1st grade Singapore struggles. Should we put math away for a while?

[talk2ham.1]

My son doesn't get the order of operations for subtraction and addition involving what we would have called carrying and borrowing in school. The way that SM teaches it, I can see as being helpful in the long run, but in the mean time it adds an extra step that is HUGELY confusing to my 1st grader.

 

Here's a sample problem.

 

24 - 9 =

 

Rather than teaching the student to borrow and count up, they want the student to separate the tens and units and then subtract 9 from 10, get 1 and add it to whatever tens and units would be left: in this case add the 1 to 14 and get 15.

 

In addition it is the opposite of the same idea.

 

25 + 6 =

 

5 + 6 = 11; and then add the tens column to that to get the answer: 31.

 

 

To me this is incredibly sensible and breaks the steps down for the sake of mental math. To my son, this is a mind boggling, frustrating, order of operations.

 

How should I be teaching this? Should I just teach him the old way of carrying and borrowing and introduce this method later?

 

He is currently sitting at his desk wailing, resigned to utter failure. This has been going on for several days. I cannot advance him and I am afraid to push him more for fear of convincing him he can't do math. Actually, he is very good with numbers. I'm almost thinking I should put math away for a few weeks and see if this blows over.

[UrbanSue]

I'm not an expert, but I think what they are going for here is a solid conceptual understanding rather than just memorizing the algorithm. I agree that some kids find it frustrating but it does pay off in the end.

[Alessandra]

I like this way of teaching and that is what I am doing as I reteach math to my dd. We made a big time investment in using Miquon, so she is familiar with (= adores) her Cuisenaire rods. They are a great teaching tool. You could also use base 10 blocks, but I think the C rods are clearer.

 

I also write out each step in a series of equations. Or we verbalize what we are doing as dd does the blocks.

25 + 6

(20 + 5) + 6

20 + (5 + 6)

(5 + 6) + 20

11 + 20

(10 + 1) + 20

10 + ! + 20

(10 + 20) + 1

30 + 1

31

 

We often do problems in more than one way. But a key is that I am very specific about each step. Now dd loves mental math and does it quite well.

 

A program that has helped a lot is Algebra Touch (computer or iPad, but iPad is more fun). The beginning part has some good basic problems. I am currently begging the author to write a program specifically for addition and subtraction. Maybe in the future???

 

SM has a supplement, Math Express, that gives mental math practice, but I find some of these are a bit hard to understand. We have found Visible thinking in Math more useful. All at RR.

 

One last thing. I emphasize a lot that we are spending time on very basic things because they are the foundation on which everything else is built.

 

Snap It Up Addition is a great game for developing mental math. My dd often tells me what cards she has and I tell her if she has a winning hand or not. Then she has to figure out the answer. Funny, she almost always wins! Math Dice Jr is also fun. Again, all at RR.

[lil' maids in a row]

No advice. I just wanted to let you know that I ran into a very similar road block with my first grader. We slowed math way down, but she is high strung and just couldn't handle the frustration. I went ahead and printed off the first 60 lessons of MEP math and we have been working on that for about 6 weeks. It is easier (because we just started with the beginning of the year again), it has some physical activities, and it is working on a different skill (lots of work on greater than and less than). We have also spent some time learning about money. We may go back to Singapore when I feel like she is ready, but I don't think she is yet. It is discouraging, but we have been learning and there have been no tears.

 

Good luck!

[Alessandra]

Miquon doesn't explicitly introduce place value until the third book. But they work with larger numbers way before place value. I'm not saying that is better than SM -- which we use too -- just that it another approach.

 

How could I forget the Education Unboxed videos? If you use C rods, they are a great inspiration.

[alisoncooks]

We're struggling with a similar point in SM. I'm considering switching over to CLE for a while... then picking back up with Singapore. IDK, I've got all my math books laid out in front of me to study tonight, LOL. Stick with what we have (we currently have SM, MiF, MM for the 1st grade level) or try a spiral approach. :p

 

Maybe some place value games would help for a while? There are some fun ones to be found on Pinterest....

[RoundAbout]

I would do something visual. The Rightstart abacus is brilliant for this.

[RoundAbout]

Oops. Double post.

