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    #13207 - 04/06/08 08:14 PM Question about algebra and radical acceleration
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Hi all,

    My second-grader is pretty good at maths and we've been working through above-grade-level books for a while at a leisurely pace 2-3 evenings a week. He's partway through a 5th grade book right now after taking a break to do kangaroo maths problems for ~3 months.

    I looked through the grades 5-8 books and discovered that they don't really present a ton of novel material. They mostly seem to do the same stuff with bigger numbers. For example, long division is introduced in 4th grade and then 5th grade long division just uses bigger numbers. The books seem to repeat a lot of stuff, too. I presume most of you have noticed this (ahem).

    So, anyway, he bought an algebra book somewhere and was reading it on his own. I've given him 3 lessons and he seems to get the ideas. I've decided to mostly skip the grades 5-8 books because I think he can learn most of it through algebra.

    I really like the type of thinking that algebra requires and teaches, and think it might be a very good approach for him. He makes a lot of careless mistakes, and I'm hoping that the stepwise approach required in algebra might alleviate the problem somewhat (then again...).

    We'll hit any missed grades 5-8 topics independently.

    Have any of you taken this approach? If so, did it work for you?

    I have to go now. My cat is trying to eat the elastic thing hanging from my jacket. Bad cat!

    Val


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    #13211 - 04/07/08 04:24 AM Re: Question about algebra and radical acceleration [Re: Val]
    Grinity Offline
    Member

    Registered: 12/13/05
    Posts: 7207
    Loc: Connecticut
    We haven't taken this approach, but that's a good sign, as we messed up big time. Our son actually completed 4th grade Math at one school and started 8th grade math an another school, but because he was doing it 'in school' and on the schools timetable, and at the expense of history class, it was a 3 month experiment that failed.

    OTOH, he is now in 7th grade doing the same '8th grade' pre-Algebra class and it's going well. I think that if we had do what you propose it would have been 'just fine.'

    I wish that there were Math books that cover 5-8 in a non repetitive way, and maybe there are. Your plan sounds flexible and totally reasonable. What have you got to lose? Nothing really.

    BTW - I really like the book "algebra to go" - a suggestion from Hoagiesgifted.org

    Smiles,
    Grinity
    _________________________
    Coaching available, at SchoolSuccessSolutions.com

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    #13220 - 04/07/08 06:51 AM Re: Question about algebra and radical acceleration [Re: Val]
    Texas Summer Offline
    Member

    Registered: 05/01/06
    Posts: 216
    Loc: Texas
    Originally Posted By: Val
    I looked through the grades 5-8 books and discovered that they don't really present a ton of novel material. They mostly seem to do the same stuff with bigger numbers.


    You are absolutely right about this. When I was in grad school I worked as a long-term substitute for about a semester teaching 7th & 8th grade math. Each day I taught the same thing in my 7th grade classes as I did in my 8th grade classes with usually only an order magnitude difference in the numbers. I definitely don't recommend 6th-8th grade math for gifted students.

    There was a good discussion on this topic in the "EG/PG and not accelerated?" thread.

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    #13221 - 04/07/08 06:58 AM Re: Question about algebra and radical acceleration [Re: Grinity]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Val,

    It makes good sense to me.

    We're seeing the same problem of repetition even earlier and even with Singapore Math, which is supposed to be one of the good ones for being linear rather than a spiral curriculum. I've actually been considering moving on to pre-algebra or some more complex geometry with my DS6 while I wait for him to learn his times tables. That seems so bass-ackwards that I've been dithering over it for some time now. But for him, it seems to make sense.

    If you have the grades 5-8 books, you can always use them to supplement any holes that pop up as you're doing the algebra. As long as he doesn't get so confused that you have to un-teach him what he's learned wrong, I don't see the harm that could come. It seems to me that in the worst case, where it is too hard or leaves him with too many holes, you go back a grade or two. <shrug> No harm done.

    K-
    _________________________
    Kriston

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    #13222 - 04/07/08 07:00 AM Re: Question about algebra and radical acceleratio [Re: Texas Summer]
    kcab Offline
    Member

    Registered: 10/02/07
    Posts: 1603
    Loc: Sparta, apparently
    I think the only thing taught in 5th-7th math besides long division is manipulation of fractions. At least, that's all I can see, or recall. I remember thinking that 7th grade math was for 1) learning tricks with numbers, and 2) hearing silly puns. DD10 is accelerated 1 year in math and there is not much new, and her friend who is +2 in math thinks she's doing the same stuff as the kids in the regular classroom.

    _________________________
    kcab

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    #13228 - 04/07/08 09:28 AM Re: Question about algebra and radical acceleratio [Re: kcab]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    I skipped 7th grade and then did Algebra I and II in one year. Didn't hurt me or prevent me from getting my PhD in math...

    To a mathy kid, it's not a problem to generalize arithmetic operations to larger numbers. They don't really need a whole year (or even a semester) to get it.

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    #13231 - 04/07/08 10:20 AM Re: Question about algebra and radical acceleration [Re: Kriston]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Originally Posted By: Kriston
    Val,

    It makes good sense to me.

    We're seeing the same problem of repetition even earlier and even with Singapore Math, which is supposed to be one of the good ones for being linear rather than a spiral curriculum. I've actually been considering moving on to pre-algebra or some more complex geometry with my DS6 while I wait for him to learn his times tables. That seems so bass-ackwards that I've been dithering over it for some time now. But for him, it seems to make sense.

    If you have the grades 5-8 books, you can always use them to supplement any holes that pop up as you're doing the algebra. As long as he doesn't get so confused that you have to un-teach him what he's learned wrong, I don't see the harm that could come. It seems to me that in the worst case, where it is too hard or leaves him with too many holes, you go back a grade or two. <shrug> No harm done.

    K-

    HI Kriston,

    I'm definitely going to mix in some of the 5-8 stuff with the algebra. I think it will fill holes nicely and provide variety too.

    You mentioned that your son still needs to learn his times tables. I moved mine forward when he had about half of them memorized, figuring he would learn them by doing division. It's worked out pretty well and he knows most of them now. I reckon they're the kind of thing everyone learns eventually.

    We don't focus on moving stepwise with our kids. They seem to thrive on a mix of topics. Hence, I started long division before my eldest had learned his times tables, but would still get him to do problems like 123*46 now and then to help cement multiplication concepts. Last night the idea of "Why do things float" came up and I taught him about Density and introduced D=m/v and how smashing up cotton ball into a smaller volume can increase its density. We have a lot of random stuff like that. Some of it sticks, some of it doesn't.

    Val

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    #13232 - 04/07/08 10:25 AM Re: Question about algebra and radical acceleratio [Re: Cathy A]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Originally Posted By: Cathy A
    I skipped 7th grade and then did Algebra I and II in one year. Didn't hurt me or prevent me from getting my PhD in math...

    To a mathy kid, it's not a problem to generalize arithmetic operations to larger numbers. They don't really need a whole year (or even a semester) to get it.


    Hi Cathy,

    It's good to hear someone else say that. When I introduced my son to long division with double-digit numbers, I said "See, it's just like regular long division, only you have to figure out how many times 25 goes into 162. Get it?" He got it and did 4/4 problems correctly without help from me.

    I understand that he's a bright kid, but still, I have to wonder if maybe the people who produce these books are perhaps setting their expectations a bit too low.

    Val

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    #13241 - 04/07/08 11:37 AM Re: Question about algebra and radical acceleratio [Re: Val]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Val, having taught math at the college level, I can tell you that there are college students who can't do long division. In that sense the books don't have expectations that are too low, but I do wonder at their ineffectiveness...

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    #13248 - 04/07/08 11:54 AM Re: Question about algebra and radical acceleratio [Re: Val]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    I'm with you, Val. Is it our GT denial, or are they just aiming low? Maybe a bit of both?
    _________________________
    Kriston

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    #13251 - 04/07/08 12:05 PM Re: Question about algebra and radical acceleratio [Re: Kriston]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Originally Posted By: Kriston
    I'm with you, Val. Is it our GT denial, or are they just aiming low? Maybe a bit of both?


