View Full Version : how important are math manipulatives?

04-13-2011, 10:57 AM
We are using Singapore Math, which doesn't integrate a lot of manipulatives, but I do wonder if I should be adding more in to give her a richer math experience. My daughter seems to understand numbers in her head very clearly. Whenever I pull out any manipulatives (other than tangrams, which she does use well), she just goofs off and plays with them. I dread any activity that calls for them, honestly.

So manipulatives, how important are they really? :confused:

04-13-2011, 11:10 AM
The only time I found them really vital was for borrowing and carrying - i used legos for that. I also try to keep the lessons short so my son has plenty of time to play w the manipulatives. how old is your daughter?

04-13-2011, 11:11 AM
For the visual learner, manipulatives are important. They help to make math concrete for them.
My oldest didn't use any of the manipulatives I bought him when he was learning decimals and fractions. He did everything in his head and those manipulatives just got in his way.
My youngest uses them a little, but like your daughter, he ends up playing with them so I have to take them away.

So, manipulatives ... important for some, not so much for others :) .

04-13-2011, 11:16 AM
Agree with the OPs. We use Singapore, too. My son hasn't needed any manipulatives to grasp the concepts, though I did use pennies and dimes to play games when he did renaming. My daughter is a more visual learner, so I made some for her with construction paper. I mostly pull them out when she's having trouble understanding something, like place value. I find that Singapore does a good job at demonstrating a new concept with pictures, so that's pretty much the same thing.

04-13-2011, 12:58 PM
I agree with everybody who has responded. It depends on the child. My son is visual, yet he picked up math easily in his mind. Manipulatives only served to confuse him and make more work for him, which was completely unnecessary.

Other children need something with which to count and to represent something as abstract as numbers.

04-13-2011, 02:01 PM
Thanks everyone. That all makes a lot of sense. We're finishing up the Kindergarten level, and I started to worry there might be some aspect to her learning that was being left out. First year jitters, probably.

MonkeyMama, I do find that the pictures engage her visual needs very well. Also, the storybooks in the Kindergarten program have added a dimension that she's responded to much better than manipulatives.

dbmamaz, my daughter is five.

04-13-2011, 03:57 PM
I think they're useful and kids should all have a chance to use them in different ways and contexts. But like everyone else said, they're not absolutely essential and some kids may respond better than others. My boys really use the C-rods and the abacus often. They use the abacus all the time now to add and subtract multi-digit numbers. But the more that I've helped show them ways to work with the manipulatives (also, the balance, the pattern blocks, etc.) then the more useful they are, so I don't think one should necessarily assume that a kid who isn't immediately interested in manipulatives can't get something out of them or find them useful with a little help. And they don't have to be anything special. One of my sons thinks the pencil cup is the best source of manipulatives when he's having trouble picturing simple problems or remembering his math facts.

04-21-2011, 02:49 AM
Agree with other replies. Both my kids have access to manipulatives, ds rarely used them, he just didn't need to. Dd on the other hands much more hands on and visual and needs to move those little babies around some ;-)

04-21-2011, 07:39 AM
Singapore uses "manipulatives" on the page, with pictures, so you really don't need any you can touch with Singapore if that works. The only time I have really needed them for our son was when it was taking too much time to draw pictures over and over and faster to show him with some wooden cubes. I have used the wooden cubes (purchased in a bulk bag from Casey's Wood Products) to show place value/regrouping, addition facts (3+4=7, 2+5=7, 1+6=7 .. showing the different ways a set number of blocks can be grouped) and multiplication. They have saved some drawing time. Also how to group things by 5s and then count by 5s, like with tally marks, or how to count quickly by 2s.

I have other manipulatives also but most of them have just been distracting and not necessary or useful. The only other ones that have been useful are from a discontinued puzzle from Pottery Barn Kids that has rods like Cuisenaire rods, but wooden, larger, and labeled. They are useful for initial addition and subtraction concepts. There is a product now called Inchimals that is very similar and can be used the same way. I honestly haven't needed any of the other manipulatives I bought.

04-21-2011, 07:42 PM
The usefulness of manipulatives depends on the child. My daughter is very visual and hands on. We use Math-U-See and I've seen a huge improvement in her math skills and attention span because she can hold and use the base ten blocks. Before we started the program, we were using Kumon Workbooks and she would squirm in her chair, mess with her hands and stare off into space. Now she has something to do with her hands. I also think that manipulatives make it easier for me to teach.

04-21-2011, 07:48 PM
Not at all necessary.
Nifty visual for some kids.
Mostly an expensive gimmick otherwise, imnsho.

04-21-2011, 09:14 PM
Not at all necessary.
Nifty visual for some kids.
Mostly an expensive gimmick otherwise, imnsho.

