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Is counting a crutch in math? Looking at RS-B.


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I am just interested in hearing your thoughts on whether, as Right Start claims, counting is not a good math strategy to teach young children. In reading the sample lessons with introduction to the program on the Right Start website, they say that counting is slow, inaccurate, & interferes with learning place value and developing number sense. How can this be, since many if not nearly all math programs use counting in the very beginning, and children do manage to learn number sense in other ways? Do you find it advantageous to teach counting at the very beginning, or the opposite, to avoid it as the RS program would have you doing? If you use and like Right Start, tell me a little bit more about it. Thanks! 

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Hopefully you will get some suggestions from parents who have used multiple levels with multiple children, but I can tell you my experience...

We used RS A and then RS B, a well as Japanese Soroban (abacus) which really discourage counting. It has really worked well, and in the times when dd (who is 4 but radically advanced in math, take it for what you will) tried to resort to counting it was problematic. Of course she CAN, but it is inefficient and not nearly as accurate!

If they can learn to visualize the abacus in their head (as in RS or Soroban) you will be amazed at how accurate they are and how much easier it is to 'visualize' math facts. In fact, when dd doesn't immediately recall an answer she closes her eyes.

I would not go so far as to say it is the wrong way, to count. I think it is an important skill and demonstrates understanding. But I now think there is a more efficient way:)

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Hopefully you will get some suggestions from parents who have used multiple levels with multiple children, but I can tell you my experience...

We used RS A and then RS B, a well as Japanese Soroban (abacus) which really discourage counting. It has really worked well, and in the times when dd (who is 4 but radically advanced in math, take it for what you will) tried to resort to counting it was problematic. Of course she CAN, but it is inefficient and not nearly as accurate!

If they can learn to visualize the abacus in their head (as in RS or Soroban) you will be amazed at how accurate they are and how much easier it is to 'visualize' math facts. In fact, when dd doesn't immediately recall an answer she closes her eyes.

I would not go so far as to say it is the wrong way, to count. I think it is an important skill and demonstrates understanding. But I now think there is a more efficient way:)

 

I can see you have alot of math on your child's plate (down below your post)... how was transferring from RS to Singapore? Does BA complement SM well for your daughter? I was curious about those three curricula especially. Thanks for your feedback about RS.

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American math programs do use counting at first. Asian math programs do not. As for which is better? Eh, I think that can be a matter of opinion rather than fact. But I will say that I *am* a "math-y" person as is my husband, who majored in math. We love RightStart because it teaches math in the way that almost every math-y person eventually figures out how to do it on their own - by grouping in 5s and 10s (and later by 100s, 1000s, etc). This grouping makes mental math so easy that it took me years to understand why everyone couldn't just do it; without explicit instruction, the math-y people figure it out naturally and the non-math-y people never do. I'm happy to teach my daughter these methods from the start and save her having to puzzle them out later.

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I wish I had been taught to visualize math instead of one on one counting.  And I wish I had known to teach math that way with my kids.  DD13 has learning challenges including with math.  We finally went back to the very basics of math, including subitization and visualization.  It has helped in ways that basic counting never did.  And I am finally able to visualize math much better myself.

 

Is counting "bad"?  I don't think I would say that.  But it DOES seem less efficient and can become a crutch that is hard to break away from, IMHO.

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I agree with the above! It's very useful in learning the math facts!

 

For example, to learn how to add 9 to a number less than 10, say 7, you can use RS's 2-Fives strategy. 

 

To teach this strategy, you enter 9 beads on the top wire and 7 on the second wire. 

 

You already know from previous lessons that the 9 is made up of 5 blue beads and 4 yellow beads, without counting them. The 7, below the 9, is made up of 5 blue beads and 2 yellow beads.

 

From just glancing at the abacus, you can see that the two sets of 5 blue beads (one set on top of the other) make up 10 and the 4 + 2 yellow beads make 6. 10 + 6 = 16

 

This is the method DD prefers. Even when adding without an abacus, she will verbalize the process, stating that the 9 has one five; the 7 has another five and that leaves 6, so 10 + 6 = 16.

 

It sounds so complicated, but it isn't, if the student learns first to visualize quickly what a 10 looks like. 