    There could be other problems in the mix: the extreme focus on minimum proficiency (exacerbated by NCLB) and the quality of the teaching.

    It's pretty appalling that college students can't do long division, but sadly, not surprising. Somehow with all the worry surrounding NCLB and "standards," all of America's students seem to be learning less and less in school. Why is that?

    Val

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    #13252 - 04/07/08 12:08 PM Re: Question about algebra and radical acceleratio [Re: Val]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    I was always shocked by how many of my Big-10 college students had done no writing during their senior year of high school except one big research paper, which was returned to them with a letter grade and no comments. How is that teaching a kid anything? One semester when I asked the question, EVERY student in the class--no exceptions--raised a hand to say that this had been their experience.

    Appalling!
    _________________________
    Kriston

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    #13253 - 04/07/08 12:11 PM Re: Question about algebra and radical acceleratio [Re: Val]
    kcab Offline
    Member

    Registered: 10/02/07
    Posts: 1603
    Loc: Sparta, apparently
    Originally Posted By: Val
    It's pretty appalling that college students can't do long division, but sadly, not surprising. Somehow with all the worry surrounding NCLB and "standards," all of America's students seem to be learning less and less in school. Why is that?
    Every last one of them is bored out of their gourd?

    I think, perhaps, intense drilling and stress can work to provide short term gains, but are not an effective strategy in the longer term.
    _________________________
    kcab

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    #13254 - 04/07/08 12:15 PM Re: Question about algebra and radical acceleratio [Re: kcab]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    True. No kids--GT or no--learn well in a "drill and kill" situation for the majority of their time.

    (Some skills--like math facts--can be learned well this way, but anything beyond rote memorization, no. And the "drill and kill" for math facts is used short-term, in quick bursts, not as a long-range, consistent teaching method.)
    _________________________
    Kriston

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    #13255 - 04/07/08 12:19 PM Re: Question about algebra and radical acceleratio [Re: kcab]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    I was looking at a fifth grade teacher's web site in a local schol district. It said that four days per week, her students do 100 multiplication problems as soon as math class starts. The goal is to get them done with 100% accuarcy in less than one minute during the course of the school year.

    Can you imagine??? In FIFTH grade? That would be dull in 3rd grade.

    Talk about bored out of their little gourds, not to mention an ideal method for killing any curiosity about mathematics.

    Oy.

    Val

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    #13259 - 04/07/08 12:56 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    OHGrandma Offline
    Member

    Registered: 01/05/08
    Posts: 830
    Originally Posted By: Dottie
    Well....do we want them to know the facts? Or not? It's only one minute, how boring can it be?

    I'm not for drill and kill mind you, but I'm more appalled by the kids that don't know their facts.

    I don't know...I just hate to see schools bashed completely. Some really are trying to make the best of a less than ideal (government enforced) situation.


    I probably have even more conservative thinking than Dottie on this subject. There have to be minimum standards, and consequences for teachers not teaching the material to meet those standards. One problem is the motivated & gifted students not being allowed to excel, but instead are held back while the slower kids need help.
    I think we need to implement a non-grade approach to classroom divisions, and keep a child in Math 1, or Reading 1, etc. until the child has mastered those concepts; then move to Math 2, Reading 2, etc. There should be no passing until the material is mastered, and there should be no holding back the children who know the material.

    FWIW, this was taken from a 4th grade teachers website, today. This is the teacher that GS8's teacher has recommended for him next year. I've edited it to remove students names.

    Quote:
    We are working on learning our times tables.
    Congrats to (3 students) for passing their twos.
    Congrats to (6 students) for passing their threes.
    Congratulations to (3 students) for passing their fours.
    Congrats to (3 students) for passing their fives.
    Congrats to (1 student) for passing his sixes.
    Big Congrats to (3 students), for passing their sevens.
    A big wow to (1 student) for passing his eights.
    Good Job (1 student) for passing your tens.
    Congratulations (1 student) for passing your twelves.
    And Wow to (1 student) who passed her mixed review!
    I predict alot of ice cream will be eaten in our room in May.


    This is the beginning of the final quarter for 4th grade. I'm worried all over again about what GS8 will do in 4th grade as he already knows this, as well as adding, subtracting, & multiplying fractions.

    Maybe what's even more worrisome is the fact that our school has around an 80% proficient rate in math on the state proficiency tests. I don't think this is asking much of our children, if 9 year olds are still learning their multiplication tables, yet 80% of them 'pass' the state requirements.

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    #13260 - 04/07/08 01:02 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    I should have explained it better: they start off with a goal of less than five minutes and work to one minute from 0*0 to 9*9 in random order. The others presumably wait around while the rest finish.

    I think my point was that this approach kills enthusiasm, and anyway, why didn't these kids learn this stuff in 3rd grade? By the time I was in 5th grade, we were way past 5*4 and 7*9. If an entire class needs to practice this exercise in 5th grade, the school has done something wrong.

    I understand that the schools believe they're doing their best and that many teachers are really trying very hard. But that doesn't mean there aren't serious problems, and the educational establishment has to carry a lot of the blame. After all, they're the ones who got us into this mess, not the government. Most students in other developed countries would find our standardized tests trivial because their school systems are far more rigorous than ours.

    ===> And they do this with less money per student (we outspend almost every other country on the planet), more students per class, and lower or equivalent teacher pay. This information is available from OECD statistics from the PISA exam. <===

    I lived in Ireland for many years, and the public schools in the poorest parts of Dublin provide the same high quality education as the ones in the ritzy parts of the city.

    Ireland has two levels of courses students can take in high school: "Pass" or "Ordinary" and "Honours".

    Here's a link to a YouTube video with some examples of what
    they learn in ORDINARY maths. Contrast with US exit exams asking for students to calculate the interest on a bank deposit. Watch and cry.

    http://www.youtube.com/watch?v=x4W_6u2KyL4

    Val


    Edited by Val (04/07/08 01:04 PM)

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    #13262 - 04/07/08 01:17 PM Re: Question about algebra and radical acceleratio [Re: Val]
    Cathy A Offline
    Member

    Registered: 05/26/07
    Posts: 1783
    Loc: West coast, USA
    Originally Posted By: Val
    Watch and cry.


    frown whaaaaa!

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    #13263 - 04/07/08 01:17 PM Re: Question about algebra and radical acceleratio [Re: OHGrandma]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    I think my problem is that all the focus on minimum standards seems to have LOWERED the age of proficiency for things like times tables. When I was in school, we knew ours by the middle of 3rd grade. And this was in a rural, not-wealthy public school.

    It seems to me that the more standardized the proficiency requirements become, the lower they get. I don't like that.
    _________________________
    Kriston

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    #13264 - 04/07/08 01:18 PM Re: Question about algebra and radical acceleratio [Re: Kriston]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    BTW, my posting overlapped with Val. I'm with her. wink
    _________________________
    Kriston

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    #13265 - 04/07/08 01:20 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    We did this in 3rd grade too and there was no waiting for the other kids either. Actually the kids really enjoyed the competition to see who could get to the finish line first! (they had race cars that moved up as they went along)

    My DS is now in 4th and some of those kids still don't know their multiplication facts down cold. I don't blame the school, the school taught the facts. I think it is up to the parents to keep the kids drilling or memorizing or whatever. And with so much other stuff to do sometimes it is hard to find the time to keep up with skills that have already been taught.

    So while I agree there are definitely problems with the school system I also think that the parents have to be sure that their child is getting what he or she needs. Just my 2 cents! smile

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    #13269 - 04/07/08 01:29 PM Re: Question about algebra and radical acceleratio [Re: EandCmom]
    kcab Offline
    Member

    Registered: 10/02/07
    Posts: 1603
    Loc: Sparta, apparently
    Well, one thing is that different presentation methods work for different students - so just doing the same thing over and over is unlikely to get it through everyone's head.

