Mental Math: Singapore, other?

[Just Robyn]

My ds in first grade will.not.stop.counting when he does addition, even *very* simple problems like 4+2. We do an oral drill every day from Calculadders (rather than writing them out), plus a sheet from Math Mammoth, plus McRuffy, which usually includes addition practice on the page. My older ds stopped counting much earlier. Perhaps it's just a matter of time, but I'm not sure I want to wait and find out in case I find out he's stuck trying to memorize addition into the third grade.

 

Some background:

 

We used Saxon in the past and will not go back to it. It caused way too much unhappiness around here.

 

I ordered one level of Singapore Math once, looked it over, gave it a try and decided there isn't enough in the HIG, but I'd be willing to try it again if it's what this child needs. *sigh*

 

We haven't done much in the way of games and such recommended in MM, so I do plan to take a look at those tomorrow while I'm at work and see if some of those look like they will help - like Making Tens, that should help.

[Farrar]

My kids also did this longer than I thought they would and still occasionally do it, but have been slowly growing out of it. I've found that playing games is the best way to practice this because the kids just have to do it a lot in order to play the game. We especially like Rat-a-Tat-Cat, Sleeping Queens (it says age 8+ on the box, but it's fine for age 5 or 6+, IMO) and Knock Out, all of which allow kids to practice simple addition (Sleeping Queens also has you practicing counting by 5's and 10's or adding 5's and 10's to get your score).

[Satori]

:iagree:Those card games are fun and easy way to practice math without realizing it.

 

I don't know if you're asking for a good math program at this age, but we for K-1, we are using RightStart math. It really does a great job with the mental math in that you are not counting on your fingers from the very start. I guess it is the "right" start, hehe. You think of numbers in groups of 5s and 10s, and use abacus, your fingers, tally marks, etc... to emphasize this concept until you really do think of numbers as these chunks. Their games like Go To the Dump are addicting to children and have them memorize their sums to 10. Overall, very great introductory experience to mental math! They've never had my daughter "count on" like some programs do. We've only made it halfway through B so far, it is more parent-intensive than I want at this point.

 

We are moving to Singapore 1B next week as our main program. I looked through the entire book thoroughly yesterday and think it is a great choice to move on to the next level of mental math. I didn't like their Kindergarten Earlybird, and after looking through Singapore Year 1, I'm really glad we started with RightStart. It doesn't give the same over-and-over drilling of the chunks of 5/10 as RightStart seems to do. But Singapore goes on to mental math addition and subtraction very nicely. I hope to continue with RightStart a few times a week to finish level B. There's so many great math curriculums to choose from, it's hard to narrow it down, but I think this combo is great for the mental math thinking.

[Spy Car]

Learning "re-grouping" skills pays huge dividends over either counting or memorizing.

 

The advantage of this approach becomes more and more apparent as you move up. Re-grouping skills "scale up" as the child encounters increasingly difficult arithmetic problems and learn strategies for solving problems in their heads rather than being forced to pencil and paper, or *gasp* a calculator.

 

The problems with counting are obvious, but rote memory of "math facts" without solid regrouping skills is a dead-end too when it comes to mental math. Very few people can subtract or do multi-digit sums in the heads using the standard algorithm technique of column addition or subtraction (or multiplication).

 

So it is a very good idea to find a way to build those skills.

 

We spend inordinate amounts of time walking through sums like 8+7=15 as a re-grouping exercise where 8 needs 2 to become a 10, the 7 becomes a 5 after giving 2 to the 8, and you now have 1-10 and 5-Units, therefore 15.

 

This can be about as much fun as the "sounding out" phase of early phonics and reading. But it pays off in the same way.

 

RS games are helpful. The "classic" Go to the Dump helps children master pairs that make 10. Other games and activities can do the same thing. It is a fundamental skill.

 

Knowing we would be using a whole-parts math approach that felts on re-grouping we started with Miquon and Cuisenaire Rods. A child (essentially) can't count using these and gets used to seeing values a parts and wholes that can be re-combined.

