Does your math whiz think like this?

[*Alyssa*]

I'm feeling perplexed with my son, who is seven years old and a math whiz.  I was wondering if anyone could shed some light on what is going on in his brain.

He does all his math problems backwards, but manages to still get them right most of the time.  He explains everything to me in a very logical fashion and he's completely correct in what he says, but it's just so backwards from how we've all been officially taught how to do math.  Let me give you an example.

Here is an addition problem he did today:

$5.19 + $1.38 = $6.57

When I do a math problem like this, I start in the units (or ones) place and move to the left.  He doesn't.  He starts in the hundreds place and moves to the right, but usually ends up with the right answer.

I don't know how to deal with this.  I've said to him, "Why don't we start in the units place first and move to the left?"  He'll reply, "No, I'd rather start in the hundreds place."   Then I explained to him why we do it my way and that in the future, if he doesn't do it this way, he'll get the answers wrong.  His logical brain says, "If that's true, then why is my way getting the answers right?" :svengo:

Do I let him do math the way it makes sense to him?  (I don't feel comfortable with this.)  Or should I try to get him to do math the "normal" way?  I worry about more advanced math when he'll need to follow a certain method in order to get the answer correct.

Can anyone shed some light on this and put me on the right path to make sure I steer my son in the right direction?

Thanks in advance!  :o

[kiana]

I do addition this way. Mathematically there's no reason you can't. 

 

I'd save the "you need to do it this way" for stuff that's genuinely mathematically wrong, rather than stuff that's just a different approach. 

[CardinalAlt]

There are lots of ways to understand a given problem, not just one right way, and it sounds to me like your son's way reflects understanding rather than just rote memorization of a method or algorithm. Some ways might be more prone to error, it's true... So you can watch for that, you can appreciate with him different ways of solving and explore which one leads to better accuracy versus introducing errors. Working left to right and then regrouping from there actually pretty common, I think, and that underlying math is why the traditional algorithm works...

[*Alyssa*]

I do addition this way. Mathematically there's no reason you can't. 

 

I'd save the "you need to do it this way" for stuff that's genuinely mathematically wrong, rather than stuff that's just a different approach. 

 

I know there isn't any reason why he can't do it the way he is, but I am anxious about what he'll do with more advanced math.  Perhaps you could set my mind at ease on how you did with advanced mathematics in high school and college?

[*Alyssa*]

I think some math programs even teach the way your son does it as a way of doing mental math. 

 

My Eldest did it that way when asked to do mental math, and did it your way if he wrote it down.

 

He has had no problems. 

 

Thanks, Julie, that helps put my mind at ease!

[JustEm]

Most people who are really good at math do it this way in their heads. It is actually faster

[Cosmos]

I know there isn't any reason why he can't do it the way he is, but I am anxious about what he'll do with more advanced math.  Perhaps you could set my mind at ease on how you did with advanced mathematics in high school and college?

 

In advanced math nobody cares how you perform your calculations. It's the reasoning that's important. Now being able to communicate your thinking IS important. So he should be able to explain to you how he did a calculation and later when he moves beyond arithmetic he should be able to explain his methods then too.

[Miss Tick]

That's how I do it in my (engineering) head. When I write it I do it the traditional way. The trick is to be sure he doesn't get caught by problems like, $3.48 + $2.71, where you have to revise your sum as you go. If he can talk you through how he does a problem like that (add the dollars, add the tens, add another dollar, add the units) then he is doing well.

 

I think Kiana teaches math at university level, so she did ok with advanced math. :-)

[JustEm]

I do math the way your son does it and made it through college calculus with no problem.  It is much faster for me to do it that way even when multiplying. I suspect if he works better that way now he'll remain that way and will have no problem in the future.

[*Alyssa*]

Thank you, ladies, you have put my mind at ease!  :o

[kiana]

I know there isn't any reason why he can't do it the way he is, but I am anxious about what he'll do with more advanced math.  Perhaps you could set my mind at ease on how you did with advanced mathematics in high school and college?

 

Well, I have a PhD in mathematics and teach it at a university, so I think I did ok :)

[Dory]

Both my boys prefer to think through it like that. I asked them to work the other way enough that they understood it and then they could do it whatever way they were most comfortable with. So long as they can understand it from more then one angle, I'm not sure why I would force them to do it the way I'm most comfortable with.

[*Alyssa*]

Well, I have a PhD in mathematics and teach it at a university, so I think I did ok :)

 

That definitely makes me feel better.  ;)

 

 

Both my boys prefer to think through it like that. I asked them to work the other way enough that they understood it and then they could do it whatever way they were most comfortable with. So long as they can understand it from more then one angle, I'm not sure why I would force them to do it the way I'm most comfortable with.