See, I disagree with that. I don't think they're something parents need to push if kids aren't into them and I don't think every kid needs them. However, I've taught middle schoolers with an *extremely* poor understanding of place value who genuinely needed the manipulatives to get to a place where they could do upper elementary level math. And I've seen younger kids grasp concepts through manipulatives quicker than they would otherwise. So while I don't think they're a must for many kids, I think they're a lot more than just a gimmick or a fun visual that some kids enjoy. In particular, I think the abacus is a manipulative that, if kids understand how to use it, can really help propel their math skills and understanding.

04-21-2011, 10:09 PM
Recently on another list people were singing the praises of hands on equations (i think thats what its called?) and someone suggested it would still help w a 12 yo struggling w algebra. I looked at some of the videos of it in action, and realized that I"d had my teen spend 20 minutes playing with an online virtual algebra balance beam, and he totally got it. on occasion when he seemed stuck, i could draw the equation on a balance beam and he got it. So i was wondering how much more you could possibly get by buying the whole set and spending so much time on it - but it seems that some kids really need more time with the visualization to really 'get' it than others do.

but really, calling anything which is happily used by many people "Mostly an expensive gimmick" is probably not a fair assesment. It may be totally useless to some and totally lifesaving to others.

04-21-2011, 10:12 PM
See, I disagree with that. I don't think they're something parents need to push if kids aren't into them and I don't think every kid needs them. However, I've taught middle schoolers with an *extremely* poor understanding of place value who genuinely needed the manipulatives to get to a place where they could do upper elementary level math. And I've seen younger kids grasp concepts through manipulatives quicker than they would otherwise. So while I don't think they're a must for many kids, I think they're a lot more than just a gimmick or a fun visual that some kids enjoy. In particular, I think the abacus is a manipulative that, if kids understand how to use it, can really help propel their math skills and understanding.

Have to agree with Farrar on this one.

04-21-2011, 11:36 PM
Oh I'm not saying I'm an expert or that I think badly of anyone who disagrees.

It's just MY opinion. For hundreds (thousands?) of years, math was taught mostly without manipulatives, so I'm skeptical that suddenly in the last 20-50 years so many suppliers are making a fortune selling them as a necessity to learning math. To ME, that seems rather gimmicky. I can see my way clear to using an abacus. But when I see these several hundred dollar programs with cases and buckets of manipulatives? My first thought is, good grief they are making it MORE complicated.

I think IF a manipulative program is helpful, it seems to have less to do with the actual manipulatives and more to do with actual math application. Far too often math is taught like rote memorization, which has it's place, but actual life application is often where understanding is formed.

Idk. I sorta feel the same about some of the writing and reading programs out there. Hours of DVD instruction and a 4 inch thick binder? Geez. It's not that complicated? For centuries all people needed to read and write was a slate and chalk and a couple books. Why is it suddenly so cumbersome now?

Of course, I completely understand special needs and various other exceptions. But for the majority of average kids? I don't think learning has to be so complicated as some very lucrative venders would like us to believe. Sometimes I think they prey on our insecurities.

Truly sorry if I offended anyone.:(

Well crap. Apparently I have annoyed my dh too. A guy that works in corporate learning and development is now lecturing me and how he agrees with me mostly, but that doesn't make ALL of it bunk. I don't think it is ALL bunk...

Sorry to ramble. Hope I didn't just further offend...

04-21-2011, 11:46 PM
lol absolutely no offense taken and truly you are right about curriculum being a very lucrative industry ;-)

04-21-2011, 11:52 PM
Oh, no offense. Just cheerful disagreement. :)

I think people probably learned math originally through manipulatives though, so I think it's actually newer that we've taken it away from physical objects and real situations. Plus, the abacus is a very old math helper.

But I so agree about it being a huge industry. The schools all invested in the sort of math manipulatives that you're talking about when they sunk their math money into pattern blocks, geoboards and the like. Those are fun and we enjoy them (we keep using the pattern blocks for new things, actually), but they're so totally extra and probably not essential for hardly any kids to understand mathematical concepts.

04-22-2011, 12:19 AM
i'm more likely to have been offensive than offended in this instance. however, i think that for 100s of years, average people DIDNT learn algebra. I think that more math is being really needed by more people as our culture progresses, and that the manipulatives are helping some people who might not have gotten there, or not gotten there as fast.

one thing that drives me nuts is when they show studies that show that XYZ increases learning in classroom studies - but it increased average test scores by 30% . . . that doesnt mean that every kid learned better this way. After all, kids who are already getting As cant really increase their scores by 30%. Its working for the kids who cant learn by the traditional methods, and its probably fun for those who can.

But of course, its being sold as 'the solution' to everyone. Hence - seems like bunk to some of us because it makes little difference to us.

otoh, i've been rambling something fierce tonight . . .

