How much should they be doing in their head in Singapore?

[Michelle]

Hi there!
I have been really loving Singapore math for my ds who is doing Preparing.... and going quickly through 2A right now. He's doing problems in his head now that a month ago would have had him running! He's a 4th grader and we do 1-3 lessons a day to catch up.

It's my dd that I have the question about. She just turned 6 and we're doing LHFHG for 1st grade and doing Singapore 1A with the Beyond.... guide. We were doing ok, but now we got to Unit 4 Day 2 and she wants to us her fingers to figure out the problems on page 33. I tried to direct her back to something like buttons instead. She got frustrated so I stopped the lesson. It seems she's not memorized the fact families and therefore, can't tell by just looking what two numbers make 6, for example. Am I expecting too much? Is she supposed to have memorized these fact families by now or should she still be using counters to solve the problems? I just don't know what to expect of her at this point. We do all of the hands on stuff too.

Any help would be great!
God bless, Michelle

[pjdobro]

I don't see a problem at all with still using counters or fingers to do this basic math especially at age 6. I went and looked at page 33 in 1A and I'm surprised that she didn't just count the frogs in the picture but it's fine that she wanted to figure it out with her fingers. I know some people are really big into memorizing math facts and feel that using manipulatives including fingers to figure things out is bad, but I don't see the need to rush into memorizing basic facts. I think it is in Ruth Beechick's book that she talks about children going from the manipulative stage, to the visual stage, and then the abstract stage of math. I feel like it is important not to try to rush that progression too much. One of the wonderful things about the manipulative stage is that it allows a child to solidify the concept in their mind that adding actually means putting more things together. I think if we try to rush them into remembering that 2+3 is five, it just becomes a fact without meaning behind it. With time, she will become comfortable with the concept and will have figured it out with manipulatives often enough that the fact will be remembered. If over time, that doesn't seem to be happening and it seems she is using her fingers as a crutch then, you might want to consider trying to do some more drilling on basic math facts. If I remember correctly though, I think there are quite a few games and activities in the Beyond manual that will help drill these concepts over time so the facts will be practiced in many fun ways over the next year.

[my3sons]

I think it's fine for her to use her fingers or manipulatives. I am wondering if she did the Earlybird Kindergarten math and activities last year? My ds is in 1B now, and he's just starting to know his facts pretty well - but I think it is a combination of last year's math and this year's that is making it stick. If she hasn't done the kindergarten math, you could back up and have her do that if you think that would be a better placement now. Otherwise, I do think they just seem to begin to know their facts doing it the Singapore way, and her using her fingers now will probably be replaced naturally by her doing it in her head eventually.

In Christ,
Julie

[Michelle]

Thanks a lot for the replies!

My dd didn't actually do the Earlybird Kindergarten math. Since I had the LHFHG guide over the summer we did go through all the math boxes and do all of the "hands on" activities, just without the Earlybird book. So....I thought since she's more math minded than my ds and she had some math in K that it would be enough.

My worry about her using her fingers is because my ds has used them as a crutch and is now in 4th grade still saying he needs to us them. Doing Singapore 2 has helped to bring that down to a minimum though. However, we do more minuses today (his arch enemy! ) and he'll probably cry! I was also wondering if it's ok to do minuses by using addition. Like; What plus 4 equals 7? To do the problem 7-4=3. He's much better that way, but should he be made to only think in subtraction or does it matter?

My biggest problem is always knowing how much to expect. I usually err on the side of too little, so trying to find a balance in math for us this year.

God bless, Michelle

[pjdobro]

That is awesome that he can do the problem what plus 4 equals 7 so easily. Most children would struggle more with that kind of problem than with 7-4. It sounds like he has had a bad experience with subtraction. I think him being able to realize that it is the inverse of addition is wonderful and a bonus. If it helps him to think about it that way, then I would let him. I would also try to show him after he does a problem in that manner that he just solved the subtraction problem (i.e. after figuring out that ?+4=7 show him that he just figured out that 7-4=?). I would also try to let him do these problems with counters, beans, or some other manipulatives so that he can see the relationship between addition and subtraction. I would think after figuring out that he was really doing subtraction all along, his fear/dislike of subtraction will start to diminish. Sometimes, especially with math, it's just our perception of the problem that makes it difficult. When we look at the problem from a different angle, we get a whole new perception of the problem and it doesn't seem so daunting.