[Alessandra]

Adding -- I see your ds is in 1st grade. This might help -- it's recommended by the author of the Math Mammoth program:

 

http://www.amazon.co...eywords=mammoth

 

BTW, I am not joking!!!!!

 

Also, you can take ownership of the difficult situation: not, "Was that problem too difficult for you?" but, "Did I make a mistake and jump ahead too fast?" or' "Math Mammoth says that problem wasn't fair."

 

Since your ds is actually crying, you might want to take some time off or do another mathy thing, like shapes or telling time.

[boscopup]

I actually taught a different method that made more sense to ME and was still valid per Singapore method...

 

24 - 9

24 - 4 - 5

20 - 5

15

 

So I subtract down to the ten, then subtract the rest. This is easier for me because I'm subtracting the whole time. The method taught in 1A has them subtracting and adding back. I showed my son both methods and let him choose.

 

This IS different from subtraction with regrouping. That's not what Singapore is trying to teach in first grade.

 

 

[Susan in KY]

I'm not an expert, but I think what they are going for here is a solid conceptual understanding rather than just memorizing the algorithm. I agree that some kids find it frustrating but it does pay off in the end.

 

 

Can I like this twice? :)

 

Use manipulatives. The time you spend on this will pay off. :)

[Alessandra]

I actually taught a different method that made more sense to ME and was still valid per Singapore method...

 

24 - 9

24 - 4 - 5

20 - 5

15

 

So I subtract down to the ten, then subtract the rest. This is easier for me because I'm subtracting the whole time. The method taught in 1A has them subtracting and adding back. I showed my son both methods and let him choose.

 

This IS different from subtraction with regrouping. That's not what Singapore is trying to teach in first grade.

 

In her book on how math is taught in Asia, Liping Ma talks about teachers who present several ways of subtracting. I think your way was probably one of them. Her point is that kids should be taught that there is not just one algorithm, but rather many different methods of attacking a problem (as long as there is a conceptual understanding, that is).

[TriciaS]

I actually taught a different method that made more sense to ME and was still valid per Singapore method...

 

24 - 9

24 - 4 - 5

20 - 5

15

 

So I subtract down to the ten, then subtract the rest. This is easier for me because I'm subtracting the whole time. The method taught in 1A has them subtracting and adding back. I showed my son both methods and let him choose.

 

This IS different from subtraction with regrouping. That's not what Singapore is trying to teach in first grade.

 

 

That is how I taught it, too. I did show my daughter both methods, but going up (or down) to the next ten made the most sense.

[blondeviolin]

I teach both methods (subtract form a ten and add back in OR subtracting down to ten and then subtracting further). My oldest preferred subtracting from a ten and then adding back. I would NOT teach the standard algorithm at this point. The point of this is for the child to be able to quickly calculate these problems, even with larger numbers. In further levels, they will expand this mental math into more than just tens and ones.

 

"Borrowing" is taught in year 2. I don't know about other students, but my girl hardly ever works the standard algorithm (even though she CAN) because adding things mentally is so much quicker. And I'm pleased she has the foundation to do that.

[nmoira]

I actually taught a different method that made more sense to ME and was still valid per Singapore method...

 

24 - 9

24 - 4 - 5

20 - 5

15

 

So I subtract down to the ten, then subtract the rest. This is easier for me because I'm subtracting the whole time. The method taught in 1A has them subtracting and adding back. I showed my son both methods and let him choose.

 

This IS different from subtraction with regrouping. That's not what Singapore is trying to teach in first grade.

 

 

This is how MEP teaches addition and subtraction crossing tens: two little jumps in the place of one big jump, reinforced conceptually with plenty of number line work.

[AKshanmar]

Don't drop it, but approach it from a different angle. It is a very important concept. I'm too lazy to get the book right now, and can't remember the title, but it explains the different approaches between Oriental and American math teachers. The author is Liping Ma, if I remember correctly. It was very insightful and would help encourage you.

[Five More Minutes]

Just want to agree with everyone here -- don't give up on the conceptual approach and revert to the traditional algorithm. It really pays off. Move on to a different topic or play games with the c-rods (Rosie's videos at Education Unboxed have good ideas) until his frustration with math in general diminishes. Then come back to this.

