Why don't C rods have lines?

[cottonmama]

I'm this close to getting some Cuisenaire rods. I know many folks have found C rods really useful, but I feel like I need to understand them before I go out and get some. I'm just lost as to how they are useful for mathematical thinking.

 

What I just don't get is why they have no lines to indicate which value the rod represents. Yes, the child memorizes that orange is 10, blues is 9, etc. -- but it seems like this is teaching the child that ten is a Thing, and nine is a different Thing, and so forth, and that as such the numbers are all separate entities, black boxes that aren't composed of anything. Without the lines, the rods seem to promote that the relationship between numbers is side-by-side comparison rather than composition. This also seems to promote numbers as things to memorize rather than things to understand.

 

I also wonder how this is a useful visualization tool later on... how is the child going to have an accurate mental image of something 6cm (or at least the relationship between something 6cm and something 2cm)?

 

Why do people like C rods so much more than unit blocks or other manipulatives? How exactly are they able to help a child's mathematical thinking?

[bluechicken]

We have these and there are lines on them.

 

http://rainbowresource.com/product/sku/024116/17dfd6f6fa2836c27eb3ee50

 

I really like them and we use them a lot.

[HiddenJewel]

I'm guessing part of it is so the student gets used to seeing the number as a whole unit instead of a bunch of ones.

[blondeviolin]

There no lines or scoring because it lowers the ability to think of a rod different than the white rod as one. For example, if we think of the orange rod as one, then the yellow is 1/2, the red rod is 1/5, and the white rod 1/10. If you think of the white rod as 5, then the yellow rod becomes 25 and the orange 50.

 

C rods have really helped my daughter be able to concretely understand WHY 5+2+3 is the same as 10 and the same as 7+3 and 8+2. You can use c rods to demonstrate all sorts of mathematical theorems and properties in a concrete way. My daughter does not think of 7 as just an abstract number we count to, but rather as a group that can be broken down into parts (5&2, 4&3, 6&1, 3&2&2, etc). Within 4 weeks, my 5yo daughter can easily solve many addition and subtraction problems in her head, and ones she can't, she has a means to solve it quickly and easily. And at this point I wouldn't call her particularly mathy.

[Sevilla]

Because you want the child to see the numbers as groups and not compositions. If my DS looks at his color coded abacus, he sees the group of 5 blues or 5 yellows as '5' without having to count the beads. Same goes for a row of ten (or an individual bead representing 10 or 100). Crods do the same thing.

 

You view quantities in comparisoin to other quantities, and it adds a different sense of spatial/visual master of the subject that is hard to explain (for me). I have found that Crods engage a different part of my brain and make me think differently about math than looking at a number line or counting individual manipulatives.

[Jay3fer]

I am always astonished at how fast my dd6 can calculate with rods - I mean AT A GLANCE. And she is not a prodigy or math whiz by any means - good, solid average. But with rods, she's a superhero. My theory is that they work in a different part of the brain and, yes, they work in a way that COUNTING does not. Counting slows us down. Counting is a very inefficient way to do math. So I think the lines are not there for that reason.

I actually just blogged about it, in fact... we don't use them all the time anymore, but we just did a lesson in area today, and they were VERY helpful and fun! If you click that link, you can also click the "Cuisenaire Rods" tag to see some of other explorations with rods.

 

BTW, I know that Cuisenaire DOES make linking rods, but because of the divot on the end and the line markings, I don't imagine these look and act the same as plain rods. Plus, I love the feel and sound of wood... :-)

Edited September 20, 2011 by Jay3fer

[chepyl]

There no lines or scoring because it lowers the ability to think of a rod different than the white rod as one. For example, if we think of the orange rod as one, then the yellow is 1/2, the red rod is 1/5, and the white rod 1/10. If you think of the white rod as 5, then the yellow rod becomes 25 and the orange 50.