 

The way RS teaches 10 starts with (in RS A) training the student to see 1 object and identifying it automatically as 1. 2 objects, as 2. 3 objects, as 3. Up to 5. You practice seeing 5 and identifying it as 5, as well as the other lower numbers using different objects: fingers, tally sticks, beads. You teach the student to internalize what 5 looks like by flashing 2 fingers or showing 3 tally sticks quickly, then covering them. 

 

Then once 5 is learned, you teach them through a cheesy but oh, so special song, Yellow is the Sun. We love it in our house!

 

6 is 5 and 1.

7 is 5 and 2.

8 is 5 and 3.

9 is 5 and 4.

10 is 5 and 5.

 

Once these are internalized, you have taught your child that numbers are 3-dimensional. They have meaning; they're flexible, to be manipulated in different ways. 

 

Also, you have taught your child (without even meaning to!) that 9 is not only 5 blue beads and 4 yellow ones, but it's also 10 beads entered with one yellow bead left all by its lonesome on the other end of the wire. 8 is not only 5 and 3; it is also 10 minus 2!

 

They learn this before they ever learn the word subtraction!

 

When my kids are first learning all this, they do better when I personalize it. If I ask, what is 5 + 1, they may or may not get it (when they're first learning!) But if I say, you have 5 candies and I give you 1 more, how many do you have now? Instantly, they can visualize it and say 6. To me, this tells me (a stay-at-home housewife, who hasn't been a student for over a decade! IOW take this all with a grain-o of salt-o!) that kids learn well when numbers have meaning, depth. 

 

Why is being able to visualize amounts/numbers better than counting? Hmmm…counting is 2-dimensional…it's a flat number line taped to the student's desk that goes all the way to the left and all the way to the right. Which is cool. So I can learn that 9 + 7 = 9 (9+0), 10 (9+1), 11 (9+2), 12 (9+3), 13 (9+4), 14 (9+5), 15 (9+6), 16 (9+7)! It's not necessarily worse. It might be quicker to visualize than to count. But it might just come down to how the child thinks. 

 

As you can tell, I love RS. I am sure other programs do this, but I've only bought this one :)

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Oh, and not who you asked the question of, but here's my take... Working between RightStart and Singapore is easy-peasy. They both use similar methods. I haven't used Beast Academy, as DD isn't ready for it. We supplement with Dreambox, which works extremely well with Asian methods as it uses non-counting methods, especially an abacus. Other resources we use are the Time-Life I Love Math series which does applied math, Penrose the Mathematical Cat which often includes advanced mathematical concepts, and Stuart J. Murphy's MathStart books which cover basic concepts in a child-friendly story format. None of those three "line up" but they all provide math enrichment which my daughter enjoys.

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I can see you have alot of math on your child's plate (down below your post)... how was transferring from RS to Singapore? Does BA complement SM well for your daughter? I was curious about those three curricula especially. Thanks for your feedback about RS.

The only problem transitioning from RS B to Singapore was that RSB did not directly cover subtraction. However, we also used the games and Activities for the AL Abacus as I wanted to teach subtraction in the RS way, simultaneously.

 

That being said, I do not have one of those kids who needs to be accelerated by say, taking the end of chapter reviews. She honestly LIKED doing all the problems. So we started with Singapore 1A and she worked her way through all of the books, all of the problems, including some IP and CWP. She just really liked doing them, and because she had covered much of it in RS, she flew through them. In fact, she also went through the book 2+2 doe not equal 5 using both the 'tricks' and then RS or Soroban style as she wanted to and I felt is useful in teaching different methods. Guess what was more useful? Even though she knew the 'tricks' for say 7+4= 11 and the related fact families (taught in that book to see tem as straight line problems and memorize them as fact families) she still reverts to 'well, 7 + 3 = 10 and 1 more is 11. (I have her use Singapore way during regular math although she also tends to visualize Soroban way)

Honestly, the biggest hurdles are place value and learning the 'Asian' way of grouping and quantifying. RS does an absolutely amazing job of this:)

 

As far as our experience with BA: she loves the comic book style. Because we tend to have several non-linear math threads going and she had already learned her multiplication tables and this beginning division (we treated them simultaneously as she learned them through the visualization/story-based method at multiplication.com long before we were even doing Singapore), the beginning subject matter of BA she was already familiar with. The beauty of BA lies in the increasingly difficult levels of application, patience-stretching, and problem-solving skills. At four, dd still has a hard time with some of that so we treat it as an ongoing process. I am not trying to push her through BA...I want her to develop long-term problem-solving skills and perseverance when the answer doesn't come easily. Much more important.