I'm not forcing him to learn it my way for my sake, but due to my own ignorance of how others think mathematically.  Everyone has put my mind at ease that it'll be okay, so I'm ready to flow with it.

[Dory]

That definitely makes me feel better.  ;)

 

 

I'm not forcing him to learn it my way for my sake, but due to my own ignorance of how others think mathematically.  Everyone has put my mind at ease that it'll be okay, so I'm ready to flow with it.

 

I so did not mean to insinuate that I thought you were forcing him. I was just speaking from my own thoughts and experiences. I'm sorry my wording was poor.

[Lucy the Valiant]

My DS8 thinks that same way, too - I simply taught him "mom's way" and showed him how they're (mathematically) the same thing. He can choose "his way" or "mom's way" based on the problem.

 

I am (slowly) learning to trust the child . . . his "odd" math is sometimes just an innate way of thinking that is actually a strength.

 

 

[MomatHWTK]

The programs my kids are using for math (and we are using several) all teach both ways.  My mathy kids really get the "other" way while for my non-mathy one I am focussing on teaching the algorithm method and memorization.  When the mathy ones do their stuff, I just wait for the final answer because I can't keep up.  ;) 

[Lilaclady]

I think Arthur Benjamin- the mathmagician actually does it the way your son did. It is faster for mental math and he is a wiz for mental math. I think as long as he can show how he arrives at the correct answer, the beauty of math is there are lots of different ways.

[lazzaroni]

My son does this too. I thought it strange at first but it works for him.  He is more accurate doing it his way too!

[SparklyUnicorn]

I bought one of those Teaching Company DVDs and it was about mental math tricks.  The math tricks involve calculating in the way you mention.  After some practice following what he said I learned how to do it, and it works very well.  I was never taught that way, and most people are not, so it never occurred to me to try it.  It's definitely easier to do math calculations mentally that way.  Trying to look at or think of the numbers basically backwards in your head then having to reverse that to give your answer adds more opportunity for screwing it up.  Makes sense if you think about it. 

 

 

 

 

 

 

[MiMi 4under3]

When adding (small or reasonable) dollar or decimal amounts, I have my kids start from the left, too.

[Cosmos]

I was never taught that way, and most people are not, so it never occurred to me to try it.  It's definitely easier to do math calculations mentally that way. 

 

I bet you have tried it, though, even before seeing the dvd. I think many people do this without realizing it. What if you are at a store and there are two items that cost $1.40 and $3.25. Don't you add the $1 and $3 to get $4 and then add the cents together? I doubt you start at the one cent place and add from right to left while standing there in the store.

 

[Sunshine State Sue]

Singapore teaches that way. 

 

I tried to supplement MUS with Singapore somewhere around 2nd grade.  Ds did not like learning a different way to add.  He already knew one way and was having none of learning a different way.  I thought it was very odd never having learned that method myself.

[SparklyUnicorn]

I bet you have tried it, though, even before seeing the dvd. I think many people do this without realizing it. What if you are at a store and there are two items that cost $1.40 and $3.25. Don't you add the $1 and $3 to get $4 and then add the cents together? I doubt you start at the one cent place and add from right to left while standing there in the store.

 

 

No.  I was taught a very rigid way of doing math that didn't involve thinking about what I was doing.  Sad, but true!

Of course I totally see what you are saying now, but I didn't until I started working on it with my kids.

[happypamama]

My now 9yo does it that way!

 

ETA: 9yo started out doing things that way, and then when I showed him Singapore, it thinks a lot like he does and breaks things down in similar ways.  I have told him that he's welcome to do things in whatever way he likes, as long as it works.  At 7 or 8, when he first started showing me how he was doing things, I was concerned that it would be difficult for him as he got into larger numbers.  So I did show him the usual way that I do it as well, and sometimes that does work better for him if the numbers are large.  But for the mental math exercises in Singapore, I see him doing it the way he prefers, and honestly, it really does make sense.  253 + 688 -- it's a little easier to realize that you're going to hit 800 and then 900 but will have another 41 left over, so it's 941, than to do the carrying from the right in your head, and it's faster than writing it all down.  I totally see why he wants to do it that way.

[Korrale]

YouTube Vedic math there are lots of good examples of problems being done this way.

 

As someone previously mentioned. I also separate my dollars ans cents. I add the dollars then the cents.