04-22-2011, 09:20 AM
Also manipulatives don't have to be expensive, someone mentioned using legos, another pieces of paper. You don't always have to use expensive little blocks marketed specifically for the task of being math manipulatives, you can use any number of small objects, pieces of paper, or even food items (candy, cereal, etc).

04-22-2011, 09:40 AM
I have to disagree with the idea that manipulatives weren't used for hundreds/thousands of years. They did use manipulatives, they just didn't go buy them to use. They used rocks, shells, berries, drew pictures in the dirt with sticks, etc. It's the same concept, just free. It has become very commercialized, though. I do agree that they get pushed as being required and can be very expensive. You can get frogs, bears, dinosaurs, discs, kidney bean shaped, etc. They come in different colors, shapes, and sizes. However, as Riceball Mommy pointed out, they don't have to be expensive. You can use any toys the kids have lots of, like blocks & legos, or food like candy or beans. We had a coffe can full of dried beans that we used for Dea when we were just starting homeschooling. It was a lot cheaper than buying the manipulatives at the local teacher store. Over the years, we have bought some - we have bears, frogs, & dinos, because I knew the kids would have fun playing with them (I bought them more as toys not tools). We also have some corlored discs, because they work great for the different Math bingo games I make for them.

04-22-2011, 10:40 AM
Hmmm. If we are expanding manipulatives to include real world application word problems with dirt and stick vs paper and pencil, then I would agree that has been around for millennia. And of course the abacus.

But otherwise I don't think so. It would have been bulky and time consuming and those are things that simply were not very practical except for the very elite of society and nothing I have read historically suggests they did that. For example, no mention of such is given for monastery education in the middle ages.

They did keep tallies and drawings, that is backed up historically, but again, I didn't consider that a manipulative necessarily. I put it on par with pencil and paper. And even "pencil" and "paper" was VERY expensive for most of history and used very sparingly.

As for algebra not being used. Algebra has been used for thousands of years. At it's base, algebra is nothing more than solving for X. Men have been doing that at least since the ancient Egyptians. Same goes for geometry. Even common men had to do it to some extent, tho they probably didn't realize there was a name for it.

I could be entirely wrong about manipulatives though.

I still don't think they are a "necessity". Helpful sometimes? Sure. But not a necessity. I think very little is actually a true "need" to educate.

Not that you can tell is my opinion by the amount of curriculum I win or have owned over the past 11 years.:D

04-22-2011, 11:48 AM
I guess I just imagine that little kids in ancient cultures learning to count would have been handed little sticks, rocks, shells, etc. to demonstrate what the parents were talking about. And, as Cara pointed out, math higher than what you could count on your fingers was only used by a very few until modern times. And when schools came into existence in a more massive way, many of the early mass education pioneers, especially for young children, like Montessori and Froebel, both used manipulatives.

I guess the term "necessary" is really at issue. Like, I think you could take almost anything in our homeschool and say it's not *really* necessary. I mean, we don't absolutely have to have a math curriculum. We could do without the computer for all the things we use it for if we had to. Heck, we could do without the white boards, most of the paper we use, etc. If we had to, we could do without the crayons and markers and pens and just use pencils. Well, you get the idea. But all those things - and manipulatives too - make learning easier in different ways. Now, do manipulatives help every kid? No and it may even be that the majority of kids don't need them. But I am convinced that some kids (and not a very few, either) actually do *need* them in order to grasp concepts - at least in any kind of timely way. At least, that's been my personal experience.

04-22-2011, 12:46 PM
Tho what I think i'm hearing is more frustration with how many curriculums come with their own manipulatives, priced for proffit margin, and often requiriing or strongly suggesting buying new ones every year. But anywhere people are insecure about something, there is more market for eploitation - math is something a LOT of people are insecure about.

04-22-2011, 01:16 PM
That issue of a "timely manner" might be the real issue. Historicly, it wasn't that counting beyond fingers wasn't done. It is that abstract math concepts were not taught, certainly not in an academic manner, before the age of 10. Now most kids are expected to do some fractions, decimals, basic geometry, long division and some simplistic solve for x (algebra) by the end of 3rd grade, which is typically around age 8ish. Just 200 years ago, they would just be having those begining abstract concepts introduced at age 10.

And really it made more sense to wait. There IS a development issue at play here. It does take significant effort to teach something beyond development readiness. If a student isn't ready for the very abstract thinking processes, they are absolutely going to need a way to make it concrete to understand it. The more society pushes for introducing these things earlier and earlier, the more complicated they are going to make teaching it. Because the earlier they push for it, the more they are trying to create understanding before development. And THAT is a very difficult and complicated thing to manage. I think this is a KEY reason so many kids graduate with so many years of complicated instruction in the 3 Rs, yet for the most part are still functionally illiterate and lack comprehension.