 

C rods have really helped my daughter be able to concretely understand WHY 5+2+3 is the same as 10 and the same as 7+3 and 8+2. You can use c rods to demonstrate all sorts of mathematical theorems and properties in a concrete way. My daughter does not think of 7 as just an abstract number we count to, but rather as a group that can be broken down into parts (5&2, 4&3, 6&1, 3&2&2, etc). Within 4 weeks, my 5yo daughter can easily solve many addition and subtraction problems in her head, and ones she can't, she has a means to solve it quickly and easily. And at this point I wouldn't call her particularly mathy.

 

My son understands all of these concepts and he did use unit manipulatives. We have an old set of Mortensen Math manipulatives. They are color coded AND they have unit markers. You can demonstrate fractions just as easily.

 

One of the first exercises with the unit pieces was to match the colors to the numbers. There are puzzle trays and an addition/subtraction tray that bases all of the addition and subtraction on how the numbers relate to 10. It really helped his mental math. He really dislikes manipulatives for doing math now, but we had a month or so where he really played with them. He can regroup numbers in his head to make addition and subtraction easier to do without paper. We did also manage to use them long enough to demo addition and subtraction pretty well. I make him look at them for multiplication now.

 

Some people are adamant about not having the lines on them. I would say that most of the reasons given, I saw my kids do with the divided sets as well. They build, they compare, they regroup; if you are unsure, get something you are comfortable using. I never used a C-Rod in my life and made excellent grades in high school and college calculus. Until I got out of college, I could do anything with paper and pencil (no calculator), now I am a bit lazy. ;) Just saying, if you want lines; get something with lines.

[RootAnn]

C rods have really helped my daughter be able to concretely understand WHY 5+2+3 is the same as 10 and the same as 7+3 and 8+2. You can use c rods to demonstrate all sorts of mathematical theorems and properties in a concrete way. My daughter does not think of 7 as just an abstract number we count to, but rather as a group that can be broken down into parts (5&2, 4&3, 6&1, 3&2&2, etc). Within 4 weeks, my 5yo daughter can easily solve many addition and subtraction problems in her head, and ones she can't, she has a means to solve it quickly and easily. And at this point I wouldn't call her particularly mathy.

:iagree:

My dd#3 is the first I've ever used a Miquon-approach to math with. Her dad & I are continually amazed at the mental leaps & the math concepts she grasps already.

 

BTW, she doesn't have the color-number correlation memorized. She does understand "greater than," "less than," "equal to," "commutative property," etc.

[cottonmama]

Thanks for all your answers! I'm starting to think that maybe we should go with C rods that have lines on them. Are there any wood ones that have lines on them? Or does anyone still want to talk me out of doing the lined ones? ;)

[blondeviolin]

My son understands all of these concepts and he did use unit manipulatives. We have an old set of Mortensen Math manipulatives. They are color coded AND they have unit markers. You can demonstrate fractions just as easily.

 

One of the first exercises with the unit pieces was to match the colors to the numbers. There are puzzle trays and an addition/subtraction tray that bases all of the addition and subtraction on how the numbers relate to 10. It really helped his mental math. He really dislikes manipulatives for doing math now, but we had a month or so where he really played with them. He can regroup numbers in his head to make addition and subtraction easier to do without paper. We did also manage to use them long enough to demo addition and subtraction pretty well. I make him look at them for multiplication now.

 

Some people are adamant about not having the lines on them. I would say that most of the reasons given, I saw my kids do with the divided sets as well. They build, they compare, they regroup; if you are unsure, get something you are comfortable using. I never used a C-Rod in my life and made excellent grades in high school and college calculus. Until I got out of college, I could do anything with paper and pencil (no calculator), now I am a bit lazy. ;) Just saying, if you want lines; get something with lines.

 

Oh, there's no question that some kids can understand all such things WITHOUT rods. I had never touched a c rod until I bought them for Abby. BUT, I think they fill a space for those who are not particularly mathy. I LOVE math and manipulating numbers in my head. My daughter is not mathy, but I believe she is making leaps some that wouldn't happen for months or YEARS because of them. My husband didn't use rods growing up, but likes math (though he says he's nowhere near the math nerd I am). He has lamented several times that he didn't do math like my daughter does.