 

My impression is MM is seeking to teach these same re-grouping skills that one finds in Singapore math of re-grouping to Tens. RS adds a secondary re-grouping to 5s strategy. Whatever you use try to build these skills. If Calculadders is trying to teach "math facts" through "memorization" I would humbly suggest putting it away for future use as "review." And to instead have the child talk though their re-grouping strategy for a good number of problems everyday until you are satisfied they have it (while knowing more of this kind of thing is coming). It is a "slower" and arguably "more complicated" method up front, but it pays off in a huge way!

 

The analogy I'd imperfect but the comparison with memorizing "sight words" vs learning phonics is not that different than memorizing "math facts" vs learning re-grouping skills. Either way we want fluency as an end, and those learning math through re-grouping do (and need to) develop automaticity and sped with those "facts" but trying to leap the hard work of working the re-grouping strategies (in a context where place value is well understood) is like learning reading via sight words. It may seem more "efficient" in the short-run, bit it sets up long-term problems.

 

There used to be an ad for Fram Oil Filters. The tag line was: You can pay me now, or you can pay me later.

 

Glad you asked? :D

 

Bill

[mom2bee]

I'm having the same problem with my 3rd grade student in math...my 1st grade student isn't even at the point where he can have this problem! I realized that none of these kids know their number bonds or even fact families. Lets not even talk about Multiplication tables...

 

I've written up some basic worksheets that I'm going to photocopy and use with them starting in March. I'm making a lot of simple manipulatives for this.

 

We're going to do some oral+manipulative work starting in March and lots of skip counting and number reading. I'm hoping that 60 straight days of daily practice will be enough to get my 3rd and 1st grader up to snuff. I'm allowing 75 days for the 5yo.

 

In April we're going to start timed pen and pencil drills for number bonds, fact families, etc. I dont think I can take another year of their current math behavior. I'm all ears for any and every good idea someone wants to toss my way.

[Spy Car]

I'm having the same problem with my 3rd grade student in math...my 1st grade student isn't even at the point where he can have this problem! I realized that none of these kids know their number bonds or even fact families. Lets not even talk about Multiplication tables...

 

I've written up some basic worksheets that I'm going to photocopy and use with them starting in March. I'm making a lot of simple manipulatives for this.

 

We're going to do some oral+manipulative work starting in March and lots of skip counting and number reading. I'm hoping that 60 straight days of daily practice will be enough to get my 3rd and 1st grader up to snuff. I'm allowing 75 days for the 5yo.

 

In April we're going to start timed pen and pencil drills for number bonds, fact families, etc. I dont think I can take another year of their current math behavior. I'm all ears for any and every good idea someone wants to toss my way.

 

An arbitrary number of days being allotted to learning a particular skill is a terrible idea. The best one can do is to commit oneselves to consistent effort and to try to understand the individual child. Pondering how they understand (or fail to understand) while seeking to break any "semantic" log-jams (a big problem with young children), and attempting to hit the same skills from a multiplicity of different angles.

 

Time tests on math facts are an equally dreadful idea. Those who can pass them with "flying colors" don't need them, and those who can't are likely to suffer from "math anxiety" as a result. Patience is a virtue when it comes to teaching children.

 

Bill

Edited February 27, 2011 by Spy Car

[siloam]

Pretty much what Bill said.

 

My kids are all dyslexic to a certain degree, and it spills into math. They have a hard time memorizing facts, especially when there doesn't seem to be any applicable value.

 

The RS math game gave the a reason to learn their math facts and that was after flash cards, calculaders and a year of Flashmaster failed.

 

Regrouping allows the child to take any problem and make it one they can do. For example my 4th grader was having the worst time converting feet to inches. Each time she tried she was making a different multiplication or addition error. :001_huh: About the third time through I called her over and rewrote the problem as 16x10 and 16x2 instead of 16x12. That worked. She even did it in her head and gave me the answer standing right there. Some kids naturally regroup, and some are very concrete and you have to not only teach them but give them permission to use it. Trust me, I am one of those concrete kids, who, by the way, counted in her fingers till she was about 30 and finally learned based 10 math. :D

 

Heather

[Cindyz]