 

In her book, Knowing and Teaching Elementary Mathematics (which I recommend!), Liping Ma talks about the ability to use the standard algorithm vs. actually understanding the problem. "Borrowing" is a misleading concept -- we are subtracting one smaller number from another larger number; where exactly are we "borrowing" from, and do we have to give it back? Instead we're decomposing a number, subtracting, and regrouping.

 

Even when we taught the standard algorithm in SM 2, we avoided the "borrowing" term and instead talked about breaking apart a 10 and keeping track of it. I'm so impressed now with the deep understanding of place value that my dd has, compared to my own at that level.

 

I would do as boscopop and others suggested -- use a different conceptual method, with manipulatives. And eventually you may come back to the method that Singapore is presenting, because it comes in handy later on when you're subtracting numbers close to 100.

[Alessandra]

Just want to agree with everyone here -- don't give up on the conceptual approach and revert to the traditional algorithm. It really pays off. Move on to a different topic or play games with the c-rods (Rosie's videos at Education Unboxed have good ideas) until his frustration with math in general diminishes. Then come back to this.

 

In her book, Knowing and Teaching Elementary Mathematics (which I recommend!), Liping Ma talks about the ability to use the standard algorithm vs. actually understanding the problem. "Borrowing" is a misleading concept -- we are subtracting one smaller number from another larger number; where exactly are we "borrowing" from, and do we have to give it back? Instead we're decomposing a number, subtracting, and regrouping.

 

Even when we taught the standard algorithm in SM 2, we avoided the "borrowing" term and instead talked about breaking apart a 10 and keeping track of it. I'm so impressed now with the deep understanding of place value that my dd has, compared to my own at that level.

 

I would do as boscopop and others suggested -- use a different conceptual method, with manipulatives. And eventually you may come back to the method that Singapore is presenting, because it comes in handy later on when you're subtracting numbers close to 100.

 

I read and reread Liping Ma as needed -- her first chapter is on subtraction. Her ideas/SM conceptual approach work beautifully with Miquon and Cuisenaire rods. One reason I'm bringing up Miquon again is that you said your son is bright at numbers. Miquon encourages kids to explore at their own pace and might be a good fit. A LOT of people here use Miquon with SM -- I am a late convert, wish I'd known about it sooner.

 

And, like others, I would highly recommend the Liping Ma book:

 

http://www.amazon.co...words=liping ma

 

If you are buying the book, check out Abebooks or wherever you get used books -- much cheaper. I see there is also a Kindle edition now.

[UrbanSue]

I read and reread Liping Ma as needed -- her first chapter is on subtraction. Her ideas/SM conceptual approach work beautifully with Miquon and Cuisenaire rods. One reason I'm bringing up Miquon again is that you said your son is bright at numbers. Miquon encourages kids to explore at their own pace and might be a good fit. A LOT of people here use Miquon with SM -- I am a late convert, wish I'd known about it sooner.

 

And, like others, I would highly recommend the Liping Ma book:

 

http://www.amazon.co...words=liping ma

 

If you are buying the book, check out Abebooks or wherever you get used books -- much cheaper. I see there is also a Kindle edition now.

 

 

Also the older editions are just as good and also cheaper.

[talk2ham.1]

Guys, all of this is so helpful both with making me feel that it is normal and that it's surmountable. I'll be looking up both Miquon and Mammoth. Maybe I'll get both. Liping's book is now on my list too. I have the RightStart game set and also Activities for AL Abacus which I refer to often. I think I may turn to math games and the abacus for a couple weeks to see if that helps. Also, my FIL is a 12th grade math teacher. His method of teaching mental math was helpful and similar to what some of you suggested: round up or down to the nearest five or ten and then subtract/add accordingly. Either way you are dealing with addends of ten and breaking down the problems from there. At first I was afraid of approaching it with ds from another angle for fear of confusing him further, but now I see that I probably should do that to see if it helps him get it more.