 

But, that's just been our (limited) experience with them...ymmv. :D

[Spy Car]

Thanks for all your answers! I'm starting to think that maybe we should go with C rods that have lines on them. Are there any wood ones that have lines on them? Or does anyone still want to talk me out of doing the lined ones? ;)

 

No you should not. They defeat the purpose, and are not Cuisenaire Rods (no matter what company may claim otherwise). Don't do it!

 

Bill

[Alte Veste Academy]

No you should not. They defeat the purpose, and are not Cuisenaire Rods (no matter what company may claim otherwise). Don't do it!

 

Bill

 

Come on, Bill. You know she's going to have to ask why. I'll save you some trouble.

 

OP, start on post 18 of this thread for a full-on discussion of lines or no-lines on Cuisinaire Rods. I'm still scarred by this conversation. :lol:

[cottonmama]

Okay, I read the other thread and still have my doubts. :tongue_smilie:

 

First of all, I'm totally on-board with teaching my kids grouping rather than counting. I've made up a deck of cards like Bill described here, and we'll use them for some games I am trying to put together. I am also planning to paint our Ikea abacus to look like the RS abacus.

 

I also don't like the "nipple" on the end of the linking C rods. I agree that that confuses things. I am at the point where I'll probably just draw lines on some wood ones to avoid that.

 

I'm just not convinced that having lines on the rods forces counting. I thought we were trying to train the child to see a group of five things as "five," and a group of seven things as "five and two," which is "seven." But an unlined rod isn't illuminating that at all. Its only relationship with the number it represents is its length, and you can't see the units that cause it to be that number. There are not seven units to group together into five and two in a black rod. I just don't see how a black, unlined rod provides the child with a visualization of what "seven" means.

 

But, people (okay, I mostly just mean Bill :lol:) are so loyal to the original un-lined C rods that I am willing to be talked off my lined-Crod cliff...

[ktgrok]

I'm just not convinced that having lines on the rods forces counting. I thought we were trying to train the child to see a group of five things as "five," and a group of seven things as "five and two," which is "seven."

But, people (okay, I mostly just mean Bill :lol:) are so loyal to the original un-lined C rods that I am willing to be talked off my lined-Crod cliff...

 

But as someone else said, you might be using that rod to represent 25, or 1/2. The lines would be confusing then, right?

[Susie in MS]

Okay, I read the other thread and still have my doubts. :tongue_smilie:

 

First of all, I'm totally on-board with teaching my kids grouping rather than counting. I've made up a deck of cards like Bill described here, and we'll use them for some games I am trying to put together. I am also planning to paint our Ikea abacus to look like the RS abacus.

 

I also don't like the "nipple" on the end of the linking C rods. I agree that that confuses things. I am at the point where I'll probably just draw lines on some wood ones to avoid that.

 

I'm just not convinced that having lines on the rods forces counting. I thought we were trying to train the child to see a group of five things as "five," and a group of seven things as "five and two," which is "seven." But an unlined rod isn't illuminating that at all. Its only relationship with the number it represents is its length, and you can't see the units that cause it to be that number. There are not seven units to group together into five and two in a black rod. I just don't see how a black, unlined rod provides the child with a visualization of what "seven" means.

 

But, people (okay, I mostly just mean Bill :lol:) are so loyal to the original un-lined C rods that I am willing to be talked off my lined-Crod cliff...

 

Lined rods work for us. My dd can SEE 5 of something instead of 1 colored rod. It is just like using counters, which I have no problem with. The child is able to understand the concept of 7 or 10. I find the lined rods are good for teaching 10s place value.

[Spy Car]

 

But, people (okay, I mostly just mean Bill :lol:) are so loyal to the original un-lined C rods that I am willing to be talked off my lined-Crod cliff...