    Also, all the comments here are about multiplication facts, which is one discrete area, but "drill & kill" seems to be applied to many other areas at my DD's school. Two months of stress over upcoming tests, followed by almost a month of testing, seems like a waste of time to me and really turns her off. And it isn't really working, DD thinks that some of the kids in 5th aren't even secure in subtraction, never mind mult.
    _________________________
    kcab

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    #13270 - 04/07/08 01:32 PM Re: Question about algebra and radical acceleratio [Re: Kriston]
    LMom Offline
    Member

    Registered: 12/14/07
    Posts: 902
    I agree tables should be learned in 3rd grade, but if that's not the case I think 1-5 minute drill will not kill anybody.

    As for skipping 5-8, I would probably cover all the areas he may have not covered yet before jumping to algebra. I would make sure he can add/subtract/multiply fractions, calculate %, area and volume of different shapes, rounding, angles. That's up to Singapore 6B, I don't have anything beyond that. I would also go through some challenging middle school problems (Singapore Challenge problems, Zaccaro middle school, Mathematical Olympiads for Elementary and Middle schools).

    DS5 does 4th grade math, but I still feel there are lots of things to cover before he starts algebra. The good news is that he is finally getting to the level when challenging problems can require some effort. There is only that much you can do in the first few years, but you can come up with interesting problems for the middle school level.

    You are all right that lots of things repeat or are very obvious and the kids don't really need to learn them, but there are still new things to learn there.
    _________________________
    LMom

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    #13271 - 04/07/08 01:34 PM Re: Question about algebra and radical acceleratio [Re: EandCmom]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Originally Posted By: EandCmom
    My DS is now in 4th and some of those kids still don't know their multiplication facts down cold. I don't blame the school, the school taught the facts. I think it is up to the parents to keep the kids drilling or memorizing or whatever.


    I disagree. Teaching maths, reading, etc. is the primary responsibility of the school, not the parents. Otherwise, why do we even have schools?

    What are kids doing in school all day if not learning? Why do they need to go home and keep doing what they were supposedly doing a few hours ago and will be doing again tomorrow?

    California schools close at ~2:30 except on Wednesdays when they close after lunch to accomodate "in service" time for teachers. Why do schools need "in service days" every week? Why can't they do this at 2:45? And 2:30 is very early anyway. Why do schools close so early in a country that spends more per student than all but one or two others in the world?

    Val





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    #13272 - 04/07/08 01:45 PM Re: Question about algebra and radical acceleratio [Re: Val]
    bianc850a Offline
    Member

    Registered: 12/02/07
    Posts: 312
    Loc: California
    My dd learned her multiplication tables in 1st grade (she was being moved to 2nd grade math) with those 5 minute drills. Twice a week, children have five minutes to complete a set of worksheets (starts with addition, followed by subtraction, then mixed addition/subtraction, multiplication, division, then all mixed). As children master once concept (able to get 100% on all questions under 5 min.) they move to the next concept. It is 10 minutes a week and by the end of the year my dd knew all the mutliplication tables to 12. It certainly was helpul when she stared doing division and multiplication to be able to easily recall those facts.

    I feel children need to master basic facts before they can move to more complex concepts.


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    #13277 - 04/07/08 04:47 PM Re: Question about algebra and radical acceleratio [Re: Val]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: kcab
    Also, all the comments here are about multiplication facts, which is one discrete area, but "drill & kill" seems to be applied to many other areas at my DD's school. Two months of stress over upcoming tests, followed by almost a month of testing, seems like a waste of time to me and really turns her off. And it isn't really working, DD thinks that some of the kids in 5th aren't even secure in subtraction, never mind mult.


    Yes, indeed! The whole reason I mentioned times tables is because that's one area where drill (and not kill) can be useful. But I think most of the areas in which the schools are drilling are not effective.

    Most kids learn best by doing, by hands-on work with concepts. Drill is a waste of time for most subject areas.

    Originally Posted By: Val
    What are kids doing in school all day if not learning?


    I SOOOOO agree with you on this point, Val! This is why we chose to homeschool. If they have the kids for 7+ hours a day, they ought to be able to teach most of what the kids need to know. If the kids aren't learning at school, then why are they there?

    Most days after school, I want elementary school-aged kids outside playing and getting some exercise!
    _________________________
    Kriston

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    #13279 - 04/07/08 05:59 PM Re: Question about algebra and radical acceleratio [Re: Val]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    Originally Posted By: Val
    I disagree. Teaching maths, reading, etc. is the primary responsibility of the school, not the parents. Otherwise, why do we even have schools?

    What are kids doing in school all day if not learning? Why do they need to go home and keep doing what they were supposedly doing a few hours ago and will be doing again tomorrow?


    I understand exactly what you are saying. However, I think this only works in a perfect world where all kids are on the same page. I also think it is definitely the parents responsibility to make sure their child is getting what they need. The schools are strapped to try to accommodate everyone and all learning levels. If they work on multiplication until every last child completely gets it, they would never get off multiplication in some instances. Some children just need to work on some things more than others so I don't think the kids who do get it faster should be penalized and wait while the others keep working on it. The teachers have to move on at some point. If my child is the only child not getting something, is it the teachers responsibility to keep working on it with him, or is it mine to get him the help he needs to keep up? (and I'm not talking about problems requiring an IEP, maybe just difficulty understanding a particular subject). Personally, I think it would be my responsibility to help him out. Just as so many here have gotten grade skips, or are after schooling or homeschooling to get their individual child the level of education they need.

    Definitely this isn't optimum. But with the way schools currently are, and I don't see a radical over haul coming any time soon (although maybe one could be used!) I think realistically it is ultimately the parents who are responsible for making sure their child gets the education they need. I'm sure others will disagree, and that is fine, but that is just the way I personally feel about it. smile

    Kriston said "Most kids learn best by doing, by hands-on work with concepts."

    I completely agree, and honestly, I haven't noticed that much drill going on. They do lots of hands on work. Last week they made orange sherbet to demonstrate physical change and today the teacher burned some paper to show a chemical change. I also played science bingo with them to help them remember some of their science facts. They loved all of it! My DS6 made paper last week and they are always doing some sort of hands on project. His class does flip its where they are timed for 1 minute doing addition on one side of the paper and flip the paper and they do subtraction on the other side. I've watched them do it and they all get a kick out of it. So all drill isn't bad. Maybe it is just how it is presented.


    Edited by EandCmom (04/07/08 06:37 PM)
    Edit Reason: thought of more stuff!

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    #13280 - 04/07/08 06:55 PM Re: Question about algebra and radical acceleratio [Re: EandCmom]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Well, I think it's about how it's presented *and* what the subject matter is. Would the kids have gotten as much out of memorizing the details of physical vs. chemical change as they got out of the hands-on methods? No way!

    Math facts are the one exception that I can think of--maybe spelling words, too?--where drill is a truly useful technique for teaching elementary school-aged kids.

    At higher levels, you might also need drill for anatomy or chemistry as well. But in elementary school, I really think rote memorization is rarely useful for anything but basic math facts and spelling words.

    You do not learn concepts through memorization. It's just too low on the learning pyramid. Better to use higher level thinking skills...and current standardized testing (aka NCLB) means there's no reward for teachers to teach higher level thinking skills.

    I think individual schools and teachers generally (though not always) try to do the best they can within the system. But I think the system is deeply, deeply flawed.
    _________________________
    Kriston

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    #13284 - 04/07/08 07:46 PM Re: Question about algebra and radical acceleration [Re: Grinity]
    cym Offline
    Member

    Registered: 05/01/06
    Posts: 865
    Loc: southwest
    Hi Val,

    For elementary math, besides division, there should be several other topics. The middle school math teacher I know says incoming kids are typically weakest in decimals, percentages, fractions. Ratios too. Algebra topics can be introduced early (my second grader is also doing some work in class), though it's an introduction. I like the idea of introducing math-talented kids to advanced topics to pique their interest and give them broader knowledge.