We completed Singapore 1A and MM 1A and I have to be honest and say that I don't think he would have learned regrouping as well as he has from MM alone. The Singapore HIG are very helpful and show you exactly how to teach it and provide reinforcement exercises as well as mental math sheets. I got worried whenever they showed the number line that my son would want to fall back to this and start counting, but regrouping was already entrenched so he didn't even bother with the number lines. Now in 1B, I worry whenever MM wants him to work a math problem in a column because as it stands, he doesn't have to write anything down to figure out the problems we've encountered. MM wants him to write the answer in the ones column first (when working in columns) and then write the tens and he just doesn't think that way. He wants to just write the final answer beginning with the tens. I do see that in a few more pages, Singapore introduces the columns as well, so I'll just sit back and go with the flow. :D

 

I guess what I'm saying is that if you want your child to learn mental math, and really be good at it, I'd go with the Singapore approach. The new HIGs are really good at telling you exactly what to do and how to teach it.

[Cindyz]

This is the HIG you want if you decide to do Singapore.

 

 

http://www.singaporemath.com/Primary_Math_Home_Instr_Guide_1A_p/pmstdhig1a.htm

[siloam]

The focus in Singapore is on the mental math. They don't cover place value, and the traditional algorithm for borrowing and carrying till level 3, but instead focuses on mental math and regrouping.

 

Heather

[Just Robyn]

My kids also did this longer than I thought they would and still occasionally do it, but have been slowly growing out of it. I've found that playing games is the best way to practice this because the kids just have to do it a lot in order to play the game. We especially like Rat-a-Tat-Cat, Sleeping Queens (it says age 8+ on the box, but it's fine for age 5 or 6+, IMO) and Knock Out, all of which allow kids to practice simple addition (Sleeping Queens also has you practicing counting by 5's and 10's or adding 5's and 10's to get your score).

 

Thank you. I will look into some of those games. I have seen them, but haven't bought any yet. We do have Zeus on the Loose which I broke back out today and was fun. And I was already hoping to finally spring for the Muggins Math games at the convention this week, so now I have an extra excuse for that one.

 

:iagree:Those card games are fun and easy way to practice math without realizing it.

 

I don't know if you're asking for a good math program at this age, but we for K-1, we are using RightStart math. It really does a great job with the mental math in that you are not counting on your fingers from the very start. I guess it is the "right" start, hehe. You think of numbers in groups of 5s and 10s, and use abacus, your fingers, tally marks, etc... to emphasize this concept until you really do think of numbers as these chunks. Their games like Go To the Dump are addicting to children and have them memorize their sums to 10. Overall, very great introductory experience to mental math! They've never had my daughter "count on" like some programs do. We've only made it halfway through B so far, it is more parent-intensive than I want at this point.

 

We are moving to Singapore 1B next week as our main program. I looked through the entire book thoroughly yesterday and think it is a great choice to move on to the next level of mental math. I didn't like their Kindergarten Earlybird, and after looking through Singapore Year 1, I'm really glad we started with RightStart. It doesn't give the same over-and-over drilling of the chunks of 5/10 as RightStart seems to do. But Singapore goes on to mental math addition and subtraction very nicely. I hope to continue with RightStart a few times a week to finish level B. There's so many great math curriculums to choose from, it's hard to narrow it down, but I think this combo is great for the mental math thinking.

 

I knew RS would come up, and thought afterwards that I should have said from the start that I don't think I can justify *another* huge and expensive math program. Also, we're all so happy with McRuffy for the most part. Singapore is less expensive and seems easier to use a supplement than RS, but I will have to look at the games (again) when I'm at the hs convention. (I hope they'll be there. I forget.)

 

Learning "re-grouping" skills pays huge dividends over either counting or memorizing.

 

The advantage of this approach becomes more and more apparent as you move up. Re-grouping skills "scale up" as the child encounters increasingly difficult arithmetic problems and learn strategies for solving problems in their heads rather than being forced to pencil and paper, or *gasp* a calculator.

 

The problems with counting are obvious, but rote memory of "math facts" without solid regrouping skills is a dead-end too when it comes to mental math. Very few people can subtract or do multi-digit sums in the heads using the standard algorithm technique of column addition or subtraction (or multiplication).

 

So it is a very good idea to find a way to build those skills.