 

One thing I have noticed as I use the abacus though, I think my son is using it as a crutch rather than as a tool. He seems to let the abacus do the thinking for him and does not want to think through what is actually happening to the tens and units as he adds/subtracts. I guess I should make him communicate the steps to me more as he does his work, but I'm not sure how to draw out his words as to what is actually happening in his head. I have a feeling he is, ummm, an "efficient" thinker? He likes to think as little as possible about the problem and let the manipulative do the work for him. Maybe this is o.k. at this age, but how do I make sure he is actually focusing on what's happening with those beads rather than just reading the numbers as they slide across the abacus?

[JessReplanted]

I used SM for 1st grade and part of 2nd with my son, and it was absolutely horrible.

He struggled with math every single day. I stuck with it because it's supposed to be

such a 'great' curriculum, and I thought that one day everything would just click for him.

Finally, after testing just barely at grade level on a standardized test, I chucked it.

 

We have used CLE math ever since, and I LOVE it. It just makes so much more sense.

I wish we had switched sooner.

[nmoira]

Don't drop it, but approach it from a different angle. It is a very important concept.

 

I'm big on concepts, but I don't think it's critical for a first grade student to use the "subtract from a 10 and add the difference to a number 10 less than the one you're given" technique when subtracting across a 10. Some kids just have trouble keeping everything in their head, and the two hops (one to a 10 and then the rest) method requires the child to mentally juggle fewer numbers even though there's technically an extra step.

[Alice]

I have a first grader also. We hit the same roadblock at the same point, complete with tears a few months ago. What worked for us was to just kind of stop and do other stuff. I found that for my son he benefited from reviewing “making 10†and number bonds and his basic addition/subtraction facts. He knew them but not as well as he could have and so when it came to doing the bigger numbers he was getting bogged down. We played a lot of games and skipped ahead to the “fun chapters†like time and shapes. We got fun math books out of the library and just kind of parked for awhile. Then we went back to it a few weeks later and used a lot of the things mentioned here, like unit cubes and manipulatives. Something clicked along the way. I think mostly it was just a little brain maturing and maybe stepping away from what was causing him stress.

 

I also have an older son and we’ve used Singapore since the beginning. I love the curriculum and see a lot of benefit to teaching things their way. That said, often my kids will do it their own way and that’s fine. I usually make them explain to me how they are doing the problem at least once so that I know they really understand it. And I’ll make sure they will understand the other way. Then they can do it however they want as far as I am concerned.

[Catherine]

We made the move to Rightstart with one child at around this age and RS teaches several different approaches to the concept of place value, subtraction, and addition. For my child, who has real difficulty keeping a lot in his head at once, it was extremely frustrating and challenging. I also knew that for him, mental math was going to be very important, because he makes SO MANY errors when he writes things down.

 

We used games, the abacus, reviewed the methods and lessons many times. I don't think he is unusual in that it took several re-teaches for him to fully own all of the methods. But wow-at 11 now, he has a deep grasp of math concepts, of place value, distribution, and he can mentally calculate very quickly. It was definitely worth it.

 

I think the place value understanding solves, or prevents, so many future problems. It is totally worth getting it right at the beginning.

 

I would also encourage you to skip over frustrating sections and move the order of topics around when the child is "stuck." Come back to it when the bad memories have faded LOL.

[Monica_in_Switzerland]

Sorry, haven't read all the replies, so I hope I'm not repeating.

 

What manipulatives are you using? Definitely try either base ten blocks, Cuisinaire rods, or both. Let your son use manipulatives FOR AS LONG AS IT TAKES until he gets it.

25+6 would look like 2 tens and 5 ones, then add in the 6 ones. Trade ten of the ones for a ten stick. Keep doing with manipulatives until this all makes sense to him. Younger kids need physical manipulatives, as the symbolic math is very abstract.

 

Also, look at the videos on Educationunboxed.com.

[Catherine]

 

One thing I have noticed as I use the abacus though, I think my son is using it as a crutch rather than as a tool. He seems to let the abacus do the thinking for him and does not want to think through what is actually happening to the tens and units as he adds/subtracts. I guess I should make him communicate the steps to me more as he does his work, but I'm not sure how to draw out his words as to what is actually happening in his head. I have a feeling he is, ummm, an "efficient" thinker? He likes to think as little as possible about the problem and let the manipulative do the work for him. Maybe this is o.k. at this age, but how do I make sure he is actually focusing on what's happening with those beads rather than just reading the numbers as they slide across the abacus?

