Math for a Quite Math Whiz Girl (Spy Car and Others ...)

[Ummto4]

This is for my 5 year old girl who is finishing up her home pre-K (5 year 4 months at the moment).

 

She intuitively knows numbers and I only made very little attempt to teach her those things. She knows addition, substraction, number up to 100 (and some in the hundreds and thousands), knows which number is bigger and can order numbers if presented with some numbers (up to 100, for certain), can solve missing addend questions for addition (she understands number bond), and can solve word problems involving addition, substraction and missing addend with ease. I haven't taught her math facts though (or how to switch addition to substraction) so I have no idea whether she knows those things.

 

She's going through the addition chapter of Math Mammoth light blue for first grade at the moment and is doing well. I also get her to play with <, =, and > sign a la MEP math and ask her to make various equation correct. She did these with ease.

 

Considering that she's quite good at math, I'm pretty hesitating in continuing with 1st grade Math Mammoth in her K year. I want a math program which will challenge her conceptually constantly. She was just like me when I was a little girl. I loved logic problems and discovered many math strategy during elementary school on my own (and am now is surprised that S-pore actually uses the same strategy as me !!). I think Math Mammoth will be pretty lame for her (it suits my son v. well though).

 

I'm intrigued with MEP and Miquon. How do you combine both ? Or is it better to just do either MEP or Miquon ? Which one is better, MEP or Miquon ?

 

As for computational drill, I also have RS and know how to teach using RS when it gets to regrouping (like 7 + 5). Or to teach regoruping like S-pore math (Math Mammoth does this, too, by the way).

 

So help help help !!!

 

Thanks

[Ummto4]

Update:

 

Turns out my daughter can also do substraction with missing addend, e.g.

5-__=2, or __-1=4. She is a bit slow on computation, but she knows that conceptually. I never taught her this, I just asked her a few minutes ago out of curiosity.

 

So ... please help me which math book and level she should start.

 

Miquon or MEP or both ?

 

Thanks

[Ummto4]

bump

[Spy Car]

I think I'd lean toward MEP, or MEP and Singapore at this point.

 

Bill

[herbalgirl]

I'd choose Singapore. :)

[Ummto4]

Thanks Bill, I'll try MEP w/ her for her K this fall.

[FO4UR]

I vote MEP for your main math, but Miquon is sure handy to have on the shelf. ;)

[Ummto4]

How do you balance the conceptual vs computation aspect of math ? She's still slow in computation because of lack of practice, but understands the concept well. By using card math games for drills frequently ?

 

I think I'm going to do MEP with her next year. But other poster and Bill suggest S-pore. Which grade then ? 1B ?

 

Thanks

[Spy Car]

Thanks Bill, I'll try MEP w/ her for her K this fall.

 

One thing I might do (and it sounds like you've already though of this) is to add-in Singapore style "number bonds" so she does both that way and as in MEP:

4 <3 7

 

Singapore:

...7

..^

3....4

 

I cross-pollinate these two different, but essentially the same, ways of saying the same thing. And the "number bonds" strike me as somewhat handier. Especially when building number bond trees, or showing how to regroup the addition of two numbers.

[Spy Car]

How do you balance the conceptual vs computation aspect of math ? She's still slow in computation because of lack of practice, but understands the concept well. By using card math games for drills frequently ?

 

I think I'm going to do MEP with her next year. But other poster and Bill suggest S-pore. Which grade then ? 1B ?

 

Thanks

 

To sharpen the ability to have math facts "at hand" I'm liking the RS games rather than "drill". But I still like to talk or work these through with him to make sure he can explain how he gets the answer, so it's not just "memorizing".

 

Bill

[FO4UR]

We like the RS games too. :iagree:

 

Another way I drill is to give ds a C.Rod and graph paper, and then have him color every "way to make the rod" So, if I give him an orange rod, he'll color 10+0, 9+1, 8+2........ My ds *sees* those rods in his head, so this is very effective for him. PLUS, he gets to color on graph paper and that's just fun for him.:) PLUS, it translates easily to 10-9=1......and the number bond concept.

[8filltheheart]

You might want to look at Kitchen Table Math recommended on the Art of Problems Solving site.

http://www.artofproblemsolving.com/Books/AoPS_B_Rec_Elem.php

 

I have several advanced math students and one significantly advanced math student. We spend hrs playing strategy games and cards, not necessarily strictly focusing on math. A large part of problem solving is strategy. :)

 

For retention of math facts, you might want to look at a workbook text like Horizons that move fairly quickly but with decent amts of review. Based on your description, she might be ready for Horizons 1.

