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#201754  09/23/14 08:24 AM
Learning math computations

Member
Registered: 05/23/13
Posts: 2154

DD8 started 4th grade and is in a sort of gifted magnet in a public school district. They gave all the kids a written pretest and had DD skip 4th, 5th, and 6th grade math and she is now in prealgebra. She knows (because I taught her) how to do long division, long multiplication, including with decimals, but by no means has practiced this a lot or is fluent. We're talking maybe 20 practice problems of long division. 4th, 5th and 6th grade math is where these concepts are practiced over and over and she is basically skipping it altogether. She has ADHD and has poor fluency in terms of math in general so this is something she would struggle with if forced to do it. In a way, the best thing for her is to just learn how to do it conceptually and then move on, which is what she is doing. But I am a bit concerned about the fact that she is not fluent at all. As she is exposed to higher level math is it really necessary...after all there are calculators to do the computations. To what extent does she need to be fast or fluent in order to do well in higher level math, like algebra? I can continue working on it at home but I'm wondering how much is really necessary. I was not expecting them to have her skip 3 years of math.

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#201756  09/23/14 08:40 AM
Re: Learning math computations
[Re: blackcat]

Member
Registered: 02/10/13
Posts: 1228

I just posted this in the other thread:
Long division is one of those "pay your dues" kind of topics. You should do some of it, but don't grind it to death. It is laborious, and it's not surprising it takes a while (but one should just get stuck into it and get it over and done with). It is important to understand how and why it works, so later you'll have no problem with (e.g.)
x^3/(x2)=x^2+2x+4+(8/(x2))

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#201758  09/23/14 08:52 AM
Re: Learning math computations
[Re: blackcat]

Member
Registered: 02/10/13
Posts: 1228

Understanding 10,000*100,000=1,000,000,000 helps understand (x^a)(x^b)=x^{a+b}.
Knowing how to multiply (1537)(824) helps to understand how to multiply (x^3+5x^2+3x+7)(8x^2+2x+4). The former is just the latter with x=10, and in fact the latter is easier, which is a common occurrence in mathematics where abstraction makes things easier. You should instinctively understand distributivity.
Arithmetic can be a warmup to (pre)algebra, but a conceptual thinker may do well just to get stuck into the (pre)algebra to get the conceptual underpinnings, and then backfill the arithmetic.

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#201759  09/23/14 08:56 AM
Re: Learning math computations
[Re: blackcat]

Junior Member
Registered: 04/12/14
Posts: 39

To what extent does she need to be fast or fluent in order to do well in higher level math, like algebra?
Unfortunately, there is no correct answer to this question, because this strongly depends on the curriculum and your teacher. In general, algebra is not about long division and numerical calculations at all, but its implementation in textbooks... Instead of the problem 2x=4 they give you 1.9875x=3.7956 On the brighter side, it is most likely that your DD will be allowed to use a calculator. So, my advice would be not to bother, just wait for awhile and monitor what kind of problems does your DD do at school (or, even better, look in her textbook).

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#201771  09/23/14 10:21 AM
Re: Learning math computations
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

The textbook has only come home once and I should have looked at it more thoroughly. She's in a "flipped learning" classroom so all she does at home is watch about 3 oneminute instructional videos online produced by the textbook company (I think?) and then take a 3 or 5 question quiz. Presumably she is getting work done in class but who knows! Another parent asked about the textbook from the previous grade (also concerned about them skipping so much) and the teacher said it's the same thing, just not as in depth.
MONa scientific calculator was on the school supply list and I failed to get it because it seemed ridiculous. I thought DD wouldn't even know how to use it. Then the next thing I knew, she was doing that pretest and complaining about the fact that I never bought her a scientific calculator and she needed it for the test. I ended up buying her a cheap $15 one from Office Max but maybe I need to look at better options. I think Dh has a better one (he majored in math). She just started kindergarten 3 years ago, I can't believe I'm trying to figure out what is the best option for a scientific calculator. I don't want her to lose a $100+ dollar calculator. And I am scared because they are moving so fast and pretty soon I will be of no help. Hopefully Dh remembers some math. Someone told me they bus kids to the Jr. High for Algebra. I think that was incorrect and they keep them at elem. for Algebra and Geometry and only bus for Algebra II. So at least it will be a sheltered environment.

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#201792  09/23/14 02:01 PM
Re: Learning math computations
[Re: blackcat]

Member
Registered: 04/26/14
Posts: 3993

I would let her play to work on math fact fluency (dice/card games, free apps, etc.), but second learning intelligent calculator use. I do find that many of my high school studentsespecially those with disabilitieshave adequate conceptual understanding of arithmetic, but find algebra and geometry substantially more laborious than they should be, because of the lack of fluency. It's kind of like riding a bike in low gear on the flat part of the road. You get there in the end, and it works okay, but it sure feels like it should be easier, especially when you see your friend zip by on the tenspeed. So I wouldn't abandon the fact fluency altogether.
_________________________
...pronounced like the long vowel and first letter of the alphabet...

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#201799  09/23/14 02:45 PM
Re: Learning math computations
[Re: blackcat]

Member
Registered: 02/08/11
Posts: 1432

She doesn't have to be super fast but she should be fluent with her basic facts or she may end up making all kinds of calculation errors in Algebra and beyond. I also second fluency with the methodology of long division so that the steps (DMSB  divide/multiply/subtract/bring down) are so automatic as to require no working memory as you will need to perform long division of polynomials in Algebra I and Algebra II.
I would definitely make sure your DD has access to a graphing calculator like TI83 or TI84 as that is the norm starting with PreAlgebra. On the other hand, I have seen recent emphasis shifting to software programs replacing some of the calculator work. For example, DS used GeoGebra a lot in Algebra I and he is using Geometer's Sketchpad in Geometry.

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#201800  09/23/14 02:47 PM
Re: Learning math computations
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

I think I'll keep bringing practice problems up every so often, like long division, long multiplication, etc. Because most people (even gifted I would imagine), probably need to do more than 20 problems to master it. And will continue to work on math facts as well since she tends to forget them.

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#201801  09/23/14 03:02 PM
Re: Learning math computations
[Re: blackcat]

Junior Member
Registered: 04/12/14
Posts: 39

I ended up buying her a cheap $15 one from Office Max but maybe I need to look at better options. I think Dh has a better one (he majored in math). She just started kindergarten 3 years ago, I can't believe I'm trying to figure out what is the best option for a scientific calculator. I don't want her to lose a $100+ dollar calculator.
I don't think they meant graphing calculator, I cannot imagine why they would need it in prealgebra. Even a scientific calculator is overkill, she should be fine even with $1 calculator .

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#201802  09/23/14 03:09 PM
Re: Learning math computations
[Re: blackcat]

Junior Member
Registered: 04/12/14
Posts: 39

The textbook has only come home once and I should have looked at it more thoroughly. She's in a "flipped learning" classroom so all she does at home is watch about 3 oneminute instructional videos online produced by the textbook company (I think?) and then take a 3 or 5 question quiz. Presumably she is getting work done in class but who knows! Too bad. Sounds like you are on your own with math. What about your local library? Ours has all textbooks for all local schools. They are not in circulation, but you don't need the textbook at home, you just need to get an idea how bad it is

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