 

He is using it as a crutch because he has not yet internalized the algorithm and memorized the facts or the ways of finding answers. RS encourages teachers to allow use of the abacus and other "crutches" like multiplication tables for as long as the student perceives the need for them.

 

At first I was a bit worried that my ds seemed to need these types of crutches for much longer than I thought he should. But what I do know is that now that he's finally, at 11, moved away from some of them, he really understands math far, far better than my older sons, who were math whizzes and well ahead of grade level in math.

[LittleIzumi]

A LOT of people hit a wall at that point in Singapore. We did. We tried coming back months later and it still was too much of a conceptual leap. We ended up switching to MEP and Miquon and are sticking with that.

[nmoira]

A LOT of people hit a wall at that point in Singapore. We did. We tried coming back months later and it still was too much of a conceptual leap. We ended up switching to MEP and Miquon and are sticking with that.

 

 

DD the Younger is fine with concepts, but has to work hard to *do* the mental math. MEP is a great fit because she has been able to progress conceptually as she works to get better with the calculations. Now that she has moved into the introduction of pen and paper algorithms (Y3b), she's starting to see that effort pay off, and we've moved her drill/practice entirely to a nifty app called Mathemagica.

[Peplophoros]

Are you using the HIG? I didn't with my first and we hit some walls that definitely would not have been so hard if I had followed the HIG closely instead of ramming it down my ds's throat all at once. Oops! Lesson learned.

[talk2ham.1]

Are you using the HIG? I didn't with my first and we hit some walls that definitely would not have been so hard if I had followed the HIG closely instead of ramming it down my ds's throat all at once. Oops! Lesson learned.

 

What is the HIG?

[LittleIzumi]

What is the HIG?

 

Home Instructor's Guide for each level of Singapore.

[Guest Chip201]

To improve mental math you could try: www.calculationrankings.com

 

Regards,

 

Chip

[LittleIzumi]

Guys, all of this is so helpful both with making me feel that it is normal and that it's surmountable. I'll be looking up both Miquon and Mammoth. Maybe I'll get both. Liping's book is now on my list too. I have the RightStart game set and also Activities for AL Abacus which I refer to often. I think I may turn to math games and the abacus for a couple weeks to see if that helps. Also, my FIL is a 12th grade math teacher. His method of teaching mental math was helpful and similar to what some of you suggested: round up or down to the nearest five or ten and then subtract/add accordingly. Either way you are dealing with addends of ten and breaking down the problems from there. At first I was afraid of approaching it with ds from another angle for fear of confusing him further, but now I see that I probably should do that to see if it helps him get it more.

 

One thing I have noticed as I use the abacus though, I think my son is using it as a crutch rather than as a tool. He seems to let the abacus do the thinking for him and does not want to think through what is actually happening to the tens and units as he adds/subtracts. I guess I should make him communicate the steps to me more as he does his work, but I'm not sure how to draw out his words as to what is actually happening in his head. I have a feeling he is, ummm, an "efficient" thinker? He likes to think as little as possible about the problem and let the manipulative do the work for him. Maybe this is o.k. at this age, but how do I make sure he is actually focusing on what's happening with those beads rather than just reading the numbers as they slide across the abacus?

 

You can have him teach YOU how to do it sometimes. That will ensure he is actually understanding what is going on.

[talk2ham.1]

Littlelzumi, I didn't even know there was an HIG. I'll check it out. I have just been using the text books and work books. I love the idea of having him teach me the problems. That would make him apply his understanding at the same time as showing what he knows. Thanks!

[matrips]

I used to use old egg cartons (cut down to 10 egg holes) when we started with that part of SM. It provided a great visual. So for that problem, we'd put 24 little counting bears in three egg cartons, and try to take 9 away. You could see that you had to take the 9 from a carton with 10 bears to have enough. There was one left over in that, plus a carton of 10 and a carton of 6. I thought I got that idea from the home instructors guide. It worked great for them. And I am so glad we did not skip over that part or jump to the borrowing method I knew. We just finished up 3B and the foundation laid in SM 1 has been incredibly helpful over time. Take your time with it. Use all the tricks in the HIG until he can really see it; it really is worth it (IMO).