 

We spend inordinate amounts of time walking through sums like 8+7=15 as a re-grouping exercise where 8 needs 2 to become a 10, the 7 becomes a 5 after giving 2 to the 8, and you now have 1-10 and 5-Units, therefore 15.

 

This can be about as much fun as the "sounding out" phase of early phonics and reading. But it pays off in the same way.

 

RS games are helpful. The "classic" Go to the Dump helps children master pairs that make 10. Other games and activities can do the same thing. It is a fundamental skill.

 

Knowing we would be using a whole-parts math approach that felts on re-grouping we started with Miquon and Cuisenaire Rods. A child (essentially) can't count using these and gets used to seeing values a parts and wholes that can be re-combined.

 

My impression is MM is seeking to teach these same re-grouping skills that one finds in Singapore math of re-grouping to Tens. RS adds a secondary re-grouping to 5s strategy. Whatever you use try to build these skills. If Calculadders is trying to teach "math facts" through "memorization" I would humbly suggest putting it away for future use as "review." And to instead have the child talk though their re-grouping strategy for a good number of problems everyday until you are satisfied they have it (while knowing more of this kind of thing is coming). It is a "slower" and arguably "more complicated" method up front, but it pays off in a huge way!

 

The analogy I'd imperfect but the comparison with memorizing "sight words" vs learning phonics is not that different than memorizing "math facts" vs learning re-grouping skills. Either way we want fluency as an end, and those learning math through re-grouping do (and need to) develop automaticity and sped with those "facts" but trying to leap the hard work of working the re-grouping strategies (in a context where place value is well understood) is like learning reading via sight words. It may seem more "efficient" in the short-run, bit it sets up long-term problems.

 

There used to be an ad for Fram Oil Filters. The tag line was: You can pay me now, or you can pay me later.

 

Glad you asked? :D

 

Bill

 

Yes! This is exactly the knock on the head I needed. When we were playing Zeus on the Loose earlier my ds had to add 7 to something like 38 and I had my hands out

 

"See? 7 is just 2 and 5. So what's 38 plus 2? Now what's 40 plus 5?"

 

and I was thinking, this is what is missing. Now I'm here reading your post and you're saying,

 

"Hey, dummy! This is what is missing!"

 

Ok, you didn't say exactly that, but maybe you should have. Goodbye Calculadders. He hates it anyway, and it doesn't seem to be working either, other than to show him that math is commutative, which I think he has figured out to death and can move on.

 

An arbitrary number of days being allotted to learning a particular skill is a terrible idea. The best one can do is to commit oneselves to consistent effort and to try to understand the individual child. Pondering how they understand (or fail to understand) while seeking to break any "semantic" log-jams (a big problem with young children), and attempting to hit the same skills from a multiplicity of different angles.

 

Time tests on math facts are an equally dreadful idea. Those who can pass them with "flying colors" don't need them, and those who can't are likely to suffer from "math anxiety" as a result. Patience is a virtue when it comes to teaching children.

 

Bill

 

:iagree: I have tried timed tests with both my older DSs and stopped with both as well. They get so frustrated it's just not worth it and it doesn't seem to help them any.

 

This is the HIG you want if you decide to do Singapore.

 

 

http://www.singaporemath.com/Primary_Math_Home_Instr_Guide_1A_p/pmstdhig1a.htm

 

Thank you. When I bought SM before I found the HIG to not be very helpful. I remember reading a thread here about how one of the HIGs is the helpful one and don't get the "wrong" one and thinking, I bet a got the wrong one. Of course, I can't remember which one I got, so I don't know if that's true or not.

 

 

Ok, well I still don't know *exactly* what I'm going to do, but I'm on the right track I think. Thank you all!

 

ETA: Ok. I've decided. I'm going to (assuming it's available) pick up SM from the RR stand at the convention this weekend.

Edited March 1, 2011 by crstarlette

[FO4UR]

Cuisenaire Rods.

 

Allow them to use Cuisenaire Rods to find the answers for as long as they need, and those facts will be a permanent fixture without drill.

 

If I notice a specific problem, I come up with a little activity that I lead to teach the missing link. One very effective activity for learning those facts is using 1cm graph paper and coloring rod pictures to match math sentences. Build it with the rods & color & write out the sentences (or dictate to mommy). Do this a *little* bit each day.