I hope that helps a bit? I am not sure our process is the process older kids would take, or even different personalities:) but it has this far worked for us. We also have 1 day a week we devote to fun hands on exploratory math (new) or rabbit trails she seized from some of our math readings and she does Hands on Equations for fun (and as a break for mom) one day per week. I don't really care if it goes anywhere but to keep her having fun. There, I can really see the results of SM as she can concentrate on the 'fun' of it and not the operational/computational part!

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That was the part about RS A that I did not like. They were memorizing facts without understanding why 5 and 3 were 8 (how do they know it's 8? You need to count to prove that!). I have taught all of my kids to count. They are all mathy. They all can do mental math just fine. I was taught to count. I naturally group by 5s and 10s and use that for mental math, just like what RS teaches. I'm mathy also.

 

Jackie mentioned above that she preferred to teach her child the strategies so she wouldn't have to figure them out on her own. I actually found the opposite to work better for my mathy children. Puzzling them out on their own makes the techniques stick better for my kids. They do mental math better if they figure out their own strategies instead of being spoonfed strategies to use. Now if the one they've puzzled out is inefficient, I might say, "Here's another way to do it that might be a bit easier," but I don't say their way is wrong and I let them choose which one they want to use. Sometimes my oldest has some oddball methods that work great for him, and my older sister with a degree in applied mathematics says that's the way she would have done it also. :lol: And let's just say it wouldn't be a way RS taught. ;)

 

Maybe, as Jackie says, the non-mathy kids need to be taught those strategies. I could see that being the case. But with my mathy kids, I really prefer to let them puzzle it out on their own and use critical thinking to find the best method. That shows that they really understand the math. While using CLE Math (very traditional), my 7 year old has often spouted out some neat way to do something that Singapore or RS would have taught explicitly. When I used Singapore with my oldest, the multiple strategies being forced on him tended to just confuse him. He really did better when he was not taught the strategies but instead allowed to find his own techniques. YMMV, of course! :)

 

Also, Singapore Standards Edition does teach counting just like most math programs. I don't know if they added that in for the American market, or if the original version had it as well (has anyone used the non-American version of K and grade 1?). They teach counting objects before they show the kids grouping objects. They teaching counting up and down before they teach adding/subtracting techniques. Singapore never teaches subsitizing, that I can recall, but I think most people will naturally do it a little bit anyway. I've never seen anyone sit there and count 3 objects past the age of 5. :tongue_smilie:

 

ETA: Another thing is that some kids are not visual thinkers, so they may not do as well picturing 5 and 3 = 8. My 7 year old is visual, and after using C-rods for adding/subtracting (first proving the length of each one before memorizing facts;) ), he would often close his eyes and picture the C-rods when figuring out a fact, until they were memorized. My other two kids aren't visual thinkers. They memorize facts in other ways.

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I think it's very rare that a child will begin RS A without first knowing how to count objects...Counting and one-to-one correspondence start for most kids at least by 3, and RS A isn't started till 4 or (more often) 5, so they understand the numbers referred to throughout the program correspond to the number of objects. I think they mainly are saying that for computation it's a lot more efficient to group and visualize than it is to count on fingers.

 

That was the part about RS A that I did not like. They were memorizing facts without understanding why 5 and 3 were 8 (how do they know it's 8? You need to count to prove that!).

 

RS A actually does show kids what 5 and 3 means in numerous ways, though, through the Alabacus of course, for easy visualization, but also through fingers, tally sticks, groupings of dots and colored tiles. So they can group in their heads and see 8 (and much higher numbers) right away, rather than having to count one by one. They understand the meaning of 8-ness, and 80-ness, and 800-ness. It doesn't mean that they couldn't count beads if they were asked to, but there's no reason for it.

With that said, I wouldn't say one method is necessarily better or more effective than another, but I'm continually astounded by how much my DD has learned from RS at a young age.