    My son seemed ready for Algebra early and I worked him a little, because the school did not want to advance to beyong pre-Algebra. It benefitted him to review concepts he reviewed early (and forgot). It was frustrating that no one was/is willing to teach a young-ish kid advanced topics, but I do think there is a maturity required for multistep operations. Definitely introduce him to topics, but expect him to need a deeper understanding before mastery.

    Just my opinion...

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    #13302 - 04/08/08 11:17 AM Re: Question about algebra and radical acceleration [Re: Dottie]
    OHGrandma Offline
    Member

    Registered: 01/05/08
    Posts: 830
    Here is a link to Ohio's website that contains materials from past proficiency tests. (For those who haven't figured it out, the 'OH' in 'OHGrandma' is where I live, not how GS8 gets my attention wink )

    Since we're talking mandatory testing I thought it might be useful for those who aren't going through the testing to see what's on the test for different grades.

    Chris

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    #13303 - 04/08/08 11:44 AM Re: Question about algebra and radical acceleration [Re: Dottie]
    snowgirl Offline
    Member

    Registered: 02/24/08
    Posts: 361
    Just to chime in on the subject of drill and rote memorization, the most effective method may well depend on the preferred learning style of the particular child. According to Silverman's theory of visual-spatial learners (which, by her estimate, are about 30% of the student population), VSLs do not learn by drill and repetition, or rote memorization, but by seeing relationships, whereas auditory-sequential learners may need some repetition to reinforce learning and fare much better with rote memorization.
    http://www.visualspatial.org/Articles/appendc.pdf (or for a fuller discussion of VSLs and math, see http://www.visualspatial.org/Articles/mthstrat.pdf and *especially* http://www.visualspatial.org/Articles/algebra.pdf )

    Incidentally, on the local evening news the other night there was a segment about recent improvements in math in a particular local school. The school had switched to Singapore math, which, according to the news story, required less drill and used more visual representations. I know I've seen discussions of that curriculum on these boards, and I admit I don't know anything about it, but I did find the news story interesting.

    just my two cents--
    smile

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    #13313 - 04/08/08 02:08 PM Re: Question about algebra and radical acceleration [Re: Val]
    Lori H. Offline
    Member

    Registered: 05/26/07
    Posts: 982
    I recently bought an 8th grade Spectrum Math book since my nine (almost ten) year old son might try to take the Explore test next year and I was curious about what 8th grade math looks like. I also noticed that it didn't seem very different from the lower level math books, so I now use problems from the 8th grade book when making up a math worksheet for him to do. He also uses Aleks middle school math online but he doesn't do it every day because he likes to do a variety of things. He likes doing multi-step word problems from a book called Calculation Capers for grades 5-8 and he did one on taxes the day I did my taxes. Some days we work on mental math which I think is good for a kid with handwriting issues. We have done math with decimals for years. He learned how to figure out 1 percent of a number by moving the decimal point years ago when we got a credit card that gives us a 1% rebate every time we use it that goes to him. It was easy for him to build on that knowledge. We also have a pre-algebra workbook that he sometimes uses.

    He likes doing a variety of math problems. He absolutely hates a worksheet full of the same type of problems. I like it that he does this because I don't have to worry that he needs to review anything.

    We just started reading a book called Painless Algebra by Lynette Long, Ph.D. but I think we will probably wait before really going more in depth with algebra because my son is more of a verbally gifted kid. He will probably learn all of the math vocabulary and how to spell the words correctly before he really gets into doing challenging algebra problems. I actually got the book for me because I was afraid that I wouldn't remember how to do algebra. He seems to like the book so far. He likes telling his sister that he is learning algebra.


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    #13314 - 04/08/08 02:18 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: Dottie
    I've found our homework also to be very non-rote. This approach might not be best for weaker students, and it never seems to be enough for the really advanced, but it definitely encourages higher level thinking skills!


    Hmmm. Could you give me some examples of non-rote that should be rote instead, Dottie? Aside from the math facts and spelling that I mentioned--which pretty much just have to be memorized--I can't even envision what you could be talking about that would be better as memorization than concept. What higher level thinking skills are involved? Analysis? Synthesis? Or just application of knowledge to solve the problem? (which isn't a whole lot higher on the pyramid than memorization...)

    As for the wacky word problems, I think those are always an issue for kids, but they're also the way math comes to us in real life, so I tend to take those in stride. I have a yard I want to fence and I need to know the perimeter, how much water does it take to fill this container, etc. It all comes with story-problem baggage. My DH hated word problems until he hit physics and realized that THAT was why they'd had all those words cluttering up his math books for all those years! LOL!

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    #13324 - 04/08/08 03:30 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: Dottie
    But the weaker students would surely benefit from more repetition in some basics of any of the math concepts (long division, fractions, etc).


    Well...I think it's like Texas Summer wrote some time ago: there are 2 sets of skills you need for math--the "tools," which are the rote knowledge of math facts, and the "concepts" which are more like the way things are done and why you're doing them. Two separate parts, and often two different ways of learning the parts.

    Repetition is usually required for memorization of math facts. In our case, DS6 has mastered virtually every part of the *concept* of even multiple-digit multiplication--that it's about multiple sets of like groupings, carrying, etc.--but he currently lacks the *tools* because he's not yet ready to memorize his times tables. He needs both to progress (or at least a good work-around until he does the memorization). Repetition would/will help him learn those tools when he's ready.

    OTOH, repetition was NOT necessary to help him with the concepts. He picked those up right away. Some kids can probably come to understand the concepts through repetition of the tools. But I don't think that this is most kids. I do think the way math concepts are usually taught is to have the class do multiplication problems ad nauseum and hope the child gets why things are done that way. But I do NOT think it is very effective.

    For example, when my father was a very young child, he could do multi-digit math problems of all sorts in his head, giving the answer the second you finished saying the problem. Wow, right? But he did it backwards, starting with the 1000s (or millions, or whatever) place instead of the 1s place. When he got to school, the teachers saw that he was using the tools "wrong" (never mind that his conceptual grasp was ideal and that he always got the right answer fast!), so they drummed it out of his head. He can't do it anymore. They focused on the tools, not on the concepts.

    For my part, I don't recall anyone explaining to me why we did math, say long division, the way we did. We were just expected to "follow the leader." The better you were at imitating the teacher exactly, the better your grade. When I got to calculus, I was a goner because we were expected to think, not to imitate, and I had no idea how to do that in a math class. It had never been asked of me before.

    Of course, these are non-NCLB examples--two old ones and one from home school. Maybe things in school are different now? I just still don't understand what, exactly, is different. Please forgive my denseness, but I really would like to know!

    K-
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    #13325 - 04/08/08 03:42 PM Re: Question about algebra and radical acceleration [Re: Kriston]
    incogneato Offline
    Member

    Registered: 10/25/07
    Posts: 2231
    Loc: up in my head.......
    Maybe the more successful students in your calculus class were homeschooled!


    hee hee hee hee

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    #13327 - 04/08/08 04:02 PM Re: Question about algebra and radical acceleration [Re: incogneato]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    LOL neato!!!!

    I do think things are different now in school. My children have been up and performing in front of their peers since kindergarten and have no fear of public speaking whereas I never did an oral report until 7th grade and about DIED to be in front of people for the first time. Also, in kindy last year, my DS now 7 was doing some pre-algebra type work!!! I asked the teacher about it and she said they were introducing the concepts at that age to get them ready for more difficult pre-algebra/algebra conceps later on. My DS10 has already done some algebra type work this year also. I don't believe I saw an "x" or a "y" until I was in 8th grade when I took algebra.

    I honestly think my kids are doing much harder work at an earlier age than I did (of course that was a long time ago so maybe I can't remember everything wink).

