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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: 3987

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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#201819  09/23/14 08:22 PM
Re: Learning math computations
[Re: blackcat]

Member
Registered: 08/24/10
Posts: 3428

She must be pretty fluent for her to have passed the pretest? Or could she have gotten lucky? I wonder if you can assess her yourself? As seen in my thread, I have a DD in 6th grade math and they are hammering upperlevel fluencyvery LONG long division problems, multistep word problems that involve doing multidigit multiplication and long division of decimals, etc. Interestingly, they are also still spending a ton of time on highlevel estimation and mental math skills, which DD hates with a passion (she really likes to be exact and just DO the problem!), but which I am starting to see the sense of (it's a number sense thing).

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#202047  09/26/14 11:03 AM
Re: Learning math computations/Prealgebra
[Re: master of none]

Member
Registered: 02/17/14
Posts: 582

Can I hop on with a prealgebra question? My 9 and 10 year olds are both in 5th grade math doing long division, story problems with multiplication and division, plus taking an after school pre algebra class that uses the "Art of Problem Solving" text book. From what I am reading in this thread, it sounds like it is a good idea to keep plugging away at the multiplication and division work because it needs to become second nature to the kids. My younger one likes the "fun" stuff with Art of Problem Solving and gripes about the boring times tables. It sounds like I have plenty of ammunition to hold her to the fire?

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#202067  09/26/14 02:11 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

I think the pretest was multiple choice and I have no idea what was on it or what grade levels it was testing. They also looked at the computerized test scores (abovelevel) for math from the past year or so and compared all the subscores like "numbers and operations", "algebra", "geometry" etc. and supposedly considered all the data to decide where to place kids. I suspect DD is REALLY good at multiple choice tests for math and is able to eliminate obviously stupid answers. Doesn't mean she knows how to do the computations. I have baiscally no idea what goes on in that class and there is almost no homework but she says she's working at her own pace and passed the first test and is on chapter two now. I think I'm going to log her into a lower level course, though, which most of the kids in her grade are doing, and have her do it as well to make sure there are no gaps and give her extra practice. The videos/quizzes are online.

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#202072  09/26/14 02:40 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 04/26/14
Posts: 3987

I noticed this same phenomenon with one of mine when we were using the Singapore Math Primary Math test books. During the brief period of time when I was experimenting with using the tests, I switched from the openresponse to multiplechoice forms mainly because of handwriting/finemotor issues, but then found that #2 was a really good guesser on mc problems. Of course, it's not really guessing; it's having good number sense, estimation, and problemsolving skills. All excellent things. Unfortunately, that does not substitute for actually being able to generate precise answers when necessary!
It did help me see that we would have to work on computation and problem solving somewhat independently, though.
_________________________
...pronounced like the long vowel and first letter of the alphabet...

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#202077  09/26/14 03:47 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

The teacher emailed me and said that he is struggling to get her to "show her work". Big surprise there, with her writing issues. I'm not sure what the solution is. I think she needs to copy problems out of a textbook into a notebook and she is not used to that. Everything up until this point has been workbooks. She is also supposed to be "taking notes" while watching the videos. She is 8 (almost 9)is this really a realistic expectation? I just don't see that happening considering she couldn't even keep up with spelling tests last year and had the words all out of order (or completely blank) on the paper. I'm brainstorming for what I want put into a 504. She has a disability, but there is also just a huge gap between her age and the age of kids who normally do this sort of work, probably 7th8th graders. Even the kids in her group are about 2 years older than her on average.

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#202079  09/26/14 04:08 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 06/30/12
Posts: 144
Loc: Seattle

Are any of those issues really impacting her? I.e. is someone else noticing she doesn't take notes, does not showing your work mean the problem itself isn't copied or just the intermediary steps and/or is the lack notes harming her comprehension?

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#202137  09/27/14 03:31 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 09/11/13
Posts: 816

blackcat, I wouldn't be too crazy about the watching videos and taking notes approach, especially if she is not a quick scribe. So is this how instruction will take place going forward? I wonder the same things you do about DD9 and multiple choice tests  she is VERY good at them, but I do sometimes wonder whether she is almost TOO good at them, KWIM? DD cannot get away with not showing her work in math class, though...under our lovely Common Corealigned EM classes she must. painstakingly, show. and. explain. her. work. (plus do the problems multiple ways). Surely, there is a happy medium? I'd still take your math over our math at this point. I think that everything DD has done so far this year has been review for her, so I am not yet sure how (if?) she will demonstrate math progress this year.