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I think it's very rare that a child will begin RS A without first knowing how to count objects...Counting and one-to-one correspondence start for most kids at least by 3, and RS A isn't started till 4 or (more often) 5, so they understand the numbers referred to throughout the program correspond to the number of objects. I think they mainly are saying that for computation it's a lot more efficient to group and visualize than it is to count on fingers.

 

Lol, yes, I can't even imagine starting a formal math program (even something as easy-going as RSA!) if a child wasn't already counting, counting on, and understanding one-to-one correspondence. I guess it would be possible, but why? There are too many fun ways to play an introduce all of that during regular activity to want to try a math program without that level of basic understanding.

 

I totally understand what you are getting at Boscopup. There has to exist an ability to use and demonstrate the ability to use and basic counting and number sense first:)

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I can't even imagine teaching beginning math without counting.  What does that even mean?

My kids learned so much from having a large number line posted on a railing in the kitchen.  They drove matchbox cars on it and counted as they went.  Best "unschooling" investment ever.

 

We used CSMP math, and they learned to count on a calculator from the beginning (0 + 1, then hit equals over and over and over) and 0 + 2 and 0 + 3, etc.  Since they were using a calculator, they could skip count without making mistakes.  It seemed weird at the time, but I did the lessons anyway and turned out to be a valuable learning experience.

 

 

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Some counting methods are better than others.  When one of mine first started learning to add numbers, for examples, he'd count both numbers.  For example, if he saw 3 + 5 he'd count: 1, 2, 3, 4, 5, 6, 7, 8 and get 8.  That's a slow method prone to error.  But if you count on, that's a perfectly decent way of doing it.  So you look at 3 + 5 and think count on from the bigger number.  So 5 is the bigger number.  Count on three.  Six, seven, eight.  Answer is eight.  Or if you learn to regroup to make tens and perform your count on our count down. 

 

I think it's normal and natural to do a lot of counting in the beginning.  And using fingers.  I see nothing wrong with that.  What are the alternatives?  Memorizing the facts?  If you do that without any method of quick calculation, you'll likely forget all the facts a month after you stop using them. 

 

After a few lessons in RS, a child can see 8 beads on an abacus and know without counting that it's 5 and 3, which is 8. They also can see 84 beads on the abacus and know within seconds that it's 50 + 30 + 4=84. Knowing that 5+3=8 isn't memorization in RS, it's visualizing 5 blue beads and 3 yellow beads. There's absolutely nothing wrong with counting to get an answer, and I agree with you that it's natural, it's the way almost all kids learn first. And both ways will get you the same answer, but counting is not necessarily the most efficient way.

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I currently let my 5 year old use (*gasp!*) fingers to add/subtract. He's visualizing just like an abacus. As he learns the fact, he stops using the fingers. It's slower to count on fingers than to just remember the fact. He can immediately tell me that 5 and 3 are 8 without counting all of his fingers. If he is adding 6 and 2 using his fingers, he'll immediately see that 5 and 3 connection and say 8. In the VERY beginning, he did need to count all 8. That was when he was a young 4 maybe? Then he moved to just seeing 5 and 3 are 8, and also being able to count on from 5 to 8. I think that's normal development, and I see nothing wrong with it. Now if the kid continually counts everything to add when they're older, that's a problem, obviously.

 

I just wasn't crazy about RS A. After 11 lessons with my middle son (who is the visual one of the family!), I sold it. He wasn't learning anything from it. He does better with pictures combined with manipulatives, and he also needed one consistent manipulative instead of 10 different manipulatives to do the same thing. His brain does not handle "Let's show you this way and this way and this way and this way all at once." Give him ONE manipulative (C-rods were great for him) and some pictorial examples along with it. He's the same in reading. He doesn't do well with programs that introduce all the phonogram sounds at once. He needs to work on ONE sound at a time, learn to use that, then learn a new sound for that phonogram. He's good at math and good at problem solving. He did really well with Beast Academy 3A and about half of 3B while still doing 2nd grade level CLE (he got bogged down in perfect squares, which was just hitting his developmental wall, understandably). The RS method was just a bad fit for him.

 

My other two kids have not needed manipulatives as much. My oldest only needed them one time, and that was to learn the adding across tens technique. Other than that, he's been pretty anti-manipulative.