[Heather in VA]

As far as balancing computation and concepts - I don't "drill" math facts until much later. Right now focus on making sure she understands what she's doing and what it all means. If she's anything like my middle dd who is very math intuitive, she'll just memorize the facts along the way. If she doesn't - then in a couple of years spend a couple of weeks solidifying the facts and she'll be fine. I much prefer that to drilling now and finding out they just memorized the facts and don't really understand.

 

Heather

[Spy Car]

As far as balancing computation and concepts - I don't "drill" math facts until much later. Right now focus on making sure she understands what she's doing and what it all means. If she's anything like my middle dd who is very math intuitive, she'll just memorize the facts along the way. If she doesn't - then in a couple of years spend a couple of weeks solidifying the facts and she'll be fine. I much prefer that to drilling now and finding out they just memorized the facts and don't really understand.

 

Heather

 

:iagree: I'm with you on this.

 

I would make one refinement. To me "computation" is applying a concept to arrive at a solution, as opposed to having a solution "memorized" which (to my mind) isn't "computation" but rather application of rote-memory.

 

Not that application of rote-memory isn't valuable or utilitarian in a number of situations, including testing. But is it "computation"? I don't think so. What say you all?

 

Bill

[Heather in VA]

:iagree: I'm with you on this.

 

I would make one refinement. To me "computation" is applying a concept to arrive at a solution, as opposed to having a solution "memorized" which (to my mind) isn't "computation" but rather application of rote-memory.

 

Not that application of rote-memory isn't valuable or utilitarian in a number of situations, including testing. But is it "computation"? I don't think so. What say you all?

 

Bill

 

 

That is true. Usually when I hear people on this board discussing concept vs computation they are talking about math facts and how to drill them so they are fast. To me that is the least important feature of young math. But looking at computation as application of a concept - then I definately do that all the time in the younger years.

 

Heather

[Spy Car]

That is true. Usually when I hear people on this board discussing concept vs computation they are talking about math facts and how to drill them so they are fast. To me that is the least important feature of young math. But looking at computation as application of a concept - then I definately do that all the time in the younger years.

 

Heather

 

I think your perception is correct, that "computation" and "memorizing" math facts are used interchangeably.

 

This seems strange to me, especially on a board if one took the same approach to reading (i.e. memorizing sight words) one would be roundly castigated :tongue_smilie:

 

And I see phonics vs sight words as pretty analogous to (true) computation vs math-fact memorization. I'm sure we agree :D

 

Bill

[HappyGrace]

Funny, I've been lately mulling over this same interesting computation/memorization issue in my head about ds6. He is advanced in math concept-wise. But then when I watch him do a single digit +/- problem, he does it pretty quickly, but he is still computing-doesn't have it memorized. That marginally longer time it takes to compute it frustrates him in more advanced problems, so I can see the benefit of actually having it memorized. (Now that he knows how to "compute") Just like if you had to stop to figure out the word "was" every time you read it-you could do it, you have the skills, but it would take just enough longer to be frustrating; having it memorized would solve that! LOVE the sight-reading/phonics example. I think that good readers, once they know phonics, do actually look at many words as "sight words"-I just recently read something to this effect, but I don't know where.

[Ali in OR]

But then when I watch him do a single digit +/- problem, he does it pretty quickly, but he is still computing-doesn't have it memorized. That marginally longer time it takes to compute it frustrates him in more advanced problems, so I can see the benefit of actually having it memorized.

 

Yes, exactly. At some point you do need to make sure math facts can be recalled instantly. I had students in Algebra who couldn't divide both sides of an equation by 3 without using a calculator. Their difficulty with basic calculations very much hampered their ability to really learn Algebra and enjoy it. So when to drill? I want my kids to add, subtract, multiply, and do simple division with facility before tackling the long division algorithm. This comes up in 3A in Singapore, so second grade and first part of 3rd grade is a good time to drill in facts if they haven't already got them down well by then. As I think about it, I'm going to want my 6 yo to know number bonds up to and including 10 well before tackling how to make a 10 in 1A (used to add say 8 + 6). That's actually a multi-step algorithm. You don't want to be counting fingers to think what number you need--you want pretty quick recall. So I would argue that there is room for some drill in first grade. Drill is not a long arduous process here--just a quick run through flash cards or some problems on a white board before our math lesson. Nothing too painful.