[Butter]

Art Benjamin, the guy who did the Great Courses Mental Math lectures, is my 8 year old's hero.  This is precisely how he does math in his head super fast.  In fact, most of the fastest mental math is done "backwards."

[EKS]

That is a common way for people to add large numbers mentally because it requires less working memory than the other way.  It is specifically taught in Singapore (and other math programs) as a mental technique and also to show how place value works when adding multidigit numbers.

[Muttichen]

I remember when my oldest ds was very young and he would do a page of subtracting fractions with different denominators and only write the answers and they'd all be right.  I asked dh, who has a PhD in math, if I should make him show his work.  He said that as long as he was getting them right, I didn't need to worry about how he got there.  He said "showing your work" could wait for Algebra -- mental math was much better for arithmetic anyway.

 

The funny thing is that I had to write the problems out to see if he was getting them right!  :)

[Monica_in_Switzerland]

More confirmation here.  Singapore teaches mental math should go left to right, algorithm is done right to left.  My son always does mental math left to right, and can generally handle one need to "carry" but not two.  So for example, in 452+381 you only need to carry a ten tens over to the hundreds, and he can do it mentally left to right.  In 568+267, you need to carry a ten over and also a hundred over, so he'd be better off doing a paper and pencil stacked algorithm (right to left)

 

 

[*Alyssa*]

Thank you all for putting my mind at ease!  Really, it means a lot and I feel a thousand times more confident my son is on the right track, so I won't worry about it.

Some of you mentioned Arthur Benjamin and I didn't know who he was, or so I thought, until you brought up Great Courses.  I happen to own, "The Joy of Mathematics", DVD course and have had it for five years now, I think.  Admittedly, I purchased the DVD set as a combo with a calculus course my dh wanted.  The calculus course was watched, but not Arthur Benjamin's.  Opps.  :o   I'm going to pull out his course now and commit to watching the whole thing to see how his mind works.  Maybe he can teach this old dog some new tricks.  ;)   Thank you all who mentioned him and the Great Courses!

Several of you brought up Singapore math.  We use a combination of MUS (for mastery) and Saxon (to fill in gaps and the spiral approach).  Maybe I should look into Singapore for my son?  What are the differences between Singapore and the ones I'm using?

 

[*Alyssa*]

I bet you have tried it, though, even before seeing the dvd. I think many people do this without realizing it. What if you are at a store and there are two items that cost $1.40 and $3.25. Don't you add the $1 and $3 to get $4 and then add the cents together? I doubt you start at the one cent place and add from right to left while standing there in the store.

 

 

Until you mentioned it, I didn't realize I do that, too.  Thanks for pointing that out!  :thumbup:

[Monica_in_Switzerland]

I love singapore math, and I am not terribly familiar with the two programs you are using.  Some notes on Singapore:

 

- There is no flluff.  There is basically a bare minumum of problems included in the WB and TB for a good math student to come up to speed on a concept.  If you need more problems, they sell additional practice books called Extra Practice, or you can just make up your own.  Some people don't like this, but I love it because it means we don't waste time.  If a concept needs more work, I make up my own problems, if it doesn't. we move on.  No trying to decide if we should do all, some, evens, odds, etc. 

 

- You will need to re-educate yourself on math concepts.  The home instructor's guides are excellent, as are the videos at educationunboxed.com.  I have a degree in physics, but I felt like I learned a ton in singapore 1!  Now we are in SM3 and I feel like I'm understanding the long division algorithm really well for the first time.  Again, I love this aspect of deepening my own mathematical undersatnding, but some people hate it.

 

- You will need to add in your own review/drill.  This is easy enough- we use timezattack and Xtramath for drill, and I do 10 problems taken from the HIG mental math and/or made up by me in areas ds needs review as a warm up before each matjh lesson. 

 

 

[*Alyssa*]

I love singapore math, and I am not terribly familiar with the two programs you are using.  Some notes on Singapore:

 

- There is no flluff.  There is basically a bare minumum of problems included in the WB and TB for a good math student to come up to speed on a concept.  If you need more problems, they sell additional practice books called Extra Practice, or you can just make up your own.  Some people don't like this, but I love it because it means we don't waste time.  If a concept needs more work, I make up my own problems, if it doesn't. we move on.  No trying to decide if we should do all, some, evens, odds, etc. 

 

- You will need to re-educate yourself on math concepts.  The home instructor's guides are excellent, as are the videos at educationunboxed.com.  I have a degree in physics, but I felt like I learned a ton in singapore 1!  Now we are in SM3 and I feel like I'm understanding the long division algorithm really well for the first time.  Again, I love this aspect of deepening my own mathematical undersatnding, but some people hate it.