 

Anyway, my point of posting in this thread is that I don't think you have to teach the RS way in order to have a child good at mental math. All of my children have good number sense, understanding of place value, and ability to do mental math. They all have their math facts memorized or are working on it and progressing well. They all problem solve well. RS was a bad fit for at least 2 of the 3. I don't know about #3, as he can pretty much learn from anything. Though I will say he's not really been drawn to manipulatives, beyond his fingers, which I sometimes have to encourage him to use (and again, he drops them when he's not needing them anymore, so I'm not at all worried about him doing calculus and still counting on his fingers :lol:). I just don't think you need to be afraid of young children counting, which is completely developmentally appropriate. And yes my kid could count before starting RS A, but he had not learned how to add 5+3=8 at that time. The lessons first taught it via the Yellow is the Sun song, and never in that 11 lessons we did, did they ever suggest counting the 5 and 3 objects to show that it was 8. Not once. They did, however, encourage learning that 5 and 3 were 8 - several times. I DID have my son count them the first time. But that's not what the program said to do. ;)

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That was the part about RS A that I did not like. They were memorizing facts without understanding why 5 and 3 were 8 (how do they know it's 8? You need to count to prove that!). I have taught all of my kids to count. They are all mathy. They all can do mental math just fine. I was taught to count. I naturally group by 5s and 10s and use that for mental math, just like what RS teaches. I'm mathy also.

 

Jackie mentioned above that she preferred to teach her child the strategies so she wouldn't have to figure them out on her own. I actually found the opposite to work better for my mathy children. Puzzling them out on their own makes the techniques stick better for my kids. They do mental math better if they figure out their own strategies instead of being spoonfed strategies to use. Now if the one they've puzzled out is inefficient, I might say, "Here's another way to do it that might be a bit easier," but I don't say their way is wrong and I let them choose which one they want to use. Sometimes my oldest has some oddball methods that work great for him, and my older sister with a degree in applied mathematics says that's the way she would have done it also. :lol: And let's just say it wouldn't be a way RS taught. ;)

 

Maybe, as Jackie says, the non-mathy kids need to be taught those strategies. I could see that being the case. But with my mathy kids, I really prefer to let them puzzle it out on their own and use critical thinking to find the best method. That shows that they really understand the math. While using CLE Math (very traditional), my 7 year old has often spouted out some neat way to do something that Singapore or RS would have taught explicitly. When I used Singapore with my oldest, the multiple strategies being forced on him tended to just confuse him. He really did better when he was not taught the strategies but instead allowed to find his own techniques. YMMV, of course! :)

 

Also, Singapore Standards Edition does teach counting just like most math programs. I don't know if they added that in for the American market, or if the original version had it as well (has anyone used the non-American version of K and grade 1?). They teach counting objects before they show the kids grouping objects. They teaching counting up and down before they teach adding/subtracting techniques. Singapore never teaches subsitizing, that I can recall, but I think most people will naturally do it a little bit anyway. I've never seen anyone sit there and count 3 objects past the age of 5. :tongue_smilie:

 

ETA: Another thing is that some kids are not visual thinkers, so they may not do as well picturing 5 and 3 = 8. My 7 year old is visual, and after using C-rods for adding/subtracting (first proving the length of each one before memorizing facts;) ), he would often close his eyes and picture the C-rods when figuring out a fact, until they were memorized. My other two kids aren't visual thinkers. They memorize facts in other ways.

I really appreciate your perspective. My son likes to "figure it out on his own." My uncle, a chemical engineer and very math-y, said that with every one of his children, if he tried to teach them "his" way of math they would balk, and would prefer to show him how THEY arrived at their own method of finding the answer. The advice he gave me was that with math, after the children learn fundamentals, they can really develop their own way of doing things... even complex algebra, he said, could be solved by letting the kids figure it out with some guidance. You reminded me of what my uncle advised. 

 

Developing fundamentals and acquiring a taste for challenge and independent problem-solving, with out too, too much repetition, is my goal for my 6 yo DS's math education in grade 1. I am inclined to go the Singapore route, with some supplementing, but I sometimes feel sorry to let the chance to do a full curriculum year of RS slip by while my son is still "that age." Or maybe he is quite beyond "that age" and will, like my uncle's kids, balk if I try to train him in an approach of my own choosing? 