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#202138  09/27/14 04:13 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

I'm skeptical of the "flipped math". So basically they watch video lectures on an ipad or something (who knowsI have her use a PC when she does it at home). And they do the actual "work" in classat their own pace. They do some of the problems in the textbook. Luckily it's not like EM, it's more like what you or I would have done. If the kids don't understand what they are doing in class they are supposed to ask the teacher for help. It doesn't seem ideal but it is way better than what she was doing last year. Listening to longwinded lectures about how you figure out 5X3 and boring workbooks at the wrong level. To "move on" to the next unit, they need to score 90 percent or something on the unit test. But none of the kids would be taking the same test on the same day, necessarily. I'm not really sure what the purpose of the notes are. Because the textbooks are right there in the classroom. If she finishes the entire book and passes the tests, then they will move her onto Algebra I, even if it's the middle of the year. I just need to find out if all the tests are multiple choice. Because if they are, that seems like a really bad idea and I can see why he wants her to show the computations then.

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#202140  09/27/14 04:41 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 02/17/12
Posts: 1390
Loc: Seattle area

My daughter loooooooved her flipped math class last year, for what that's worth.

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#202141  09/27/14 04:53 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 04/26/14
Posts: 3987

Our oldest also had a flipped math class at one point, with a similar structure, which worked out fine. But the notes were graded only for their existence, not their length or quality. Actually, I think the teacher treated the notes more as documentation that the videos were watched.
_________________________
...pronounced like the long vowel and first letter of the alphabet...

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#202144  09/27/14 05:29 PM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

That's a good point about documentation. I'm guessing that's the thought behind it. I know he can see whether the kids took the quiz online and how long it took them to complete, but not sure if he can tell if the videos were watched. I suppose just because a kid hits "play" that doesn't mean they are watching. anyway, I'm glad that flipped math can work out well, because it seems like a good idea in theory. It probably depends on how much time the teacher has to help each kid, and whether the child is actually watching the videos and comprehending them.

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#202664  10/03/14 07:30 AM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 08/24/10
Posts: 3428

Ohhh, multiple choice. That's not good, if so. I have a good guesser here also. I would think a lot of our kids are good guessers!
I would assess her yourself, for your own peace of mind. It wouldn't be too hard. I just did a bit of this the other day with my DD because I suspected she didn't really understand a concept but just applied the "take the numbers in this problem and do something with them" approach, and it happened to work. (I was right, too.)

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#202667  10/03/14 08:13 AM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

I talked to him (teacher). It sounds like so far it's Algebra and she's not writing out the steps, she's figuring out X in her head. So she's not showing how she is getting X. I had suggested using some kind of app for writing, like modmath but I don't even know if that's possible with Algebra. I think she might have dysgraphia. He says most of these chapter tests are NOT multiple choice, which is good. He also said that she scored over 50 percent on the test for the grade before this one (7th grade math? Whatever comes before prealgebra) so he thought it would be a waste of time to have her do that course if she knew most of it already. This made me laugh considering that the district requires kids to score 98 percent percent on tests to skip/accelerate otherwise. Does anyone know if this would be mostly a repeat? Because obviously she's gotta get that 50 percent that she missed from somewhere.

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#202672  10/03/14 10:29 AM
Re: Learning math computations/Prealgebra
[Re: blackcat]

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

Does anyone know if this would be mostly a repeat? Because obviously she's gotta get that 50 percent that she missed from somewhere. It is impossible to know, because only your teacher knows what material he is going to cover, and sometimes even he might be surprised. Once in the middle of prealgebra course our district decided that everybody should immediately learn something about geometry. Teachers had to put aside all the previous materials, and use some printouts sent by the district.

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#202674  10/03/14 11:02 AM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 07/13/12
Posts: 1478
Loc: NC

Funny, almost everything pure math before algebra is intuitively derivable from other math (and much of algebra is in many ways; and yes (you know who you are) all of math is derivable.) Whether any individual student will make those leaps and connections is guesswork and experimentation for everyone involved. Whether their leaps will be compatible with random entity X's philosophy of math execution is another question.
Personally, I think having a teacher believe in a kid and their capability is well worth letting it ride.

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#202707  10/04/14 08:25 AM
Re: Learning math computations/Prealgebra
[Re: blackcat]

Member
Registered: 05/23/13
Posts: 2154

I sat down with her and said "look, if you subtract something you have to actually write it on both sides of the equation, if you multiply, here's how you "show it", etc. I have a feeling this was covered in the previous course and she just had no idea. It certainly wasn't in any of the videos. Combine that with the fact that she hates writing, and everything was worksheets up to this point (as opposed to copying out of a textbook into a notebook) and I can see why she was finding X in her head. I'm a bit concerned about the amount of material that she is missing from previous courses, but one of the teachers made a comment that this is largely a repeat because of the "spiraling". So probably random things like this will come up againlike not knowing how to write things the proper way, because it's assumed the child has been exposed to it before. So far she says everything is easy. If she was getting agitated I'd be more concerned. I'm open to move her down a level though...we'll see how she's doing on the tests.

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