 

- You will need to add in your own review/drill.  This is easy enough- we use timezattack and Xtramath for drill, and I do 10 problems taken from the HIG mental math and/or made up by me in areas ds needs review as a warm up before each matjh lesson. 

 

So are you saying I should start with Singapore Primary Mathematics 1A/1B like this one, regardless where he is now, to understand the concept of Singapore math?

 

For math, I've always used two programs, so extra practice won't be needed.  My kids love math, but probably wouldn't appreciate too much extra.  ;)

 

Thanks so much for your help!

[Sunshine State Sue]

Several of you brought up Singapore math.  We use a combination of MUS (for mastery) and Saxon (to fill in gaps and the spiral approach).  Maybe I should look into Singapore for my son?  What are the differences between Singapore and the ones I'm using?

 

We used MUS from K through Algebra.  Somewhere around 2nd grade, we had a failed experiment with Singapore TB/WB.  It was too different for both of us, I think.  FWIW, I have a degree in math.  I did discover Singapore's Challenging Word Problems, though, and we supplemented MUS with those (a year behind ie. CWP 3 while doing 4th grade math) for many years.  I thought they were fabulous (imo MUS is weak in word problems).  Ds thought they were evil.  :w00t:

 

Although, I would have loved Saxon as a child (I was the type to bring math workbooks along for fun on vacation), ds would have found it extremely tedious.

[The Governess]

I would have him try a placement test. Singapore offers free placement tests on their website. You could probably start with 2a/b.

 

If your son enjoys mental math and is quick at picking up new concepts he will probably really enjoy Singapore math!

[Alte Veste Academy]

I asked both of my older kids (DS11 and DD10), and they both did it left to right. DS8, my stealthy little guy, added $5.20 and $1.40 and then subtracted three cents. Despite his youth and relative inexperience, he actually solved it faster than they did.  :lol:

[CaffeineDiary]

The way your son is doing it is actually better. Ever do a math problem and get the answer not just wrong, but wrong by orders of magnitude? That won't happen to your son as often because the method he is using starts by getting the most significant figures right.

[kiana]

The way your son is doing it is actually better. Ever do a math problem and get the answer not just wrong, but wrong by orders of magnitude? That won't happen to your son as often because the method he is using starts by getting the most significant figures right.

 

Yep. This is a huge bonus to this type of addition.

 

It is also very useful for estimation. If I have 3 things to buy and they cost 21.99, 23.49, and 27.19, I can immediately say it's going to be more than 60 bucks from looking at the leading digits, and before I get to the decimal places I can already say 'a little over 70 dollars'. 

[Monica_in_Switzerland]

I would not go all the way back to SM1, but SM2 does a TON of mental math techniques that I think would make starting later in the series a bit harder. 

[*Alyssa*]

Alright, you all convinced me that I should give Singapore math a try.  The workbooks are relatively cheap, so why not?   He is sick today and sleeping right now, but I'll have him do a placement test when he's feeling better.  :)   I look forward to seeing the method it uses!

 

We used MUS from K through Algebra.  Somewhere around 2nd grade, we had a failed experiment with Singapore TB/WB.  It was too different for both of us, I think.  FWIW, I have a degree in math.  I did discover Singapore's Challenging Word Problems, though, and we supplemented MUS with those (a year behind ie. CWP 3 while doing 4th grade math) for many years.  I thought they were fabulous (imo MUS is weak in word problems).  Ds thought they were evil.  :w00t:

 

Although, I would have loved Saxon as a child (I was the type to bring math workbooks along for fun on vacation), ds would have found it extremely tedious.

 

I think MUS has both weak and poorly worded math problems, but I really do like how Mr. Demme explains things with the manipulatives, so we stick with it.  If Singapore is strong with word problems, I will order some workbooks right away just for that alone.  Evil word problems are good for the mind.  B)   I struggled with them as a child and now make it my mission to make sure my kids understand them.

I agree with your son, Saxon is tedious in many ways.  I keep it around for a well-rounded math education.  We do a lot of the problems together on a white board and my kids love that over doing it on paper.  I let them be "teacher" and tell me how to do the problems.  This is how I discovered my son's way of thinking.  He taught me something in the process, I'm realizing.  ;)

[Farrar]

I wouldn't use either MUS or Saxon for a young kid who's really good at intuiting math. So yeah, I'd think about switching to Singapore possibly. Or trying something else outside the box to go with one of them maybe, like using Miquon or Primary Challenge Math or some fun supplements.

