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2+2=What? Parents rail against Common Core math

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Re: 2+2=What? Parents rail against Common Core math

#61

Post by groovy2shoes »

hga wrote: post #4

Without reading the fine article except for searching for "calculus", I'll note that I've confirmed an accusation at the other end: the Common Core does not even reach precalculus by the end of high school. No student in a school solely based on it will be taking AP Calculus, let alone be able to attend MIT or Caltech (the former requires you to be ready to learn the calculus, the latter demands you've already learne…

I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning calculus (I also never took any "prealgebra" and managed algebra just fine). I can't even imagine what a pre{calculus,algebra} course would possibly teach.

Re: 2+2=What? Parents rail against Common Core math

#62

Post by unclebucknasty »

rplst8 wrote: post #53
DanBC wrote: post #41

Earlier quoted context omitted.

> Bah... I can tell you why the [...] You are not a six year old child learning arithmatic. You have missed the point. > The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a l…

We're saying the same thing. I understand that children need to understand the underlying concepts. I'm saying there are already well established methods for teaching those. Waving a hand and saying the "old way" is simply an algorithm and a poor method because it glosses over the details is like saying teaching someone how to use a calculator will make them forget how math works. That common core method for subtract…

>That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.

That was a point I made elsewhere on this thread. When helping my second-grader with her homework, it sometimes seems that they are just changing what the student is required to memorize (and also increasing the volume), without necessarily imparting additional understanding.

That problem relies on what they call the "Add it Up" method, and it is specifically a technique with which I've helped my daughter. I observed that kids can completely learn the method and ace a test without understanding the concepts behind it.

Re: 2+2=What? Parents rail against Common Core math

#63

Post by maxerickson »

groovy2shoes wrote: post #61
hga wrote: post #4

Without reading the fine article except for searching for "calculus", I'll note that I've confirmed an accusation at the other end: the Common Core does not even reach precalculus by the end of high school. No student in a school solely based on it will be taking AP Calculus, let alone be able to attend MIT or Caltech (the former requires you to be ready to learn the calculus, the latter demands you've already learne…

I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning ca…

They introduce some of the fundamental concepts of the later courses (and try to tie them into previous knowledge).

In the U.S. system, they also serve as a review, I guess with the hope of shoring up knowledge that students were missing (but I think such an approach for math education is pretty optimistic; figuring out what they don't know and fixing that must be more valuable than just showing them things again).

Re: 2+2=What? Parents rail against Common Core math

#64

Post by hga »

groovy2shoes wrote: post #61
hga wrote: post #4

Without reading the fine article except for searching for "calculus", I'll note that I've confirmed an accusation at the other end: the Common Core does not even reach precalculus by the end of high school. No student in a school solely based on it will be taking AP Calculus, let alone be able to attend MIT or Caltech (the former requires you to be ready to learn the calculus, the latter demands you've already learne…

I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning ca…

Precalculus as I'm using it is a level of math, not a particular course (although there are of course courses with that title). In addition to what you learned in high school, assuming your Algebra II was like mine, plenty of analytic geometry, it would also include trigonometry.

To do as well as you did, you obviously picked that up on your own, as did I.

(While in theory I took a trig and further analytic geometry course in high school, followed by a semester of the calculus, the teacher flatly refused to teach anything, and trig at that level in that textbook was absolutely boring and unmotivated (e.g. didn't mention you needed it to do calculus on rotation including AC electricity); I only stayed in these automatic A courses so I'd have them on my transcript (I'd already taken my first go at the calculus in a summer course taught at a university before this, but focused most of my attention on a PDP-11/70 running UNIX(TM) Version 6, which ended up being infinitely more valuable (as it turned out, perhaps lifesaving; the introductory programming class that was my excuse for using it was easy, so I focused on UNIX(TM), Adventure and other games, wandering around the filesystem (very much like Adventure :-), software engineering, helping others debug their final class project, and using nroff for my class project which had more exposition on software engineering than code; included that in my college applications)).

Expanding on maxerickson's comment, I gather formal precalculus courses also start teaching you about limits and stuff like that; since basic differentiation, especially speed and acceleration, is relatively simple, I'd hope it would teach an intro to that, which goes along nicely with the limits. It could also be a fancy name for a (further) analytic geometry course, and/or include trig motivated by the calculus vs., oh, surveying.

Re: 2+2=What? Parents rail against Common Core math

#65

Post by nodata »

DanBC wrote: post #34
nodata wrote: post #3

Well what are the four ways to do addition?