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I was always good at mental math. I never fully learned to use a calculator as I didn't need it. I think I also developed tricks on my own. I did not develop the 7+4 is the same as 10+1 methods that RS and Singapore use a lot. When I do math facts, even to this day when checking my son's work I visualize dice/domino patterns up to 6 and cards for 7-9. Using those things was a big influence on how I taught my son. He did very well adding dominos, dice and cards before he learnt to count. Then we taught counting forward and backward and he learnt facts the Jones Genius' dot matrix way. It worked okay. But he wasn't a great counter until he was close to 4. (He is only 4.5 so I was not concerned about it.) And he is now becoming proficient in skip counting.

I think what was hard about counting with my son was that he has weird memory recall issues. Nothing major, but unlike a huge majority of kids he can't learn and recite a slew of nursery rhymes. Despite years of me teaching them to him. I think he can say Twinkle Twinkle Little Star, and oldly parts of the Jaberwocky and the Queen of Hearts. But I don't think he knows much else. I have spent 2 years singing yellow is the sun and he can only say the number portion due to holding his fingers up. Not by learning the song. So likewise counting a slew of numbers was not working for him. Learning number facts by rote was not either. Reading numerals, and seeing the amounts laid out worked. I don't think there is a strict right or wrong way to teach when they are so little. There are just different ways.

RS worked for some, but not for others.

Miquon or the use of C-rods is another method that does not rely on counting in the early stages. I struggle with visualizing it. And my son never really go it. Probably due to my inability to get my head around it.

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Question: how on earth would you stop a little kid from counting? I mean, most kids are starting to count when they are 1 or 2, not when somebody starts actually showing them arithmetic. Or do we value learning to count to such an extent that most every parent automatically pushes it without really thinking about it? 

 

There might be an analogy with learning the alphabet. I read somewhere that it would be better if kids weren't taught the alphabet because 99% of them learn the letter names without learning the letter sounds, and then some of them have problems such as thinking that y makes a w sound. Apparently it would be better if kids learned the first sound of each letter, and the letter names not till much later. So maybe kids would be better at subituzing and grouping if they hadn't had counting drilled in first?

 

Although from what I have read, there is meant to be a 'normal' progression from counting to other strategies as the child matures. So when my just-turned-6yo occasionally counts on because she's forgotten an addition fact, that is OK. But when my 11yo does the same thing, I can safely assume that he is delayed, because he should be past that stage by now.

 

If you did manage to avoid the counting, and your kid has memorized that '5 and 3 is 8', how do you know that they actually understand what that means? 

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That was the part about RS A that I did not like. They were memorizing facts without understanding why 5 and 3 were 8 (how do they know it's 8? You need to count to prove that!). I have taught all of my kids to count. They are all mathy. They all can do mental math just fine. I was taught to count. I naturally group by 5s and 10s and use that for mental math, just like what RS teaches. I'm mathy also.

 

Jackie mentioned above that she preferred to teach her child the strategies so she wouldn't have to figure them out on her own. I actually found the opposite to work better for my mathy children. Puzzling them out on their own makes the techniques stick better for my kids. They do mental math better if they figure out their own strategies instead of being spoonfed strategies to use. Now if the one they've puzzled out is inefficient, I might say, "Here's another way to do it that might be a bit easier," but I don't say their way is wrong and I let them choose which one they want to use. Sometimes my oldest has some oddball methods that work great for him, and my older sister with a degree in applied mathematics says that's the way she would have done it also. :lol: And let's just say it wouldn't be a way RS taught. ;)

 

Maybe, as Jackie says, the non-mathy kids need to be taught those strategies. I could see that being the case. But with my mathy kids, I really prefer to let them puzzle it out on their own and use critical thinking to find the best method. That shows that they really understand the math. While using CLE Math (very traditional), my 7 year old has often spouted out some neat way to do something that Singapore or RS would have taught explicitly. When I used Singapore with my oldest, the multiple strategies being forced on him tended to just confuse him. He really did better when he was not taught the strategies but instead allowed to find his own techniques. YMMV, of course! :)

 