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    #13329 - 04/08/08 04:25 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    Originally Posted By: Dottie
    kids get very little repetition on any one skill.


    Oh yea this is soooo true. My DS10 has a math test pretty much every 4 days on some new concept. They move very, very, very fast in math. Luckily he catches on pretty easily and the teacher does do comprehensive tests every few weeks to make sure they are getting it, but there is virtually no drill involved. You have to move fast to keep up!

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    #13333 - 04/08/08 04:36 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    But WHAT is different? Can you give me a specific example? HOW are they making it conceptual? To be honest, what it sounds like is that they just aren't doing much teaching at all, either of tools or of concepts. Navel-gazing isn't teaching, and that's the impression I'm getting of it (albeit perhaps wrongly).

    I don't call word problems conceptual (and those have always been around anyway). Is there more to it than that?

    FWIW, DS6's workbook from 1st grade was no different than the ones we used when I was in school from what I could see. Not conceptual at all. Lots of repetition of the tools. I saw there were maybe more manipulatives in class than we used, but nothing else seemed significantly different. Certainly nothing "on its head" about the math he was doing. But that was only 1st grade, so I realize I don't know much here...
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    #13337 - 04/08/08 04:45 PM Re: Question about algebra and radical acceleratio [Re: EandCmom]
    kimck Offline
    Member

    Registered: 09/20/07
    Posts: 1134
    Originally Posted By: EandCmom
    Originally Posted By: Dottie
    kids get very little repetition on any one skill.


    Oh yea this is soooo true. My DS10 has a math test pretty much every 4 days on some new concept. They move very, very, very fast in math. Luckily he catches on pretty easily and the teacher does do comprehensive tests every few weeks to make sure they are getting it, but there is virtually no drill involved. You have to move fast to keep up!


    Do you know what curriculum it is? We are using 1st grade Everyday Math and it does have this kind of model. But it still seems very slow. And the spiraling! I swear it was after x-mas break when we actually got a NEW concept. I got a note today that it was a goal by the end of the year to have the kids memorize a small sub set of single digit addition. I'm quite sure we knew the whole addition table in first grade. I did go to an extremely kill and drill private Catholic school. We memorized incessantly without reason - all the presidents, countries and capitols, etc etc etc. So great for visual spatial me. crazy I'm saying this as a mathy person with a mathy kid that goes to a very NCLB test score focused school. This is a school that hired a full time teacher this year just to focus on bringing up math scores for the bottom third of the class.

    I remember sitting and learning long division trying to figure out WHY it worked. When I taught DS addition and subtraction with renaming I had to come up with a proof with manipulatives why this really worked. Once we did that, he was good to go. But before that, he didn't want anything to do with it. That and he can do a lot of 2 and 3 digit addition and subtration in his head.


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    #13338 - 04/08/08 04:51 PM Re: Question about algebra and radical acceleration [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Thanks, Dottie. That helps. I see now. It doesn't seem like navel-gazing (smirk), and it does seem better than the old-school method overall.

    I guess I like the more intuitive start, but then I'd also want to make sure they drill sufficiently on the tools. I don't know why they can't do both. Neither is sufficient on its own, I don't think. Though 6 problems is a lot better than the 50+ we'd have to do...and none of that "do the last 10 that are hardest and skip the rest" stuff for us either. Ugh. That right there was enough to make me hate math forever. Calculus just put the nail in the coffin!

    A more conceptual tack would have appealed to me, for sure.
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    Kriston

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    #13340 - 04/08/08 04:52 PM Re: Question about algebra and radical acceleration [Re: Kriston]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    We crossed paths, kimck, but as usual, I agree with you. The WHY would have made a big difference to me, as it does with DS6.
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    Kriston

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    #13342 - 04/08/08 05:01 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    LOL! Concepts, tools, or both? grin
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    Kriston

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    #13343 - 04/08/08 05:14 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    incogneato Offline
    Member

    Registered: 10/25/07
    Posts: 2231
    Loc: up in my head.......
    Are you guys talking about reform math? Hasn't that been around conceptually since the late 60's or something like that?
    This is oversimplifying it, but it's about taking numbers apart and putting them back together. Playing with the numbers as opposed to straight memorization, if you will. I warned you, oversimplification! I've seen that instead of memorization they teach the itty bitty's to add/subtract using manipulatives, number lines, hundred's graph etc.

    Even peeking over my shoulder at DD8 doing aleks, they teach quotient and remainder totally different then I remember.
    I never remember doing estimating a sum. Doing a larger calculation in your head by rounding up to the larger numbers, adding/subtracting, etc. than subtracting away the number you added by rounding up to get the answer.

    I kind of wish they taught math like that when I was younger, it seems more fun.

    I think DD's favorite part of the day is the mental math test they have everyday. I agree with Kriston, drills have their use but mix it up, people, please!

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    #13347 - 04/08/08 05:29 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    incogneato Offline
    Member

    Registered: 10/25/07
    Posts: 2231
    Loc: up in my head.......
    Math wars hee hee hee

    Please tell me people arent' going to war over this stuff!

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    #13348 - 04/08/08 05:33 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Oh, and I just dug out DS6's old workbook from public school at the start of the school year: it's "Everyday Math," too! Does everyone use it?!? LOL!

    Now, I was in elementary school in the mid-'70s, so maybe I am a new math kid, too, but it sure seems like we did all the same stuff the 1st graders today are doing. But it seems to be low concept and high repetition to me (though maybe not quite as bad as ours was), and it did NOT look like they were learning new concepts AT ALL fast when DS6 was in there! What's up? Our different takes on the same material? Different teaching styles in different classrooms? Something else?

    Of course, we didn't make stick around until winter break, so maybe we just got out too soon to move quickly! LOL!
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    #13350 - 04/08/08 05:42 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    kcab Offline
    Member

    Registered: 10/02/07
    Posts: 1603
    Loc: Sparta, apparently
    Originally Posted By: Dottie
    Not even close, actually!!!! There was a big Math Movement several years back, that turned mathematical teaching upside down and then some. It is much more conceptual and deeper thinking, but some think they tossed the baby out with the bath water on this one, as kids get very little repetition on any one skill.

    It still spirals around too much for GT kids, and too quickly for below average, but it is WAAAAAY better than "the good old days" (if you ask me!)
    OK, I haven't finished catching up yet, but I have to say this is NOT universally true. Not all schools are heavy into concepts these days.

    That's all until I catch up...


    Edited by kcab (04/08/08 05:43 PM)
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    #13353 - 04/08/08 05:48 PM Re: Question about algebra and radical acceleratio [Re: Kriston]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    We use Houghton Miflin math curriculum. I don't think it is wonderful in 1st grade but the 4th grade book has been really great. (at least for my DS)

    Originally Posted By: kimck
    I got a note today that it was a goal by the end of the year to have the kids memorize a small sub set of single digit addition.


    Kim, that doesn't sound too great. My 1st grader is doing 2 digit addition and subtraction right now and has done some geometry, time, etc. I haven't been as pleased with his math work this year as with other subjects. They have such a push on reading in the 1st grade that I have wondered if they don't push math as much because they want to concentrate on the reading more? I don't know but I don't worry with him because he is a mathy kid. He's already doing some multiplication and he can manipulate numbers really well and can see their relationships without ever being told how to do it, so I figure he's doing fine.

    Quote:
    Kriston said - What's up? Our different takes on the same material? Different teaching styles in different classrooms? Something else?


    I think there can definitely be different takes on the same material and the teacher makes a huge difference. It all depends on how well your child responds to the curriculum and to the teacher that determines how you feel about it.

    And I'm with 'neato - I hope there are no "math wars" going on out there!!!! LOL!!!!