1) "counting on". 19 + 7 is (starts counting on) 20, 21, 22, 23, 24, 25, 26 (realise that 7 fingers have been used, stop counting on) 26 1a) "partitioning" 8 + 7 is 8, jump 2 to 10, then jump 5 to 15. 2) "thinking and estimating". 3998 + 4997 is nearly 4000 + 5000 and is exactly 4000 + 5000 - 5 3) traditional columns with units, tens, hundreds, etc. Note that these are teaching small children how to manipulate number…

So they are being taught some optimisations that they'd normally learn later? Doesn't sound too bad.

Re: 2+2=What? Parents rail against Common Core math

#66

Post by j2kun »

Why are we worried that elementary school children might misunderstand arithmetic? This is the problem with the Common Core math standards, that they think you need to have a perfect understanding of something before you can move on, and if you have moved on then you have a perfect understanding of everything that came before it.

That's just not how math works at any level! Understanding counting and arithmetic and numbers is a continuously evolving process. Children should be exposed to these things: the difference between a number and its representation, alternative ways to understand counting, etc., but to require every student understand all of them before moving on is ridiculous. And likewise, in later grades (even in high school!) one should revisit the concepts they thought they mastered from the different perspectives that their more mature coursework allows them to. There are important things to say about counting and arithmetic from first grade all the way through a PhD.

Re: 2+2=What? Parents rail against Common Core math

#67

Post by j2kun »

dkhenry wrote: post #43

You know when I in my job try something new and it doesn't work out my company might lose a contract or in a really bad case I lose my job. When we as a society decide unilaterally that we are going to change a few century's worth of teaching style for something new we risk raising a generation of children who can't do simple math. I am not worried about if this method is "better" according to research. I am worried…

We are already raising generations of people who can't do simple math. In fact, we raise generations of people who are proud of that fact.

Re: 2+2=What? Parents rail against Common Core math

#68

Post by sitkack »

lclarkmichalek wrote: post #29
hga wrote: post #17

Earlier quoted context omitted.

If you don't learn your math tables by rote memorization, how are you ever going to be adept at algebra or anything based on it? If you can't just look at something like 2x = 4y and instantly simply it....

I used a calculator the other day to do 73 - 52, yet I can pass a third year university algebra course. Sure, tables are useful, but they are very far from the be-all-end-all of primary school education, which they very much were for me when I was younger (you were good or bad at maths based on how good you were at your times-tables, which is hardly a good way to motivate people who enjoy mathematics, but don't excel…

That diagram was teaching the fungibility of numbers. Afaik CC doesn't say that these things _must_ be taught this way.

To solve your problem with the same technique as the article, you would have added 1 to 52, 73 - 53 = 20, then + 1 for the answer.

You would need to know ball park anyway to see if the calculator answer made sense.

Re: 2+2=What? Parents rail against Common Core math

#69

Post by j2kun »

bglazer wrote: post #54

I think this quote from a parent at the very end of the article is quite telling: "To me, math is numbers, it's concrete, it's black-and-white. I don't understand why you need to bring this conceptual thing into math — at least not at this age." I am not a professional mathematician, but I get the overwhelming impression from professional mathematicians that "this conceptual thing" is really quite important in the bi…

I am a professional mathematician, and yes, the parents in these articles will almost always say things that reveal their own fears and misunderstandings of math. This doesn't make the Common Core implementation any better, and part of the reason is that these same parents (people of equivalent mathematical experience) are the ones teaching the kids and writing the state-wide tests and writing the textbooks.

Re: 2+2=What? Parents rail against Common Core math

#70

Post by sitkack »

hga wrote: post #32
kasey_junk wrote: post #27

Earlier quoted context omitted.

It's anecdotal I know, but for me the math table rote memorization was extremely detrimental to my learning of mathematics. It forced a mind set that implied that to be good at math you needed to be able to remember senseless unrelated facts, when in reality most of the advanced mathematics this will lead you completely astray as you cannot keep every formula in your head and it is much better to be able to derive th…

It certainly has its detriments, but my point still stands: if you go into Algebra I without knowing your math tables, you're going to hit a brick wall. "Motivation" at a higher sense is something that's sorely lacking in US public school (free government school) math. Especially prior to real algebra, the teachers tend to be generalists who don't know to tell you "you need to learn X so you can learn Y which will al…

Rote solves everything and nothing. Faster time to correct answer, yet no understanding of solution. I'd rather have people who can reason and fumble through a problem than can rattle off memorized facts.
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