready for this. They're not just thrown into all of the methods at once. They're taught one of the time, starting with the most concrete, and the ones they have previously learned are spiraled in (repeated) so that they can get more practice and not forget. And now my students can figure out "hey, I usually use counters for problems but this is a big number and I do not have enough counters. What are some of the other strategies I learned? Oh yeah, I could use repeated subtraction!" It moves from concrete (manipulatives) to abstract (standard algorithm) in stages and over the course of *years*.
Isn't that a girl?
@H0LD My B33r, refer to previous post
@H0LD My B33r, you can never tell these days, and god forbid you ask!
@H0LD My B33r, call me Caitlyn?
I read that as Meth and was very confused on what meth homework was
@Oneiric , *transfers to a school that teaches meth making*
@CaptainQuzzle10, professor white, you will learn from