 

What's it going to take? :D

 

The kids don't need them....trust me.

 

Step back from the abyss :tongue_smilie:

 

Bill

[chepyl]

No you should not. They defeat the purpose, and are not Cuisenaire Rods (no matter what company may claim otherwise). Don't do it!

 

Bill

 

I did read the whole other thread and am still not convinced. DS does not count. He regroups numbers in his head for mental math:

 

7+9

He makes 9, 6+3, adds 3+7, adds 10+6, gets 16. He does this fairly quickly.

 

We did not use anything claiming to be c-rods. We used Mortensen Math blocks and the old smiley face series. At 4, in a few short, fun lessons ds was adding 3 digit numbers. AND understanding.

[boscopup]

My first was like this (I used base ten blocks which were lined). Now with my second he wants to count everything. Although, the other day I asked him to show me various numbers with the non lined c-rods and he had no problem with it. So I don't know what to make of that.

 

My middle son would want to count everything as well. With the non-lined c-rods, he just knows the number. He doesn't know that 6+4=10 yet, but if you put a 6 rod next to a 10 rod and ask him to find the missing piece, he'll immediately pick up the 4 rod. Note that I haven't used color names here because *I* don't remember the color/number correspondence yet. My 4 year old and my 7 year old, neither of which have had more than one or two lessons with using c-rods, both know which is which very easily... without having to count. ;)

 

I'm glad I have the non-lined ones. I don't think the lines are necessary. I also have base 10 blocks if we do need lines for something.

[zenjenn]

Somewhat a spinoff on this topic.. I have been toying with the idea of getting these.

 

Is the big expensive $70 set advantageous to have or is the $14 "intro" set sufficient?

 

This is primarily for my older child (9 yr old), mild dyslexia, who doing great with math concepts but still has trouble with mental hiccups when it comes to computation. I am thinking maybe something that helps her compute visually/conceptually might be worth trying.

Edited September 21, 2011 by zenjenn

[Spy Car]

My middle son would want to count everything as well. With the non-lined c-rods, he just knows the number. He doesn't know that 6+4=10 yet, but if you put a 6 rod next to a 10 rod and ask him to find the missing piece, he'll immediately pick up the 4 rod. Note that I haven't used color names here because *I* don't remember the color/number correspondence yet. My 4 year old and my 7 year old, neither of which have had more than one or two lessons with using c-rods, both know which is which very easily... without having to count. ;)

 

I'm glad I have the non-lined ones. I don't think the lines are necessary. I also have base 10 blocks if we do need lines for something.

 

Children are learning animals. As you say, it takes no time for a young person to see a 6 cm rod and a 4 cm rod together are the same length as a 10 cm rod.

 

They get that right away. Conserving value by length is a great way of understanding values in a young mind. Adding "counters" may (or may not) undermine the mental process and lead to "counting."

 

Speaking generally:

 

Adults, I'm afraid, sometimes impose their own fears and anxieties on their children. If it is not as easy for the adult-mind to pick-up the value of the rods as it is for the child then just play with the children and the rods and have them teach you. It won't be the last time they will need to teach you things :D

 

Bill

Edited September 21, 2011 by Spy Car

[cottonmama]

I've been thinking about this entirely too much for the last few days, but anyway I wanted to share some thoughts here since in the end we did decide to use regular old unlined C-rods, and I thought others who are trying to understand this might be struggling with the same things my husband and I were.

 

The thing we didn't like at first about what C-rods do is that they have the child using groupings that he didn't create, and that he can't even see. I don't doubt all of you who say your dc can do addition and subtraction with them really early, but I just wondered how much they understood of what they were doing. One of the worst situations a math student can be in is that of being able to follow all the algorithms without understanding what they are doing. C-rods looked like this to me at first.