 

Put out an = sign (on a 3x5 card) and put two rods on either side and have her make them =. 10 on side and a 3 on the other...she has to put a 7 with the 3 to make them =. For teaching regrouping, modify and have one side be a 7+8 and the other side be 10 + ?.

 

Put out a rod, and a shorter rod on top of it and ask "who is missing?" You can extend this activity in so many ways.

 

Let your dc simply play with C rods...build a tower, house, stick people, a track for matchbox cars, whatever...this builds an intuitive knowing of the values/relationships. My 4yo knows that he needs 2 red to equal a purple even though we haven't started even a hint of formal math...he knows b/c when he likes things to be symmetric when he builds things.

 

:iagree:with Bill on math. Take the time to struggle through 8+7 now. It's not just knowing 8+7, it's the process of figuring these things out and mentally working to own it. I'd rather my dc do 1 of these problems and REALLY understand how to figure it out next time, than a whole page of rote memory.

[poetic license]

I love miquon (cuisinaire rod approach) for this type of thing. You can't count, you learn to identify numbers as whole pieces. Also agree with the approach Bill mentioned--I think that is one of the missing pieces in US math teaching today. Although I would add that it helps for the child to be "fluent" in the 1-10 sums, then you can essentially use the regrouping technique to add anything after that.

 

I also use fingers on an informal basis with DS to help him see the numbers as groups. For example, when you are doing 7+3, seeing it on the fingers reflexively shows you the answer without having to count.

[StephanieZ]

FWIW, I don't rush the kids on counting and/or using manipulatives. In fact, I encourage them to use beans/counters/whatever whenever they feel like it. . . they have all dropped them by the time they are doing 2nd grade math or so. Meanwhile, making it concrete with manipulatives (and/or counting on fingers) just makes perfect sense and works great.

 

No hurry, no worry. . .

 

(Of course, keep doing fact drills until those facts eventually gel.)

 

Also, I use (and love) SM, but actually it teaches 'counting on' as a primary technique for addition. :)

[Just Robyn]

Also, I use (and love) SM, but actually it teaches 'counting on' as a primary technique for addition. :)

 

Gah! Don't tell me that! Okay, I guess I'll be *looking* at SM - and some C rod books, and RS games - and wel'l just see. sigh.

[Spy Car]

The primary technique of addition in Primary Mathematics is "re-grouping."

 

This is reinforce though number-bonds, and then teaching on-going strategies for mental math. it also teaches the standard algorithm (column addition for addition) and other methods, but re-grouping is a primary and fundamental part of the Singapore math program, and it is taught well IMO.

 

I do wish that their Pre-K and K materials (and ongoing) used Cuisenaire Rods as the manipulative. They missed the boat here, as C Rods are really "concrete number bonds" and resemble the whole-parts representations of the bar diagram method. In part this is why many find such utility in combining Miquon and Singapore. I just don't know how easy it is to "go back."

 

Bill

[Just Robyn]

The primary technique of addition in Primary Mathematics is "re-grouping."

 

This is reinforce though number-bonds, and then teaching on-going strategies for mental math. it also teaches the standard algorithm (column addition for addition) and other methods, but re-grouping is a primary and fundamental part of the Singapore math program, and it is taught well IMO.

 

I do wish that their Pre-K and K materials (and ongoing) used Cuisenaire Rods as the manipulative. They missed the boat here, as C Rods are really "concrete number bonds" and resemble the whole-parts representations of the bar diagram method. In part this is why many find such utility in combining Miquon and Singapore. I just don't know how easy it is to "go back."

 

Bill

 

Well that's something to stew on.

 

FWIW, most of those techniques are things that came to me naturally, without explicit instruction. I was taught to count on, do column addition, etc. and sometimes I count on in my head (or on my fingers), and sometimes I do number bonds. Though they were never taught, they just seemed the obvious way to do it. I would say the same about some of the methods taught in reform math.

 

Now I'm going to be up all night thinking about math.

[Spy Car]

Well that's something to stew on.