[Spy Car]

Funny, I've been lately mulling over this same interesting computation/memorization issue in my head about ds6. He is advanced in math concept-wise. But then when I watch him do a single digit +/- problem, he does it pretty quickly, but he is still computing-doesn't have it memorized. That marginally longer time it takes to compute it frustrates him in more advanced problems, so I can see the benefit of actually having it memorized. (Now that he knows how to "compute") Just like if you had to stop to figure out the word "was" every time you read it-you could do it, you have the skills, but it would take just enough longer to be frustrating; having it memorized would solve that! LOVE the sight-reading/phonics example. I think that good readers, once they know phonics, do actually look at many words as "sight words"-I just recently read something to this effect, but I don't know where.

 

I think you've stated this brilliantly!

 

We all want to get our children where they read fluently (without sounding out every word phonetically) and also don't have to "compute" every math fact to solve an equation. It's just how one gets there, and what "balances" one strikes in teaching.

 

It makes me happy in some ways when my almost 5 year old reads a sentence fluently, rather than sounding out every letter or blend. But it does make me suspicious that me may just be "memorizing" words. So I do a "rear-guard" action, to ensure the phonics don't get missed.

 

Same with the addition facts. I love that 7 + 6 is "instantaneous", but we've also modeled this repeatedly with number bonds, C Rods, abacus, etc. So I now it's not empty knowledge.

 

Recently he "learned" from a coop friend that 9 X 9 = 81. It's a good "parlor trick" to ask him, as the unwary are impressed. But I know unless he can explain this, or model it, it means almost nothing.

 

I'm for getting to reading fluency, and math-fact "fluency". I just don't want to miss a step. And with math, quite unlike reading and phonics, this lesson does not seemed to be as widely embraced as I would expect.

 

Bill

[Ummto4]

I just had a look closely at Y1 MEP, and I think it looks good in striking the balance between computation and concept. I reckon we will spend a good 4-5 months on mastering the concept and computation of 1-10 the MEP-way.

 

May be I should get my 1st-soon -to-be-2nd grader to do select problem of Y1 MEP for number 1-10 during summer as well.

 

By the way, I'm curious as to whether MEP teaches strategy for adding or substracting numbers which needs regrouping, like : 9+9, or 18-9. It looks like the book plays with teens number, but I'm not sure whether it actually teaches strategy.

 

Any input ?

[Spy Car]

By the way, I'm curious as to whether MEP teaches strategy for adding or substracting numbers which needs regrouping, like : 9+9, or 18-9. It looks like the book plays with teens number, but I'm not sure whether it actually teaches strategy.

 

Any input ?

 

It's a great question. And one I don't have an answer for (not being there yet in MEP). I have to think "of course they do" but have to admit I don't know what it is. Where I do understand (and have implemented) the strategy from Singapore. Hmm.

 

Reinforces my feeling that it's good to do two (or more) complementary math programs, and means I'm likely going to spend the "holiday weekend" reading ahead in MEP. Thanks a lot :D

 

Bill

[HappyGrace]

Mom2moon2-see that's where we got messed up in MEP yr 1-ds6 needs to solidify those math facts, but is bored with MEP1 because he wants the challenge conceptually. That's why I'm thinking about the RS math games to do the facts, then jump into MEP yr2 for the conceptual in the fall (along with Singapore.) Of course, with one so young, you'd stick with MEP yr 1. But you might find yourself at this same point that I'm at in several months, so it's something to keep in mind.

 

So I can't tell you the answer about that strategy because we stopped partway through MEP1. I know Singapore does this, so does RS.

 

On that note, I am warning you that with a bright child in math, it may be worth pulling from a couple different math programs. That way when you hit a wall on something, you can move laterally with the other program for awhile before moving forward. This is important because many of the conceptual type math programs move fairly quickly-Singapore, RS, MEP. They make mental jumps that may be a stretch conceptually sometimes. So there will be times when you need to just stop and park somewhere for awhile, and having another math program to pull from is very helpful at those times. (This was a BIG thing with older dd that I did NOT understand-we kept plugging and she got lost and frustrated and hates math now.) Or use the other program to show a different way of doing the same thing, which math-advanced students often appreciate. Or it would enable you to move forward more quickly than just plugging away through one program, because you can telescope aspects of both programs, make sure they've got it from a couple different angles, and move on.