 

But my husband made a good point... later in math, we sometimes let the students do easy problems but tell them to solve it the hard way, and an older student will (usually) have the self-control to refrain from doing the problem the easy way, and by doing it the hard way, he will learn the more advanced skill we are trying to teach. But a young child can't "turn off" the easy solution of counting, so we take away the lines entirely. So with C-rods, instead of being tempted to count to eight when we are adding three and five, the child is forced to learn that adding a three-group to a five-group results in an eight-group.

 

The other thing I was missing was how C-rods teach grouping skills rather than just avoiding interfering with grouping skills. And I think the answer is that there are two major grouping skills: the first is creating groups from "ones", e.g. by seeing three separate items as "three," and the second assembling those groups into larger groups, i.e. seeing that a three-group and a five-group make an eight-group.

 

C-rods are mainly focused on the latter of these two skills, and that is clearly the more advanced skill. By isolating the skill of assembling smaller groups to create larger groups, without requiring the child to create the smaller groups (because the smaller groups are provided to the student ready-made), the rods let the child spend his time practicing the more advanced grouping skill. It is assumed that the child will not have trouble with the first skill (grouping "ones").

 

Technically a child can use C-rods to practice grouping ones, but the point is for them to skip that step most of the time.

 

Phew. I feel better now.

 

ETA: I'm honestly not sure I addressed my initial complaint about how much the child understands of what he's doing. I guess the point is that we're isolating skills for him to practice, so it is valuable even before he makes the connection between what he's doing and the numbers the rods represent. Eventually he will make that connection... it's not like it's that huge a leap for the child to make to see that the black box that we call "seven" really represents seven things assembled together....

Edited September 22, 2011 by cottonmama

[Spy Car]

I've been thinking about this entirely too much for the last few days, but anyway I wanted to share some thoughts here since in the end we did decide to use regular old unlined C-rods, and I thought others who are trying to understand this might be struggling with the same things my husband and I were.

 

The thing we didn't like at first about what C-rods do is that they have the child using groupings that he didn't create, and that he can't even see. I don't doubt all of you who say your dc can do addition and subtraction with them really early, but I just wondered how much they understood of what they were doing. One of the worst situations a math student can be in is that of being able to follow all the algorithms without understanding what they are doing. C-rods looked like this to me at first.

 

But my husband made a good point... later in math, we sometimes let the students do easy problems but tell them to solve it the hard way, and an older student will (usually) have the self-control to refrain from doing the problem the easy way, and by doing it the hard way, he will learn the more advanced skill we are trying to teach. But a young child can't "turn off" the easy solution of counting, so we take away the lines entirely. So with C-rods, instead of being tempted to count to eight when we are adding three and five, the child is forced to learn that adding a three-group to a five-group results in an eight-group.

 

The other thing I was missing was how C-rods teach grouping skills rather than just avoiding interfering with grouping skills. And I think the answer is that there are two major grouping skills: the first is creating groups from "ones", e.g. by seeing three separate items as "three," and the second assembling those groups into larger groups, i.e. seeing that a three-group and a five-group make an eight-group.

 

C-rods are mainly focused on the latter of these two skills, and that is clearly the more advanced skill. By isolating the skill of assembling smaller groups to create larger groups, without requiring the child to create the smaller groups (because the smaller groups are provided to the student ready-made), the rods let the child spend his time practicing the more advanced grouping skill. It is assumed that the child will not have trouble with the first skill (grouping "ones").

 

Technically a child can use C-rods to practice grouping ones, but the point is for them to skip that step most of the time.

 

Phew. I feel better now.

 

Hallelujah, you've seen the light! :D

 

Good analysis BTW, It took you a while, but in the end.....

 

Please give your husband a hug from me :tongue_smilie:

 

Bill

 

ETA: I'm honestly not sure I addressed my initial complaint about how much the child understands of what he's doing. I guess the point is that we're isolating skills for him to practice, so it is valuable even before he makes the connection between what he's doing and the numbers the rods represent. Eventually he will make that connection... it's not like it's that huge a leap for the child to make to see that the black box that we call "seven" really represents seven things assembled together....