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    #13354 - 04/08/08 05:51 PM Re: Question about algebra and radical acceleratio [Re: kcab]
    kcab Offline
    Member

    Registered: 10/02/07
    Posts: 1603
    Loc: Sparta, apparently
    OK - mostly caught up. DD10's former school sounds like Dottie's - Everyday Math + other stuff. Her current school is not like that at all. Listen, she is bringing home packets of math problems that are 10-20 pages long, sometimes with 20-30 problems on a page (varies depending on the topic). Now, maybe she can use this sometimes, I don't think it's bad for her to get a lot of practice with mixed fractions for instance - especially since she skipped the initial lessons on that. But...there is virtually no discussion or conceptual learning. We talk about things at home, that's it.

    Last year her 4th grade class had to do single digit multiplication problems for about half the year, until the teacher felt that almost all the kids had their mult facts. She had learned them in 3rd...
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    #13356 - 04/08/08 06:03 PM Re: Question about algebra and radical acceleratio [Re: EandCmom]
    kimck Offline
    Member

    Registered: 09/20/07
    Posts: 1134
    Originally Posted By: EandCmom

    Kim, that doesn't sound too great. My 1st grader is doing 2 digit addition and subtraction right now and has done some geometry, time, etc. I haven't been as pleased with his math work this year as with other subjects. They have such a push on reading in the 1st grade that I have wondered if they don't push math as much because they want to concentrate on the reading more?

    Ok - we've done some geometry. Shapes and qualities of those shapes. And telling time. I just feel he could have gotten through 1st grade Everyday math in a month a year ago. He knew a lot of it in preschool. I have no idea where he really is in math. Conceptually he gets square roots and fractions. He is working on multiplication and division at home.

    Quote:
    I think there can definitely be different takes on the same material and the teacher makes a huge difference. It all depends on how well your child responds to the curriculum and to the teacher that determines how you feel about it.


    I think this is very true! I know our first grade teacher is not mathy at all and I imagine privately loathes it. She is not remotely creative or innovative with presentation - it's straight out of the Everyday Math book. sleep

    She does give DS and a few other kids some very quality open ended 2nd grade stuff to work on when they get done with their 1st grade stuff.

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    #13359 - 04/08/08 06:16 PM Re: Question about algebra and radical acceleratio [Re: EandCmom]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: EandCmom
    My 1st grader is doing 2 digit addition and subtraction right now and has done some geometry, time, etc.


    The very end of the 1st grade "EM" workbook is knowing math facts to 18. Nothing higher than 9+9, though they do "count up" to 100 with a number grid. They tell time to the quarter hour only (after telling it to the half hour in K!). They tell who has more and by how much with pictures of blocks in stacks of 10s and 1s, but not with any numbers attached. They add and subtract money.

    Houghton Mifflin sounds a lot better in 1st grade, EandCMom!
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    #13362 - 04/08/08 06:19 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Ah! Good catch! I didn't know there was a second one.

    I must say, I was appalled!
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    #13364 - 04/08/08 06:24 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    kimck Offline
    Member

    Registered: 09/20/07
    Posts: 1134
    You've done some great advocacy/acceleration though! I can't imagine getting to where you are in our school. So again - kudos to you.

    I can't imagine DS sitting through 2nd grade math next year. crazy Although, rumor has it our school actually ability groups for math starting in 2nd grade (by thirds). Which for a MG child would probably be perfect.

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    #13373 - 04/08/08 08:38 PM Re: Question about algebra and radical acceleratio [Re: Dottie]
    cym Offline
    Member

    Registered: 05/01/06
    Posts: 865
    Loc: southwest
    Our schools adopted Houghton Mifflin this year and I think it's confusing (I have to read the 4th grade question 2-3 times sometimes before I understand what they're asking for...what do you think DS6 understands?) The district is doing a month of Singapore math presentations because someone high up think that's superior (sounds like some on this board would agree).
    At least Saxon is gone.

    Connected math in middle school--I still think is too sluggish for HG kids. DS9 is frustrated with ALEKS because it bounces him back for careless mistakes. I dunno anymore. I wish I could teach my kids but they don't want afterschooling. I like the idea someone came up with on another thread of school 4 hrs/day, then there would be time for our afterschooling/supplemental work without sacrificing their fun, sports, music, theater, etc. time.

    EPGY Honors Algebra course used "Beginning Algebra" by Lial, Hornsby, McGinnis. It's definitely better than the text used in our High School (can't remember title), but not easy to grasp. AoPS (Art of Problem Solving) Intro text is very good, but advances quite quickly (no threat of repetition there).

    I think working problems with an enthusiastic and capable math coach for competition prep with a group of talented math students would be great to supplement normal, challenging course, but haven't tackled that idea yet to make it a reality.

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    #13379 - 04/09/08 06:00 AM Re: Question about algebra and radical acceleratio [Re: cym]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: cym
    I like the idea someone came up with on another thread of school 4 hrs/day, then there would be time for our afterschooling/supplemental work without sacrificing their fun, sports, music, theater, etc. time.


    Not to sound like a smart-aleck, but this is called "homeschooling!" wink [teasing!]
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    #13384 - 04/09/08 07:09 AM Re: Question about algebra and radical acceleratio [Re: Kriston]
    LMom Offline
    Member

    Registered: 12/14/07
    Posts: 902
    Originally Posted By: Kriston
    Originally Posted By: cym
    I like the idea someone came up with on another thread of school 4 hrs/day, then there would be time for our afterschooling/supplemental work without sacrificing their fun, sports, music, theater, etc. time.


    Not to sound like a smart-aleck, but this is called "homeschooling!" wink [teasing!]


    I hope we will get away with 3 smile

    BTW There are states in Europe where elementary students go to school for 20-25 hours per week.
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    #13388 - 04/09/08 07:26 AM Re: Question about algebra and radical acceleratio [Re: LMom]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    2-3 hours a day of sit-down schoolwork is what we usually do, though the day is full of learning opportunities and extracurriculars, as well as time to play.

    Sometimes less really is more! smile
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    #13395 - 04/09/08 09:09 AM Re: Question about algebra and radical acceleratio [Re: Kriston]
    bianc850a Offline
    Member

    Registered: 12/02/07
    Posts: 312
    Loc: California
    My dd8 (she just had a birthday!) spends 8 hours at school (7 regular hours plus one elective class after school). Out of the seven she has 1 hour of math, 1 hour of Language arts and 1 1/4 hour of recess/lunch every day. The rest of the day is what I would like to call extracurriculars (art, science, music, spanish, drama, etc.). She elects to take that extra hour at the end of the day. Most of the time she signs up for art. Right now is is taking a digital photography class where the art teacher is combining photography with oil, charcoal and water painting. She also taking a science class called "making six different kids of slime".

    My point is that school doesn't have to be boring or hard or too long. If your child is in the right environment 7 hours go by fast. If a child is in an environment that is toxic (not challenged, bullied, bored, etc) even 2 hours is too much.

    I know I have become sort of a cheerleader for my dd school. I just see that whatever they are doing, it is working and wish every child (gifted or not) had the opportunity to have as perfect a fit as my dd has right now. It pains me to see that unfortunately she is in the minority by far. Schools like hers are few and far between. I love the fact that it is such a small school, on the other hand that means they can only serve a very small amount of kids (278 total in grades 1-8).

    I specially love upper school. My favorite is LEAP wed when children get to decide how they spend their day. This year some children formed a band with the music teacher, they can spend all day taking art or science or working with a mentor in math.

    Going back to the math curriculum. This school offers classes all the way to calculus for the "mathy" kids and has a national champions mathcounts team.

    This kind of learning environment is what every child deserves and should be getting. It is a crime that the school system is not set up in a way that high potential can be nourished. After all, the potential return on the investment should make it worth it.




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    #13396 - 04/09/08 09:26 AM Re: Question about algebra and radical acceleratio [Re: bianc850a]
    questions Offline
    Member

    Registered: 11/24/07
    Posts: 864
    bianc850a - I wish DS could go to your DD's school! Lucky DD! btw, in a 6 hr. 20 minute day, DS gets 20 minutes of lunch followed by 20 minutes of recess. I have no idea how long they spend on any one subject each day, and on Mondays, they don't have reading - at all!

