Math, Abacus, Number lines - Oh my!

[FairProspects]

We have a math dilemma. Ds hates the abacus and just doesn't get it for re-grouping AT ALL. This is not a new problem - we've done 18 months of Right Start now, all of A and more than a third of B and it has happened the entire time. I keep thinking it will eventually click and we stick with it because *I* am visual and *I* like the way Right Start teaches, but after more than a week of tears everyday, I gave ds last week off math. I've been looking ahead at the material and there is no way we can move on right now. The next few lessons go more in depth on concepts he doesn't get (namely place value and trading up 10s) and are based on the manipulatives that caused the tears in the first place.

 

However, we have been doing MM as a supplement and ds LOVES number lines. They just completely make sense to him and I don't even have to explain the concepts because he just naturally GETS it.

 

So, I'm stuck. Do I set RS B aside for awhile and give the concepts time to marinate? Do I switch to a program that uses number lines instead of an abacus? What would that even be? Is the abacus/re-grouping concept essential to arithmetic or are other methods like number lines just as useful for early math concepts?

 

What do I do:confused:? I am not a natural math teacher!

[PeterPan]

Is this dc a 6 yo K5er or a young 1st grader? If he's a K5er, I'd put it all aside and just do some Kitchen Table Math and fun stuff. I have nothing against MM, am using it quite happily with my dd right now, but there IS a developmental timetable to kids. Sometimes something isn't clicking, you wait 3 months, and it just happens. He may need a growth spurt and that next mental leap.

 

I had some of those blank look times with my dd. And really, when we took off, I mean really took time off, she usually came back ready for it. It was a waiting thing. I called it treading water. Sometimes these curricula are so efficient that you actually hit a wall with what the student is ready for developmentally. Then you have to tread water a while. Take what he knows and go do some other things. Go play games. Does he play Uno? Any games where you keep score and do mental math? We've been playing Ticket to Ride Europe, don't know if he's ready for that. We had a game called Checkof when my dd was that age. Dice games are good. Anything from the RS games, Corners, etc. is good. Take off a month and see what happens. If it irks you to take totally off, go do some of the geometry or measurement units in your MM.

[mom2bee]

Removed by the Author.

[FairProspects]

Well, he's technically the age of a 1st grader, but because of some wiggliness and other OT issues, I red-shirted him so this is his official K year even though he is doing some K work and some 1st grade work. We do have time though if I need to set it aside for awhile. Its funny you should mention Kitchen Table Math because I just ordered it today.

 

I think the issue with the abacus is just that its just not his go-to strategy for problem solving even though he can use it when asked. He is really good at mental math so I haven't pushed it, but when I ask him what he is picturing in his head to do addition, he says a clock or a number line rather than the abacus and re-grouping that RS teaches. I'm wondering if this matters and if that means RS isn't working for him or if I should just let it go, keep doing RS anyway, and let him do what works for him.

[PeterPan]

As long as he's picturing SOMETHING and getting the math done, I'd go with it. If he's picturing NOTHING, then he may have visualization problems. If he can't do the math, he needs more time. There are lots and lots of ways to think of math, so that's not the issue. I just wouldn't feel compelled to rush forward without being ABLE to think through the math properly. Have you done it with the place value cards and base 10 picture cards? You might back up there for a while and see where it gets you.

 

I remember hitting walls both with math and spelling with dd. These programs we use just have no fluff in them to hold the kid back, kwim? Sometimes you hit on those walls. A little bit of time can make a big difference.

[FairProspects]

Well, its the base-10 cards that caused the tears in the first place. He completely understands the place-value cards and can manipulate them well, but he just doesn't recognize the relationship between the pictures and the hundreds & thousands on the base-10 cards. Plus, jumbling them all up and having to sort them really throws his orderly mind for a loop.

[boscopup]

Not every child needs manipulatives all the time early on. My oldest doesn't need them most of the time, and he does very well with mental math. We're doing MM and he loves it. Is there a reason why you don't just let him use MM if he likes the method better? Or does he still have issues with writing on those pages?

[Crimson Wife]

You could always just find some lessons in RS B about some different topic and work through those for a while. Just because Dr. Cotter put topic X before topic Y when she wrote the program does not mean that you have to do it that way. That would give your child some time to mature without completely stopping math.

 

I needed to do this with my DD when it came time for multi-digit multiplication and long division. I knew she wasn't going to be able to do it until she memorized her times tables but it took ages for her to get them down pat. I skipped that chapter in Singapore 3A and then came back to it after she finished the rest of 3A and 3B.

[PeterPan]

Well, its the base-10 cards that caused the tears in the first place. He completely understands the place-value cards and can manipulate them well, but he just doesn't recognize the relationship between the pictures and the hundreds & thousands on the base-10 cards. Plus, jumbling them all up and having to sort them really throws his orderly mind for a loop.

 

Just trying to understand what you're saying here. The base 10 picture cards have the picture representations of the beads. The place value cards are the numbers that you can stack to create 4 digit numbers. You should have had a "stations" activity where you formed a 4 digit number with the base 10 picture cards, the place value cards, the abacus, and by writing on the board. This activity is specifically to bring his understanding full circle.