Also, Singapore Standards Edition does teach counting just like most math programs. I don't know if they added that in for the American market, or if the original version had it as well (has anyone used the non-American version of K and grade 1?). They teach counting objects before they show the kids grouping objects. They teaching counting up and down before they teach adding/subtracting techniques. Singapore never teaches subsitizing, that I can recall, but I think most people will naturally do it a little bit anyway. I've never seen anyone sit there and count 3 objects past the age of 5. :tongue_smilie:

 

ETA: Another thing is that some kids are not visual thinkers, so they may not do as well picturing 5 and 3 = 8. My 7 year old is visual, and after using C-rods for adding/subtracting (first proving the length of each one before memorizing facts;) ), he would often close his eyes and picture the C-rods when figuring out a fact, until they were memorized. My other two kids aren't visual thinkers. They memorize facts in other ways.

Yes, yes, yes! This totally describes me, a fairly mathy person. I definitely devised my own strategies as a kid, and I naturally began to think in 5's and 10's. But when we were using Math Mammoth, which teaches a billion ways to do every problem, I could understand why my dd was driven mad by it. That explicit teaching feels like overkill, and it can definitely be confusing. Maybe dd won't be mathy like me, but I'm choosing to trust her mind to work out its own strategies (with suggestions from me when appropriate).

 

This reminds me of when I was teaching LSAT prep classes for Kaplan. Their strategies can be helpful for some people, I guess, but breaking everything down so intricately actually seemed confusing to me. I felt like taking lots of practice tests (which is all I did to prep for the LSAT) was something everyone should certainly do to prepare for the test. But that tedious approach seemed like it would have just confused me if I had prepped that way.

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Question: how on earth would you stop a little kid from counting? I mean, most kids are starting to count when they are 1 or 2, not when somebody starts actually showing them arithmetic. Or do we value learning to count to such an extent that most every parent automatically pushes it without really thinking about it?

 

There might be an analogy with learning the alphabet. I read somewhere that it would be better if kids weren't taught the alphabet because 99% of them learn the letter names without learning the letter sounds, and then some of them have problems such as thinking that y makes a w sound. Apparently it would be better if kids learned the first sound of each letter, and the letter names not till much later. So maybe kids would be better at subituzing and grouping if they hadn't had counting drilled in first?

 

Although from what I have read, there is meant to be a 'normal' progression from counting to other strategies as the child matures. So when my just-turned-6yo occasionally counts on because she's forgotten an addition fact, that is OK. But when my 11yo does the same thing, I can safely assume that he is delayed, because he should be past that stage by now.

 

If you did manage to avoid the counting, and your kid has memorized that '5 and 3 is 8', how do you know that they actually understand what that means?

I purposely avoided counting. It wasn't that hard. We would see three ducks and I would just tell him there were three ducks. I didn't say that there were 1,2,3 ducks. When reading books I didn't count the items. I just pointed out the numeral and I would use my finger to circle all the things and tell him the total amount. Then my son started just telling me how many things there were. Mind you he was 1-3 year old at this point in time.

 

Likewise I would point to letters and I always called them by their sound. I never called them by name. He was a precocious reader. He was reading well by the time he learnt his letter names. I did intend to eventually teach him letter names when we got to spelling, but he learnt them on his own as he had a singing spider that lit up and sang the alphabet when he was about 3.5. We didn't have many other battery operated toys for him to learn counting and letter names from. And we didn't watch TV. I was home with him and I don't have family near by to have taught him.

 

As for knowing what 5+3 was, I had no doubt that he knew it was 8. I would out down a group of 5 things (usually Cheerios) and a group of 3 things and he would push them together and tell me that there were 8. He didn't have to actually count them. In time he could take his wooden numerals and use them instead of manipulatives.

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Wow, you must have done your homework early :) Actually I did the same as you with the letters, but I suppose it never occurred to me to avoid counting. Perhaps because early literacy is given more emphasis than early numeracy, I didn't research how to promote numeracy when my kids were tiny.

 

 

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I've been doing the same thing as Korrale. My son is not yet three and he can identify quantities through ten without counting. He expresses these with his fingers since he doesn't talk well yet. I purchased the Activities for the Al Abacus book so I would know how and what to teach that I would incorporate into play, just the way kids usually learn counting first.