 

In my experience they are best way to help a young child understand what they are doing. When they can solve equations themselves they develop competence and autonomy and this makes math a fun and comprehensible subject. Be prepared that they may want more "math" (of a "thinking" variety) than you were prepared for ;)

 

It is good that you are taking all this so seriously. Believe me, you have a kindred spirit here who has the same issues and concerns you have.

 

Have fun!

 

Bill

[kristinannie]

To the PP who asked about how many Crods to get, I suggest the classroom size. I bought the intro set and ended up ordering more later. My son uses them as blocks and builds things. I cannot even tell you how much math he is learned just from playing with the rods. The other day we were driving and he just blurted out, "Mommy, if you have 2 8's and you want 20, you need a 4." I love rods.

 

Oh, and good decision getting the unlined rods! You can teach fractions with rods and definitely wouldn't want the lines. Kids don't need them either. Just have them line them up as a staircase at the beginning of each section. They will learn the colors and what they equal way faster than you will!!! ;)

[FO4UR]

If your child has enough experience *playing* with the C rods before you begin math work, this is all a non-issue.;)

 

 

They will know the values of the rods, even if they don't have the vocabulary to verbalize it. You can then give them the vocabulary and really get to work. (They should do plenty of finding the values with white rods at first.)

 

Play with the C rods!!! Leave them accessible. Let your dc make a big mess of C rods & match box cars & Polly Pockets & etc... They will know that yellow and red = black long before you pull out the Lab Sheets....they will know yellow = 1/2 of orange...they will know 3x light green = blue....etc etc etc. All that leaves for you to do is give these things a vocabulary and show them how to express it on paper.

 

 

I think, for some, the failure of Miquon is trying to go from abstract to concrete...when the whole point is to go from concrete to abstract.

[LittleIzumi]

If your child has enough experience *playing* with the C rods before you begin math work, this is all a non-issue.;)

 

 

They will know the values of the rods, even if they don't have the vocabulary to verbalize it. You can then give them the vocabulary and really get to work. (They should do plenty of finding the values with white rods at first.)

 

Play with the C rods!!! Leave them accessible. Let your dc make a big mess of C rods & match box cars & Polly Pockets & etc... They will know that yellow and red = black long before you pull out the Lab Sheets....they will know yellow = 1/2 of orange...they will know 3x light green = blue....etc etc etc. All that leaves for you to do is give these things a vocabulary and show them how to express it on paper.

 

 

I think, for some, the failure of Miquon is trying to go from abstract to concrete...when the whole point is to go from concrete to abstract.

 

Aaaaaah. That makes more sense (to me) than the usual explanations.

[Spy Car]

I think, for some, the failure of Miquon is trying to go from abstract to concrete...when the whole point is to go from concrete to abstract.

 

Well stated!

 

Bill

[cottonmama]

If your child has enough experience *playing* with the C rods before you begin math work, this is all a non-issue.;)

 

But the issue is not "will the child figure out which rod is which" but rather "once the child has figured out which rod is which, how much knowledge about mathematics has he gained?" And I think that's a reasonable concern -- it's very important that the child is getting real mathematical knowledge from working with the rods, rather than learning to do tricks that look like mathematics.

 

At this point I think there is a good case for saying that the student is developing mathematical thinking by working with the rods. But it's not obvious (even to my very mathy husband), and I think it was worth a good discussion. :)

[Spy Car]

But the issue is not "will the child figure out which rod is which" but rather "once the child has figured out which rod is which, how much knowledge about mathematics has he gained?" And I think that's a reasonable concern -- it's very important that the child is getting real mathematical knowledge from working with the rods, rather than learning to do tricks that look like mathematics.

 

At this point I think there is a good case for saying that the student is developing mathematical thinking by working with the rods. But it's not obvious (even to my very mathy husband), and I think it was worth a good discussion. :)

 

I can understand how (on an intellectual level) you might be concerned that putting together rods to find sums and differences might not develop mathematical knowledge and might appear to be either a trick or a crutch. I really do understand this. And there may even be situations where the latter is true.