 

If he doesn't understand, I would back up to that point and see where the glitch is. One thing Dr. Cotter says is that a good manipulative creates confusion at first. If they immediately understood it, they wouldn't NEED the manipulative. The goal of the manipulative is to stretch their understanding of the subject. So I would back up, try the stations game, and see exactly where the glitch is. You form a 4 digit number with all the methods, then form another. Now you add or subtract those two numbers, whatever your target skill is, using ALL the methods. If he can't do this, even with the manipulatives in hand, then I would say it's probably a developmental thing, something that would resolve with a break doing something else. Have you done money or time or geometry lately? You could google to find some activities and designs you can make with your geoboards.

 

BTW, the base 10 picture cards are a pictorial representation of the beads of the abacus. You may need to go back and re-establish this connection, if he doesn't see it. The 100 would be 10 abacuses stacked. You may have the little 3 dimensional paper hundreds you can assemble and manipulate. If not, you might be able to get manipulatives from the teacher resource section of your local community college. If you let him do the math with the manipulatives, eventually the algorithm clicks. These concepts are pretty foundational, so I wouldn't just skip over them in favor of doing things by rote.

[Snowfall]

These concepts are pretty foundational, so I wouldn't just skip over them in favor of doing things by rote.

 

:iagree:and I couldn't agree more! I understand where you're coming from with him not liking the manipulatives, so if you can figure out a way for him to understand regrouping without them, then that's great. But if he actually doesn't understand regrouping, then I think you need to stop for a while, not just move on in something else. Number lines are great, but if he doesn't get the point - if he doesn't understand that you're crossing over a ten - then IMO you should either work on that with him until he can do the math without a number line or give it a rest for now and come back to it when he understands what's happening.

 

I think someone already mentioned that there's really a level of mental maturity that has to happen before kids can grasp that, and I totally agree. We had to take 2 or 3 weeks off and do other things when we got to adding to 9s in the higher decades (like 29+4 or 24+9) because dd just couldn't understand it. We did other things for a few weeks, and every day I would ask her ONE of those types of problems. She got it wrong every day for 2 or 3 weeks. When she finally got it right, we picked back up at that lesson the next day. From that point on she completely understood it, and it seemed like she'd never had a problem with it at all. Once they're ready for something, they're ready. It was weird to see it happen (it was my first time :D) but it was cool.

[PeterPan]

Snowfall brings up something else I had forgotten! On some of those really long lessons, we literally did one problem a day. Yes, it took a long time to get through them, lol. We would do *1* 4 digit addition or 4 digit subtraction (anything that was tedious at the time, requiring the manips, etc.), and then we'd go do something else. It's ok for this process to take time. You're waiting for things to click, and then don't always click when we think they should.

[Spy Car]

One thing Dr. Cotter says is that a good manipulative creates confusion at first. If they immediately understood it, they wouldn't NEED the manipulative.

 

Before I go on to say this is non-sensical, let me say I have great respect for Dr Cotter and have gained a good deal from reading her writings, borrowing on her ideas about teaching place value early and using her games and place-value and base-10 cards--but this idea (which I'm not certain she believes) is non-sensical.

 

There was a whole mega-thread (something like "Why RS doesn't like Cuisenaire Rods") where this issue was thrashed out. A manipulative ought to bring clarity, not confusion. It it is causing confusion it isn't working well.

 

The base-10 cards are not "pictorial representations" of the beads on the abacus. There is a layer of abstraction between one bead equaling 1000 and therefore equaling a picture of a "cube" and another single bead (on a different wire) being equal to "flats" or sticks, or units. These associations are an intellectual leap a child may (or may not) find easy.

 

The base-10 cards are pictorial representations of concrete base-10 manipulatives. Which are very similar to Cuisenaire Rods and the two can be intermixed being the same scale.

 

I think for some children the abacus is great. For others it causes confusion. I do not see that confusion as a positive. I would not try to bend a child to something that is causing confusion when there are alternatives that provoke clarity.

 

I know my son, a bright kid without learning issues, found almost instant understanding when we used base-10 "flats" and C rods to do Right Start inspired place value work (including using their place vale cards that are pretty much pictorial forms of what were were using as "concrete" manipulatives, where trying to do the lessons on the abacus often caused confusion.

 

With an abacus there is no "conservation of value" by area.

 

I think one needs to go with what works for the individual child and be able to know when to say when.

 

Bill

[PeterPan]

I did refer her to using manips to bridge between the abacus and base 10 picture cards. And we told her to do the math *all* the ways using the station game and variety of manips, rather than leaving it to just the abacus. If she does these things and he can do the math in some of the ways but doesn't prefer another, no biggee. If he can't do the math ANY of the ways, something is wrong.

 

My dd didn't particularly like the abacus either, so we used it to introduce something and moved on. She didn't need it to get the concept and didn't like visualizing with it. However I made sure could actually do the concepts. You don't have to do the abacus to get there.