 

FWIW, most of those techniques are things that came to me naturally, without explicit instruction. I was taught to count on, do column addition, etc. and sometimes I count on in my head (or on my fingers), and sometimes I do number bonds. Though they were never taught, they just seemed the obvious way to do it. I would say the same about some of the methods taught in reform math.

 

Now I'm going to be up all night thinking about math.

 

By "go back" I was thinking particularly of manipulatives. We used them heavily at the outset, and now use them mostly when introducing a new concept or when there is some sort of confusion to overcome. They easy to use when needed with my son because they were his "friends" starting out and using them is "natural".

 

But some kids, especially when introduced to manipulatives when they have moved past the learning stage where they "need" them find them "baby-ish" or otherwise reject them. You never know though. These things can go either way.

 

Bill

[Just Robyn]

By "go back" I was thinking particularly of manipulatives. We used them heavily at the outset, and now use them mostly when introducing a new concept or when there is some sort of confusion to overcome. They easy to use when needed with my son because they were his "friends" starting out and using them is "natural".

 

But some kids, especially when introduced to manipulatives when they have moved past the learning stage where they "need" them find them "baby-ish" or otherwise reject them. You never know though. These things can go either way.

 

Bill

 

Oh, good. That's much less stressful than how I was taking it. I was thinking of doing just a few C Rod activities per day when we would have done Calculadders. I don't think he'll protest, especially if he knows what it's replacing. :D

[Spy Car]

Oh, good. That's much less stressful than how I was taking it. I was thinking of doing just a few C Rod activities per day when we would have done Calculadders. I don't think he'll protest, especially if he knows what it's replacing. :D

 

I hear you talking :D

 

As to "going back" and working on the re-grouping skills, that IMNSHO is essential.

 

Best wishes!

 

Bill

[poetic license]

Oh, good. That's much less stressful than how I was taking it. I was thinking of doing just a few C Rod activities per day when we would have done Calculadders. I don't think he'll protest, especially if he knows what it's replacing. :D

 

I don't think a first grader would mind going to C rods; he'll probably find it fun! Good luck! I think this age is far from being too late, they pick up so quick at that age. And the way that they pick up the concepts with C rods is so painless and fun. It helps to make number sense intuitive.

[anabelneri]

My daughter was counting on her fingers far too much to my liking, and we were using Singapore at the time. We'd used their Early Bird for K, and were in year 1 when I finally called a halt to it. We switched to Right Start, and it was exactly what she needed. She learned a TON, and now has a lot of mental math strategies at her disposal. She hated Right Start's presentation style, though, so we switched again, this time to MEP. MEP has been great, with a clear emphasis on mental math.

 

So what we're using now is MEP with the "Activities for the AlAbacus" book for helpful ideas and teaching methods. Now and then I'll pull out the RS games, but at this point (halfway through Year 2) I feel like she gets plenty of math each day just with our usual math lesson, and she's getting faster and more accurate as the weeks go by.

 

:)

[mystika1]

Hi,

If you really like the idea of RS but don't like the price then Activities for the AlAbacus may be your best bet. It is RS without the script. Does your child respond well to manipulatives or an abacus? Mine hated the abacus cause she said it was for babies. I think it is great but... this kid is super hard headed.:001_huh: The glazed over look when I pulled it out made me feel like I may as well be talking to the cat instead of her!:D MUS blocks had the same warm reception. :tongue_smilie:

 

That said....My dd was the same way as far as counting instead of regrouping. We have tried alot of math programs...poor baby is only 8 but we have used Saxon, RS, MUS, MM and finally settled in with SM very nicely. Honestly...It may be a maturity issue but she really has shown great understanding of math now that we are using SM. I have no doubt that the other programs we used are just as good but my dd needed the presentation method of SM to really have it stick. I can now drill math facts with 9's Down Math Facts. She actually talks outloud while she is working through the drill sheets saying things like... 8 wants to be a 10 so it takes 2 away from "such and such" number. I think drill work is good when the child has established regrouping habits.

 

I think that practice using material that the child understands will get the job done. I am sold on SM because it is the only curriculum that didn't produce tears in our house...she gets it. None of the other math programs we used ever clicked.... but what works great for one child may be terrible for another. MM may be working great and they just need time and practice.

 

HTH,

 

Penny