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    #13399 - 04/09/08 09:47 AM Re: Question about algebra and radical acceleratio [Re: Dottie]
    bianc850a Offline
    Member

    Registered: 12/02/07
    Posts: 312
    Loc: California
    Dottie,

    Are you sure you cannot be convinced to move to the west coast? We have a family that moved from Korea!

    My point is that there should be one school like my dd's school in every town. I have tried to talk Dottie into starting her own in her living room grin

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    #13400 - 04/09/08 09:49 AM Re: Question about algebra and radical acceleration [Re: Kriston]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Originally Posted By: Kriston
    But WHAT is different? Can you give me a specific example? HOW are they making it conceptual? To be honest, what it sounds like is that they just aren't doing much teaching at all, either of tools or of concepts. Navel-gazing isn't teaching, and that's the impression I'm getting of it (albeit perhaps wrongly).

    I don't call word problems conceptual (and those have always been around anyway). Is there more to it than that?


    Hi Kriston,

    My sons' school uses a spiral system called Everyday Mathematics (EM). These systems are called "Reform Mathemathics." I wrote a letter to the school detailing my ideas about EM's weaknesses. I used specific examples from the books. If anyone wants a copy, PM me and I'll send it.

    Overall, EM has a "spiral" approach that spins from one topic to the next. So in 1st grade they do, say, classical addition for a few days and move to learning shapes. Then they go on "numeracy" which is taught using a grid that looks like a calendar and goes from 1 to 100. Etc. etc. They evertually work back to slightly more advanced classical addition problems and the spiral starts again.

    EM books are wordy and include exercises that ask kids to cut pictures of triangles out of magazines or write the name of the presidents and mottos on various coins.

    They have a limited number of numerical operations. This increased in the 2nd grade book, but all the problems in the 1st half were 1st grade level from what I could tell (entire pages of 8+4, 11+8 etc).


    Critics argue that reform maths systems are superficial and that they don't allow ideas to sink in. Many originally relied heavily on calculators, even in 1st grade. I think the resulting uproar *may* have killed the worst of the calculator stuff. I'm not sure; my kids' school just skips the calculator stuff.

    Google "Math wars" and you'll see what I mean.

    My feeling is that the Reform systems are a swing of the pendulum in the opposite direction from too much rote drilling.

    ALso, EM has a lot of exercises that look mathematical on the surface but really aren't. For example, in grade 1, they cut out a ruler and measure 3 things at home. When they hand in the homework, the teacher has *no way of knowing if the measurements are accurate*. Sure, the parents should have helped, but what if they didn't for some reason or didn't pay close attention?

    Why can't the book just draw a few lines and get the kids to measure the lines? If the goal is to teach them how to measure something, there has to be a way to *assess learning*.

    One of my biggest problems with EM was the number grid approach to addition. This is a twist on counting on a number line, and kids are supposed to "hop" "forward" to add and "backward" to subtract.

    The grid has 10 row of 10 numbers from 1 to 100 (no zero). Because it starts at 1, 10 is on the same line as 1-9 and 20 is on the same line as 11-19, etc. This approach completely fails to show kids that 10, 20, etc. begin new groups of ten. And of course, 100 is on the same line as 91-99.

    Also, I'm not sure why moving across a grid and then down a row to add, say, 8+3, is a better way to teach addition than just using a pile of bingo chips or drawing some circles. Ditto for subtraction, which is less intuitive than addition and requires that you start with a pile of bingo chips (or whatever) and then take something away.

    Also, the grid forces kids to count by ones to add and doesn't TEACH the idea of addition. I think the idea is let them figure it oiut for themselves. But the system is too complicated and many kids can't see the forest for the trees.

    EM makes an assumption that children can understand certain concepts intuitively when they can't. Moving backwards and up a row to do 11-3 is NOT intuitive the way that watching a pile get smaller is.

    So overall, these systems can look attractive to people weary of drill and kill. But they are deceptive and close inspection shows their weaknesses.

    Hope that answers your question?

    Val


    Edited by Val (04/09/08 09:58 AM)

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    #13401 - 04/09/08 09:54 AM Re: Question about algebra and radical acceleratio [Re: incogneato]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Originally Posted By: incogneato
    Math wars hee hee hee

    Please tell me people arent' going to war over this stuff!


    You would not believe the uproard in some areas.

    http://www.mathematicallycorrect.com/

    Val

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    #13403 - 04/09/08 09:56 AM Re: Question about algebra and radical acceleratio [Re: Val]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Okay, sorry to come in so late to all of this! I was teaching yesterday and then had to get my slides ready for a presentation on Friday.

    Val

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    #13405 - 04/09/08 10:34 AM Re: Question about algebra and radical acceleratio [Re: Val]
    incogneato Offline
    Member

    Registered: 10/25/07
    Posts: 2231
    Loc: up in my head.......
    You know when I was a teenager I thought my dad was the biggest idiot in the world. He used to say all kinds of cliche simpleisms like: "Moderation is the key". As I have grown into an adult I realize my dad isn't a simpleton. smile
    He's simply brilliant.
    Such a simple phrase applies beautifully to almost any situation, almost all times.
    I will say I think reform math is actually more intuitive to a certain type of person, but it's not a great learning style for all people, at all times. Also, sometimes you have to use memorization. I think a good teacher is flexible and good at assessing differnt learning styles in the kids. That's the kind of teacher I hope for when my kids are in school.
    And while I'm the first person to say drill and kill is bad for gifted kids, I also think some of the most important scientific breakthroughs have resulted from long, tedious and repetitive processes.
    I'm for balance and moderation.

    Neato

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    #13424 - 04/09/08 01:16 PM Re: Question about algebra and radical acceleratio [Re: incogneato]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    I agree 100%, 'Neato! Variety in teaching styles and methods is so key! Teachers who don't understand that scare me a little...
    _________________________
    Kriston

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    #13425 - 04/09/08 02:10 PM Re: Question about algebra and radical acceleratio [Re: Kriston]
    Val Offline
    Member

    Registered: 09/01/07
    Posts: 3296
    Loc: California
    Variety is the #1 thing for us too. We mix concepts and practice as a rule.

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    #13444 - 04/09/08 08:05 PM Re: Question about algebra and radical acceleratio [Re: Val]
    squirt Offline
    Member

    Registered: 03/31/08
    Posts: 323
    Loc: Back in Texas, alas!
    I read somewhere in some thread about math and "going deeper instead of higher". How do you do that at elementary levels? I mean, adding and subtracting can only go so deep. Then, you pretty much have to move on to bigger numbers and multiplication and division? Or, am I missing something? And, if the school is completely against acceleration, what would be the point of having my son (6.5) do EPGY or another program to challenge him at home? Wouldn't sitting through school math be just that much more boring? He can play Monopoly and be the banker and do all that but sometimes still counts on his fingers to add 3 and 6. He's also showed that he can follow the logic of simple algebraic equations (he can't do the multiplication, but he can tell me the steps).

    What am I missing?

    (Sorry this post got so crotchety - it's been a bad week!)


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    #13446 - 04/09/08 09:05 PM Re: Question about algebra and radical acceleratio [Re: squirt]
    Texas Summer Offline
    Member

    Registered: 05/01/06
    Posts: 216
    Loc: Texas
    Originally Posted By: squirt
    I read somewhere in some thread about math and "going deeper instead of higher". How do you do that at elementary levels?


    Check out Ed Zaccaro's materials.
    http://www.challengemath.com/

    Originally Posted By: squirt
    ...if the school is completely against acceleration, what would be the point of having my son (6.5) do EPGY or another program to challenge him at home? Wouldn't sitting through school math be just that much more boring?