 

One of my boys was very, very attached to doing math like that. I appreciated the good impulses behind it but to get him to learn the other way, I made him work some really, really long chains of numbers, just to illustrate why you eventually need to sometimes do it the other way starting with the units place. Once you get into five and six digit numbers, it gets cumbersome unless you end up with friendly numbers.

[*Alyssa*]

I would not go all the way back to SM1, but SM2 does a TON of mental math techniques that I think would make starting later in the series a bit harder. 

 

You posted while I was writing my other post. 

 

That's good to know!  I'll still test my son, but I'll probably end up buying both SM1 and SM2, because I have a younger son (5yo) who is anxious to start his own math.  :)

[*Alyssa*]

I wouldn't use either MUS or Saxon for a young kid who's really good at intuiting math. So yeah, I'd think about switching to Singapore possibly. Or trying something else outside the box to go with one of them maybe, like using Miquon or Primary Challenge Math or some fun supplements.

 

One of my boys was very, very attached to doing math like that. I appreciated the good impulses behind it but to get him to learn the other way, I made him work some really, really long chains of numbers, just to illustrate why you eventually need to sometimes do it the other way starting with the units place. Once you get into five and six digit numbers, it gets cumbersome unless you end up with friendly numbers.

 

Whoa, slow down there.  You just threw a wrench in my thought process here. :laugh:

 

Okay, so why is Saxon and MUS not good for his way of thinking?  Please elaborate.  :o

 

I have Edward Zaccaro's book on word problems and really like it, so I'll buy his PCM book, too.  (That's the author you're talking about, right?)

 

I'm not familiar with Miquon at all.  The little bit I can review looks like a colorful version of MUS and Saxon in some ways.  How is it different, if I may ask?

 

I agree that I thought it was cumbersome to do it his way with large numbers, which is why I was concerned about higher levels of math.  I'd be curious what the other ladies think about what you said.

[kiana]

I think that a kid who's good at adding left-to-right can learn the standard algorithm very quickly once s/he gets to numbers that are big enough to require it.

[*Alyssa*]

I think that a kid who's good at adding left-to-right can learn the standard algorithm very quickly once s/he gets to numbers that are big enough to require it.

 

Sweet!  I'll keep letting him do it how it works for him until we run into problems.  :thumbup1:

[Farrar]

My experiences and the many reviews I've seen just suggest that MUS and Saxon aren't great for kids who intuit math well. Saxon is really based on drill. That can be a math-love killer for kids who get it fast. MUS moves more slowly. Neither program includes really challenging material as part of their regular program and neither program includes any outside the box thinking, such as teaching lots of different methods. I think of Singapore (and to a lesser extent Math in Focus) as being better for kids who intuit math more quickly in part because Singapore has better word problems and includes more challenging problems. Plus, it doesn't focus on drill but on that deeper understanding. I think MUS and Saxon may be great for some students, but those things make me think they're not great for most gifted, accelerated, or mathy kids.

 

Yes, Primary Challenge Math is another Zaccaro book - it's like Challenge Math, just geared toward younger students. I think it's about right for 2nd/3rd for most kids.

 

I mention Miquon just because it was really good for my mathy ds, but it's really different and not right for every kid. I don't know if I'd call it colorful... the text is in color, but there's almost no pictures. Miquon relies on the Cuisenaire rods, but the C-rods are different in some small but key ways from the MUS blocks (look up old threads about whether the C-rods should have notches if you want to see some kerfuffles). Miquon does a better job than any other program I've experienced of introducing really tricky concepts through really simple, intuitive examples and then slowly building on those. So, for example, I think multiplication with fractions is a concept introduced in the first grade books, which is much earlier than you'd see it in most programs. But it's with really simple examples like 1/2 of 10. That thread is followed through though to help kids understand on up through to much more difficult problems by the third grade books. My ds who loved Miquon went into Beast Academy, which is another great mathy kid program.

 

[Farrar]

Adding... I don't think that means you have to switch. If it's working, don't listen to us and there's no need to become a curriculum collector. :) I'm really just tossing out options and ideas.

[happypamama]

Saxon would bore my math whiz kid to tears, I think.  He likes the diagrams and little tricks and all that Singapore teaches.

[myfunnybunch]

At that age, my ds (now11) made up his own procedure for multi-digit addition and subtraction. I let it go, except for a bit of "Show me your way. Now I'll show you my way," on a daily basis. Eventually he realized that "my" (standard) way was faster, and switched on his own.

 

I want to encourage flexible thinking in mathematics. Even now, we will sit down and solve problems together, and he will solve differently than I will. :)

 

Cat

[gevs4him]

Wow - my son started to do this and I made him change :(