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I would say we are kind of average/ a little bit behind grade level. We are certainly average for depth but probably behind for breadth (we are heading into first grade). He does not know the name of geometrical shapes. We do not play with pattern blocks, never have. We had been unschooling in nature, and reading good books, until we added phonics and penmanship about a year ago. I had no idea what type of math, formal or fun, we might try, and all I wanted was to get to a first-grade reading level by first grade, that I just kept math limited to playing shop with real money, and putting up a big hundred-board on the wall and letting DS study it and count on it and skip down it to add tens. He can add tens; he can figure out what half of 40 or 60 is (and he sort of knows why half of 50 is 25, and of 30 is 15, in the context of money, time and using the 100 board to prove it)... its a process that he has more or less lead himself into. I really want him to still feel that he is somewhat in control of that process as we enter into formal math. I think RS would give him that, so would Singapore. He really likes the hundred board, so maybe a book of hundred-board games for it would get us started. I wish RS were not so expensive and I wish SPM were not so elusive to me! 

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I was always good at mental math. I never fully learned to use a calculator as I didn't need it. I think I also developed tricks on my own. I did not develop the 7+4 is the same as 10+1 methods that RS and Singapore use a lot. When I do math facts, even to this day when checking my son's work I visualize dice/domino patterns up to 6 and cards for 7-9. Using those things was a big influence on how I taught my son. He did very well adding dominos, dice and cards before he learnt to count. Then we taught counting forward and backward and he learnt facts the Jones Genius' dot matrix way. It worked okay. But he wasn't a great counter until he was close to 4. (He is only 4.5 so I was not concerned about it.) And he is now becoming proficient in skip counting.

I think what was hard about counting with my son was that he has weird memory recall issues. Nothing major, but unlike a huge majority of kids he can't learn and recite a slew of nursery rhymes. Despite years of me teaching them to him. I think he can say Twinkle Twinkle Little Star, and oldly parts of the Jaberwocky and the Queen of Hearts. But I don't think he knows much else. I have spent 2 years singing yellow is the sun and he can only say the number portion due to holding his fingers up. Not by learning the song. So likewise counting a slew of numbers was not working for him. Learning number facts by rote was not either. Reading numerals, and seeing the amounts laid out worked. I don't think there is a strict right or wrong way to teach when they are so little. There are just different ways.

RS worked for some, but not for others.

Miquon or the use of C-rods is another method that does not rely on counting in the early stages. I struggle with visualizing it. And my son never really go it. Probably due to my inability to get my head around it.

You know, I am glad you brought up Miquon. I think Miquon might work well if we break the hundred-board into bars (DS loves that hundred board!) But I feel that at age 6, I need to accelerate him by grade level, and I must also say I need something that meets or exceeds common core, since he will be tested at some point in the future (I think 3rd grade in my state, I better look into that!). SO, with Miquon being how it is, I might need to rely on a program by grade level. I might invest in Miquon anyway, however, because I have a baby who will in short time inherit anything his bro doesn't use up in our homeschool : ) 

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I am inclined to lean toward Right Start again because it is paced nicely and now meets or exceeds CC. It is Montessori-inspired which is good to me, and although it has gotten criticism for being teacher-intensive, I feel that that can be beneficial to my late-bloomer son, and if he actually ends up being math-y I can always "allow" him to do another program parallel to it, or move into SM, or MM, or BA... If Singapore didn't seem like such a threshold to cross (for me to have to put the lessons together myself, for my son to have to embrace the workbook approach, etc.) I would be more inclined to go that route, or if I thought my son wouldn't count each picture by ones... I am not the kind of person that wants to have to do the workbook page *for* him just to be efficient, which is a risk I take if we go the SM route. (This would be over with in a heartbeat if the initial RS program cost were not so high).

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Okay, the votes are in... I decided to go with Miquon supplemented with Singapore-style mental math workbooks for first grade. I overrode my desire for CCSS curriculum. I have Math Mammoth as a back-up or for extra practice (it was a little advanced for my DS, and I needed help with using manipulatives, so we shelved it). I am confident that we will be starting first grade on the right foot. I might revisit the RS approach if it seems my DS is not math-y and needs a new approach, but, for now I am confident. Yes! 

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