I struggle when it comes to what to expect of my children as well. As a homeschooler, I'm always wondering if they are getting everything they need. One of the wonderful things about HOD is that Carrie has done that work for us and if we just follow the program, we know they are getting more than enough. I think the same is true of Singapore math (after all, it's the one Carrie chose ). As long as he is able to do the problems without struggling and seems to be understanding the concepts, he is doing fine. Ultimately, it all comes down to doing what God expects of us and letting the rest fall into place. I try to remind myself of that all the time, thus my signature line

[Michelle]

Thanks pjdobro and Julie!

I guess I gave the wrong impression about his "reverse minus" abilities. He actually worked on this a little in math in 3rd grade. He was taught about reversing the subtraction problem to make it into an addition problem. I first taught him this so he could check his subtraction problems last year. Doing subtraction in this way makes it seem a lot less difficult for him so I let him do it. He's capable of doing a lot in his head, but he has this invisible wall when it comes to subtraction!

He also doesn't like to write the number at the top when borrowing. (he's really lazy!) He prefers to just remember and most of the time he does. He did A LOT of subtraction with borrowing and addition with carrying over last year and NEVER wanted to write the numbers at the top. He would do 30 problems without adding any numbers at the top and do really well! However, it did catch up with him and I have been insisting that he write it this year.

So....it's ok of he turns his subtraction problems into algebra?

Thanks, Michelle

[funkmomma71]

My daughter is also doing 1a, we are a little further along, but she does not know her math "facts" very well, but she knows how to figure out the answer which I think is more inportant. She also does alot of her subtraction with addition, which again, I think is better since it shows that she knows how to figure out the answer rather just having memorized a "fact". I'm confident that she will learn her basic math facts, but more importantly she'll know WHY 4+3=7 and 7-3=4, that's what the manipulatives are for, to teach the WHY not just the WHAT. KWIM??

P.S. It sounds like your son is teaching himself algebra, nothing wrong with that!

[Carrie]

Michelle,

The ladies have given you terrific advice that is filled with so much wisdom. I agree that mathematical thinking is the goal and knowing more than one way to solve a problem is a wonderful way to show that kiddos are thinking mathematically. So, it sounds like your kiddos are doing well in math. At age 6, there are no worries in having your daughter use her fingers (which are one of the easiest manipulatives to use because they're always with you).

As far as your son goes, doing the inverse of a subtraction problem to figure out the answer is a wise strategy. Either way, he still has to understand what he's doing and be able to come up with an answer that makes sense.

On a sidenote, If your son is still struggling with his math facts, you may at some point wish to go through a deck of addition flashcards with him and set aside any cards that he doesn't know within 3 or 4 seconds. This exercise will help you know how many facts he is truly struggling with. Then, if he's only struggling with up to 10-12 facts separate up that pile of cards and have him practice 3 the first week. The next week, add one more to the pile, so he is practicing 4 and so on, until all the cards are learned.

If, on the other hand, he is struggling with a great many addition facts, instead have him make a set of index cards flashcards for the 0's (i.e. 0 x 0, 0 x 1, 0 x 2, 0 x 3, and so on up to 0 x 12). Then, use masking tape on the back of the card to write the answer in pencil. Have him practice all 12 cards until he can get them down in 30 seconds. When he passes the 30 second test, move onto doing the 1's instead. You may wish to pay him 25 cents or 50 cents for each set that he passes. We did this with my oldest son (who did not use Singapore and did not know his facts either).

Just a thought.

Blessings,
Carrie