04-22-2011, 01:30 PM
i assume, tho, that its just an extreme spiral, or rather like the WTM approach to history - expose kids to things when they are younger, so when it comes back in a deeper way years later, they arent intimidated by it?

otoh, they probably dont do algebra at age 8 in finland lol

04-22-2011, 03:39 PM
I don't know about Finland, but they do algebra at age 8 in Singapore. :D

Cara, that's one of the reasons I never even really considered RightStart. When I saw that there was a tiny marked bag of popsicle sticks for manipulatives, I was like forget this.

04-22-2011, 04:03 PM
That's how I felt about Math U See.
When my friend brought over a suitcase full of manipulates, I instantly thought "forget this mess."
Felt the same way when another friend brought out the hours of DVD instruction for the teacher to learn how to implement the huge binder of a program that is IEW. My first thought was forget it. If it is that complicated, then I'm not interested.

Another was Spelling Power. I actually like the concept, but crickey what a mess to slog through! Luckily, once I had used it for a couple years, I switched to Natural Speller bc I felt it contained what I found most effective in Spelling Power without slogging through all the other gunk.

04-22-2011, 04:30 PM
I've avoided IEW due to cost mostly . . . tho i've doubted myself on occasion. However, Orion completed a really good, IMO, 5 pp essay (ok, it was actually 6 because he felt 1 needed to be split) about the first emporor of china. So my panic is abating and I'm not interested. And i'm using singapore . . . and yeah, i used legos w my younger and that virtual balance beam (http://nlvm.usu.edu/en/nav/category_g_4_t_2.html ) with my older one. oh, and my younger is now using t4l mostly, and both on khan academy . .. i can imagine using manipulatives more if someone was struggling, but no, not spending money on stuff i could do with whatevers around the house.

but then again - i tend to generally think i can do it better myself. not everyone is like that. they might find it easier to let someone tell them how. i mean, seriously, i think half the writings about LA programs in homeschool circles are rave reviews of IEW, no?

04-26-2011, 12:52 PM
Well our hands are manipulatives (10 fingers), so that our most familiar number system developed into our decimal, base-10 system. The abacus has been in use for about 5000 years. People have used anything they can find such as rocks/pebbles. So I think manipulatives were pretty important in the past.

The RightStart abacus has been an amazing tool for us when learning math. We're now using Singapore and using our old MUS blocks and c-rods. They're helping my daughter visualize concepts when she first learns them, and now she's better able to do her mental math. She doesn't need them once something is learned, but they help a lot in the beginning. This physical, hands-on approach works very well for some people. For example, I was doing online geography puzzles which wasn't too hands-on but were pretty easy once you did it a few times. Then I made my own puzzle and was finally adequately challenged. I was able to learn more effectively just holding the pieces in my hands, turning them around and fitting them together.

You don't have to spend a lot of money on manipulatives and could make your own.

07-17-2011, 04:36 PM
My kids love to use manipulatives and we have boxes full of them that are used a lot, not only during math lessons but also to play with.
Reu and Toby need their manipulatives for math, they need to hold the manipulatives in their hands and play with them to really understand their math work.
We have hundred boards, snap cubes, counters, base ten sets, dices, rainbow fraction manipulatives, play money, judy clocks, tangrams, attribute blocks, scales, balances, geometric shapes, flashcards, pattern blocks, weight sets, place value manipulatives, math games and more, and everything is being used on a daily basis.

For us math manipulatives are very important.

Accidental Homeschooler
07-17-2011, 05:13 PM
My 5 (almost 6yo, where did the year go?) hates manipulatives. Thankfully I spent only about ten bucks on them. She really likes to use her fingers or a number line. I made the number line with cardstock and clear packing tape (cheap lamination). Maybe we will use the manipulatives later though.

08-08-2011, 08:14 PM
We use the Montessori method, so to us they are vitally important. We don't begin to write anything down in abstract until they understand the concrete first. Until they can show me 2+2= 4, they don't write it. Which is highly annoying when family members find out we're working on addition and say dumb things like "what's 7 + 12, dd?" and she responds with a blank stare.:rolleyes: The whole point of our philosophy is that when first learning maths, they don't even realize they are learning it.

If learning a new concept, I think they can be very beneficial, but not always necessary. But, when you expect them to use manipulatives for something they already easily understand, asking them to use manipulatives would be extremely boring for anyone. It's the homeschool equivalent of "showing your work" which I think every PS kid hates/d.

08-15-2011, 07:23 PM
In particular, I think the abacus is a manipulative that, if kids understand how to use it, can really help propel their math skills and understanding.

Hmmm... it had never occurred to me to use an abacus to help ds learn math because I was never taught to use one. But it might be worth a try since so far he seems to be a very hands on learner. What do you use to teach use of an abacus? What age can it be introduced? Which kind do you recommend? (I didn't know there were different kinds until I googled)