    If your child is gifted in math, he/she will probably already know the math concepts before they are taught regardless of any math enrichment you provide. I have provided minimal math enrichment and my dd knows 95% of the grade level material before it is taught. She learned about multiplication two years before it was taught in school because she asked me a question about it on the way home from school.

    Also, because of the way math spirals, a gifted child can be taught the basics of a concept and extrapolate by herself/himself or ask questions until his/her curiosity is satisfied. My dd learned to tell time by the hour on an analog clock in kindergartern. She wanted to know more than just the hour. The teacher would not instruct her because she was not scheduled to learn more until 1st grade. My dd came home wanting to know more so I explained it to her. She learned the concept in minutes.

    It really doesn't matter whether they learned the material 6 months or 6 years earlier. The process of listening to the teacher explain a known concept to the other students and waiting for the students to learn will still be boring.

    So why provide enrichment at home? One reason is because these kids often beg for it. My dd loves ALEKS and is unhappy with me right now because I didn't renew our subscription. I have been told that the district has purchased a license for my dd (and about 50 other GT students), but it is not ready to be activated yet. Still, my dd asks me about it every few days.

    Also, I believe that children should be engaged or challenged in areas of their strengths especially if this challenge is not provided at school. I personally do not want my dd to spend 5 years not learning any math.

    I find it interesting that we tend to look at math differently than we look at language. Would any of us deny our children the privilege of reading a particular book because they will have to read it again in a higher grade? Math kids hunger to learn more math the same way language kids devour books.

    I recommend providing opportunities and following your child's lead.

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    #13447 - 04/09/08 09:55 PM Re: Question about algebra and radical acceleratio [Re: Texas Summer]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Originally Posted By: Texas Summer
    Would any of us deny our children the privilege of reading a particular book because they will have to read it again in a higher grade?


    Absolutely not...but many schools do. Sad!
    _________________________
    Kriston

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    #13458 - 04/10/08 05:32 AM Re: Question about algebra and radical acceleratio [Re: Kriston]
    incogneato Offline
    Member

    Registered: 10/25/07
    Posts: 2231
    Loc: up in my head.......
    Unfortunately, the only learning the girls have actually been super excited about happens at home. That's fine because I enjoy working with them and we all have a lot of fun.Also, they are getting lots of other things from attending school and at the moment it works well for them.

    Neato

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    #13461 - 04/10/08 05:53 AM Re: Question about algebra and radical acceleratio [Re: incogneato]
    OHGrandma Offline
    Member

    Registered: 01/05/08
    Posts: 830
    Originally Posted By: incogneato
    Unfortunately, the only learning the girls have actually been super excited about happens at home. That's fine because I enjoy working with them and we all have a lot of fun.Also, they are getting lots of other things from attending school and at the moment it works well for them.

    Neato


    Neato, that's happening more and more with GS8. I got a bit rattled when he was accepted in the gifted program for this semester, and I was thinking, "what if he continues to get farther ahead of his classmates?" And I decided I'd deal with it when it became a problem. Then at the beginning of this final quarter he took another reading test which showed he'd gained over a year GE in 1 quarter, putting him at 8.1 GE for reading. And I got rattled again, wondering what we'll do if he continues to get farther ahead. That's when I realized, what we are doing is working! He's getting a lot of other things from school, we have fun after school, and he's learning! It is working well for him, too.


    Edited by OHGrandma (04/10/08 05:54 AM)

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    #13462 - 04/10/08 05:54 AM Re: Question about algebra and radical acceleratio [Re: squirt]
    LMom Offline
    Member

    Registered: 12/14/07
    Posts: 902
    Originally Posted By: squirt
    I read somewhere in some thread about math and "going deeper instead of higher". How do you do that at elementary levels? I mean, adding and subtracting can only go so deep. Then, you pretty much have to move on to bigger numbers and multiplication and division? Or, am I missing something?


    Yes, you need to move on to bigger numbers, multiplication and division. You are completely right, you can get only that far with addition and subtraction. Once you cover multiplication adn division things get more interesting, you can do Zaccaro, you can also look into Singapore Challenging Word Problems (3 and up. I wouldn't really bother with the lower ones).

    You can also do things like Venn Perplexors, I suggest LevelB (3rd-6th grade). You don't even need multiplication or division for this. Kriston, your son may like it.

    Of course we still add new concepts in like prime numbers, addition of fractions, geometry, ... It's pretty much unavoidable, but like I said you can go deep from a certain level and give them problems which will require some effort.
    _________________________
    LMom

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    #13464 - 04/10/08 06:06 AM Re: Question about algebra and radical acceleratio [Re: LMom]
    Kriston Offline
    Member

    Registered: 09/19/07
    Posts: 6145
    Loc: Midwest
    Oooh! I've never heard of Venn Perplexors. I'm hitting Amazon right now. Thanks, LMom!
    _________________________
    Kriston

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    #13467 - 04/10/08 06:23 AM Re: Question about algebra and radical acceleratio [Re: Kriston]
    LMom Offline
    Member

    Registered: 12/14/07
    Posts: 902
    _________________________
    LMom

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    #13550 - 04/11/08 08:46 AM Re: Question about algebra and radical acceleratio [Re: LMom]
    Dazed&Confuzed Offline
    Member

    Registered: 04/05/08
    Posts: 1815
    Yes - now I have Venn Perplexors on my to buy list.

    Thanks for the info!

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    #13561 - 04/11/08 05:27 PM Re: Question about algebra and radical acceleratio [Re: Dazed&Confuzed]
    EandCmom Offline
    Member

    Registered: 11/09/07
    Posts: 516
    Originally Posted By: Dazed&Confuzed
    Yes - now I have Venn Perplexors on my to buy list.


    Our local Hobby Town USA carries lots of these products. I think that is a national chain so if you have one near you, you might check it out before you order and have to pay shipping.

    smile

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    #13569 - 04/11/08 06:25 PM Re: Question about algebra and radical acceleratio [Re: OHGrandma]
    Grinity Offline
    Member

    Registered: 12/13/05
    Posts: 7207
    Loc: Connecticut
    Originally Posted By: OHGrandma

    Neato, that's happening more and more with GS8. I got a bit rattled when he was accepted in the gifted program for this semester, and I was thinking, "what if he continues to get farther ahead of his classmates?" And I decided I'd deal with it when it became a problem. Then at the beginning of this final quarter he took another reading test which showed he'd gained over a year GE in 1 quarter, putting him at 8.1 GE for reading. And I got rattled again, wondering what we'll do if he continues to get farther ahead. That's when I realized, what we are doing is working! He's getting a lot of other things from school, we have fun after school, and he's learning! It is working well for him, too.


    Yippee!!!!
    ((Sun parts the clouds and a ray reaches down to shine on dear OHGrandma's lovely satisfied face!! Flower petals drift to earth and dazzle in the sunlight.))

    I've read (somewhere) that the higher the level of teaching the greater the spread will of achievement will be. I believe this to be true, and hope that this doesn't put folks off of excellent educations. It's not our faults, it's just the nature of things.

    I'm quite sure that every child in my son's school could be far above where they currently are if we individualized education to every child and filled schools with large numbers of folks who loved to learn and teach their particular subjects - not as full time teachers - perhaps as little as 1 hour a day, or through pre-recorded programs or really well designed computer based learning. Or turn every school into a farm where all the learning activities were based on real life problem solving? We just don't know yet, but we will, if we keep looking. And yes, my guess is that the variety of achievements and the variety of achievement levels would increase tremendously.

    Love and More Love,
    Grinity
    _________________________
    Coaching available, at SchoolSuccessSolutions.com

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    #13570 - 04/11/08 06:29 PM Re: Question about algebra and radical acceleratio [Re: LMom]
    aline Offline
    Member

    Registered: 12/13/07
    Posts: 155
    Loc: Southwest
    Ok 'Neato My Dad used to say how good it would be for me to fail at something. Scary thing is, now that I'm a middle-aged parent I understand it...

    aline

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