 

I just know that in my experience, and in the related experiences of many other parents with whom I have conversed, nothing of the negative sort that concerns you has been a real issue. Conversely, the amount of real mathematical knowledge that young children have gained, and retained though C Rods and Miquon-like methods has blown many of us away.

 

They are a tool that serves a period of intellectual development, one that can go away when no longer needed or until a new topic arises when they may prove useful once again (say with decimals, fractions, or demonstrating the distributive property).

 

I have found them to be mind-expanding tools, and just the sort of concrete tool manipulatives many young children need to move their thinking towards abstractions in a developmentally appropriate way.

 

They set up the understanding that the sum of parts makes a whole, that if you have a whole and a missing part you can find the difference. The whole Singapore style of math from number bonds to bar-diagrams is all right there in the Rod play for a child to discover and make his or her own.

 

It is really a powerful way to learn.

 

Bill

Edited September 22, 2011 by Spy Car

[FO4UR]

But the issue is not "will the child figure out which rod is which" but rather "once the child has figured out which rod is which, how much knowledge about mathematics has he gained?" And I think that's a reasonable concern -- it's very important that the child is getting real mathematical knowledge from working with the rods, rather than learning to do tricks that look like mathematics.

 

At this point I think there is a good case for saying that the student is developing mathematical thinking by working with the rods. But it's not obvious (even to my very mathy husband), and I think it was worth a good discussion. :)

 

 

Sure, it's worth the discussion.

 

Playing with the rods is baby-step #1. (imVHo, of course) This isn't the end product.

 

If that first baby-step is skipped, I find there to be a gap in actually understanding what 2+5=7 *means.* I find the pencil/paper thing a "trick that looks like mathematics" (or rather arithmetic)...if it's divorced from the concrete model. That's the gap that the C rods fill, that concrete model.

 

concrete - pictorial - abstract ; That is the Singapore Math way. Miquon (with those C rods) is simply a well-thought-out way to master the concrete level, making the next two steps seamless. Eventually, kids outgrow the need for a physical concrete model b/c they can visualize the pictorial and communicate that with the abstract easily. But first, most kids need something that they can hold in their hand.

 

 

You could argue for other manipulatives (There is a long thread on C rods vs Abacus.:lol:). I argue for trying out the C rods b/c my dc have benefitted from their play....er,use. My 8yo has figured out *most* of the concepts that he knows now by using those rods. The nature of each color representing a value makes the C rods unique. The ability to say, "If blue is 1, then what is light green?" takes the lesson on fractions from "talky-talky-talky" to the nuts and bolts of the math. Sure though, at ages 4 and 5, it is simply noted that 3 light greens are the same length as 1 blue...and that's only important b/c we want to make a track for our cars and things have to line up just so...baby steps.

 

Now...certainly, you can't stay stuck in that concrete mode, never progress, and call that a math education...but I don't think anyone has ever advocated that.

[kristinannie]

I honestly believe that my son has learned a lot from just playing with the rods. Of course, we do Miquon so he has learned a lot from the rods doing Miquon. However, he has spent hours just playing with the rods (outside of math class). He usually makes garages for his cars, roads, buildings, etc. He usually makes them with the orange (10) rods. He uses all kinds of combinations to make them the same length. Sometimes he will call out and say, "2+3+2+2+1 is 10 Mommy." I think that we are so used to looking at worksheets and tests for success, but rods (especially when used with Miquon) gives kids a true understanding of math that is really hard to quantify. My son just gets it and I really attribute a lot of that to his free play with the rods. Of course, people are free to have a different opinion, but I will use rods and Miquon with all of my kids because it has worked so well for us.

[cottonmama]

I find the pencil/paper thing a "trick that looks like mathematics"

 

That is a very, very good point. :)