We pull from several sources, including the Living Math site, for a well-rounded math picture. I made so many mistakes with first dd; determined to correct it with ds!

Edited July 3, 2009 by HappyGrace

[HappyGrace]

Yes, Ali-that's what ds is doing-he's computing: to do 8+6 it takes him a second extra to think, "take 2 from the six to make 10, then add 10 and 4". And that frustrates him and makes three-digit addition have even MORE steps than it would have if he just KNEW that 8+6=14. So that's why I'm thinking the automation of those facts is almost necessary to help him move on. Thanks for the confirmation!

[Spy Car]

Mom2moon2-see that's where we got messed up in MEP yr 1-ds6 needs to solidify those math facts, but is bored with MEP1 because he wants the challenge conceptually. That's why I'm thinking about the RS math games to do the facts, then jump into MEP yr2 for the conceptual in the fall (along with Singapore.) Of course, with one so young, you'd stick with MEP yr 1. But you might find yourself at this same point that I'm at in several months, so it's something to keep in mind.

 

So I can't tell you the answer about that strategy because we stopped partway through MEP1. I know Singapore does this, so does RS.

 

On that note, I am warning you that with a bright child in math, it may be worth pulling from a couple different math programs. That way when you hit a wall on something, you can move laterally with the other program for awhile before moving forward. This is important because many of the conceptual type math programs move fairly quickly-Singapore, RS, MEP. They make mental jumps that may be a stretch conceptually sometimes. So there will be times when you need to just stop and park somewhere for awhile, and having another math program to pull from is very helpful at those times. (This was a BIG thing with older dd that I did NOT understand-we kept plugging and she got lost and frustrated and hates math now.) Or use the other program to show a different way of doing the same thing, which math-advanced students often appreciate. Or it would enable you to move forward more quickly than just plugging away through one program, because you can telescope aspects of both programs, make sure they've got it from a couple different angles, and move on.

We pull from several sources, including the Living Math site, for a well-rounded math picture. I made so many mistakes with first dd; determined to correct it with ds!

 

Sage advice.

[HappyGrace]

I was just rereading your OP, and it seems to me that since you have the programs, the best thing you could do is to read it all ahead *yourself*, maybe even including the Singapore HIGs, if you can swing it to get them. Then when you come up to a certain thing in, say, Miquon, you have the tools in *your* toolbox to be able to present it a couple different ways, like the RS way or the Singapore way.

 

I would probably just pick one to use as a spine, and then read through and pull from the others as needed. I think I learned the most by just reading through all the programs myself. It sounds like you are doing this already!

[Spy Car]

I was just rereading your OP, and it seems to me that since you have the programs, the best thing you could do is to read it all ahead *yourself*, maybe even including the Singapore HIGs, if you can swing it to get them. Then when you come up to a certain thing in, say, Miquon, you have the tools in *your* toolbox to be able to present it a couple different ways, like the RS way or the Singapore way.

 

I would probably just pick one to use as a spine, and then read through and pull from the others as needed. I think I learned the most by just reading through all the programs myself. It sounds like you are doing this already!

 

It has sure been helpful to me in our short math journey to be able to pull on different methods, or to let one "rest" as you mention when we hit a wall.

 

I like having different ways to teach the same basic concept, as one never knows which explanation (or combination of explainations) if going to be the one that clicks. And the value of having material to work on when one program suddenly gets too difficult.

 

Yep. My thinking is like yours.

 

Bill

[Ummto4]

I'm quite a math junkie. I have RS, Math Mammoth (perfect for my son who needs comfortable pace), Math on The Level ... and of course MEP.... :blushing::blushing: I'm quite familiar with the S-pore technique since Math Mammoth also teaches the same thing, and that's also the very technique I discovered on my own back when I was at elementary school.

 

May be for teens and regroup I won't use MEP Y1 - may be I'll use RS or Math Mammoth to cement the substraction / addition-over-10 strategy when dd is 1st grade.

 

For my dd's K year (this fall), I'll limit to MEP Y1 (all the math facts and number connection for <10) and working with 2-digit number with no regrouping, and of course clock, money, measurement, etc, if my dd is up to it. Who knows ?

 

My older son (non math whiz) found it easier to do the mental 2-digit- number computation (with no regrouping) than doing the teen regrouping. So I'll do the teen stuff next year when he's at the second grade. I guess teen regrouping needs more conceptual understanding than 2-digit number calculation with no regrouping. Sigh sigh .. .. live, learn, and teach.