Is This How Simple Addition is Taught Now?

[PachiSusan]

Is this how math is taught now? I admit I am not in the school system so it could be totally normal and I have just missed it - but this seems WAY more complicated and confusing than simply stacking the numbers like I am used to doing.

 

Is this just supposed to be to learn the concept and then they move on to stacking?

 

 

If you use this method, could you explain the thought process behind it? I see it's trying to teach place value, but if this is how the child is supposed to do it all the time, I feel sorry for how long Math is gonna take!

[LucyStoner]

I teach addition lots of different ways until the concept and all the related information like place value and self checking is rock solid and the problem can be done in a few different ways, including without a pencil. The standard algoritm for addition is useful when you have a pen and paper but is that how you work that problem quickly in your head? From right to left and mentally carrying and adding each column? Not for most people. Mentally, people work problems in different ways, usually some variation of left to right. If someone can only solve that problem with a pencil working right to left they are not gaining the fluency and number sense that benefits students long after they are done with arithmetic. That said, I don't use TERC or like it much. I do grow weary of people making fun of the alternatives to the standard algorithm that advance math fluency. The standard algorithm has its place and should be taught. But on its own? It's not sufficient IMO.

 

And no, of course people don't solve a problem like that each and every time. My son learned to line up his numbers and carry when he was in the first grade at school. It took him longer to be able to estimate or identify how many digits a sum would have based on a glance at the numbers. When I made him stop with the standard algoritm for a while and add the thousands, hundreds, tens and ones, he finally knew why he was doing what he was doing and not just how. How without why leads to errors that the student may not be able to identify or spot IME.

[PachiSusan]

FYI : I was not ridiculing it.

[Free]

I liked the video. I liked how well the girl seemed to have internalized the concept of addition and how easily she seemed to be explaining it. I also liked how well she was drawing those boxes for 1000 :)

 

Yes this is how my ds learnt place values in school. And no they don't have to do every addition problem this way. They moved on to the traditional method soon enough. I am not a fan of teaching the algorithm (carry over one and so forth...) until the child has understood why he needs to carry over.

 

Having a strong base in visualizing addition in the mind is very useful IMO for being able to understand multiplication and division and for solving problems involving large numbers.

[Lily_Grace]

Yes and no. This takes the idea behind montessori-style math manipulatives and draws them. We use actual manipulatives at home (using base ten or MUS blocks) to create addition, subtraction, multiplication, and division problems when learning the basic principles. Then we move on to color-coded graph paper to learn the stacking method (corresponding to the colors of hundreds, tens, units in repeating lines to create up to the hundred-thousand place) and eventually move on to sideways notebook paper.

 

It works, it helps to internalize place value and number sense, but it's not necessary to continue to use it once the concepts are grasped. However I'll still find my son crossing his hands as he's doing a multiplication problem, visualizing the grid of squares as he's working it mentally. LOL

 

My 14yo went from MUS + Montessori to AOPS, so I can't say it has caused him much harm. ;)

[mathmarm]

I like my primary students to understand multiple ways of doing math and by understanding numbers, place value and the properties of real numbers, then mental math becomes exceedingly easy. Fortunately, when I was in school I was mostly allowed to work the problems anyway that I liked, so long as I got the right answer, which I always did. I never use the Right to Left methods personally, I have always done arithmetic Left to Right because it is faster for me. I support each kid doing the work in whatever way it is that their teacher asked them to, though I often re-explain the work in several ways until I find what clicks for them. Then we talk about why solving the problem in Teachers Preferred Way Works and what we can learn from it.

 

I am not AGAINST a child understanding math in this way. The little girl seemed quite comfortable with the explanation that she was giving (yes, she's lost count) using the graphics, but she knew what was supposed to happen and she knew why it would happen. I was impressed with her 3D rendering of a cube also.

[Farrar]

This video was discussed here awhile ago. I remember.

 

Yes, I think that's how a number of these new math methods teach. I think it's useful as a first step. And then they hold on to it as a method for way, way too long, doing damage to kids. I don't think understanding this hurts them but spending months thinking this is "the way" you do addition does. And that it's sad that the child's mother had to teach her "stacking." After all, she clearly grasped both methods.

[duckens]

This is reason #3,671 why we homeschool.

 

I would, however, not blame the teacher. These days, teachers rarely get much choice in the curriculum they use, or how it is implemented.

 

Paraphrase: "We're not allowed to do stacking at school," haunts me.

 

Our local middle school math teachers asked for a boring type curriculum to teach "traditional math." The powers that be ignored all input from the teachers and went exactly the opposite direction: with something experimental. :glare:

[nmoira]

I would have been interested to hear the girl reasoning her way through the vertical addition. It's not just about getting the right answer.

[Shellydon]

MUS uses math blocks to help kids understand place value, then moves them on to regular addition.

[PachiSusan]

I guess what I am having a hard time with is that I was not taught and don't teach Melissa just to Memorize" the algorithm and don't understand the insistence of some (not here) that stacking DOESN'T allow for understanding of place value.

 

Thank you for explaining this in more detail to me. :)

[Farrar]

I guess what I am having a hard time with is that I was not taught and don't teach Melissa just to Memorize" the algorithm and don't understand the insistence of some (not here) that stacking DOESN'T allow for understanding of place value.

 

Thank you for explaining this in more detail to me. :)

 

I think it's easy for kids to understand how to stack and not really understand why it works. I think some kids think in the tens, hundreds, thousands and so forth columns that they're adding ones. And that when they "carry" the one, that it's some kind of "trick." Those are problems, IMO. They're problems that this type of addition in the video could solve. So could working with base-10 blocks or Cuisenaire rods or an abacus. So could just better explanations.

 

Have you read the Liping Ma book? I feel like it helps one see where American teachers often go wrong in these types of matters.

 

To me, the problem is not teaching this method per se. It represents a positive thing of trying to get to the why of the place value. To me, the problem is that they make this drawing the new algorithm. This drawing method is a tool for understanding. Just like you don't want your kids to have to carry a large abacus or a box of C-rods around in order to do math, you don't want them to think that this is "the way."

 

I also question whether this particular method is a very good teaching tool. There are some positive things about the concept, but spending that much time writing and drawing for a young child is inevitably distracting and difficult. I mean, no wonder the poor girl lost count. Kids also have to estimate space for all these boxes, which is a pretty complex visual thing to do for most 7 yos who might be learning this level of addition. Surely having manipulatives would be superior for a number of reasons.

[Monica_in_Switzerland]

It wasn't clear from the video if the girl understood either method- she did not say WHY 1000 was a cube, 100 was a square, etc, just that those were the symbols to draw. If they had worked in class with physical base ten blocks, she would know this, but it wasn't clear from the video if she understood why the symbols were assigned as they were.

 

It also wasn't clear from the video if she understood the stacking algorithm.

 

I would think working with physical base ten blocks for a while, followed by the algorithm would be the way to go. I would not do the middle step of drawing the base ten blocks, as it seems like a lot of wasted time, and as the girl noted in the video, there is lots of room for error with all that drawing and counting.

[Spy Car]

There are very good reasons for teaching addition as shown in the video. If one used physical manipulatives (rather than a whiteboard) the process would be much faster. In any case, the fastest method of finding the correct answer is not necessarily the best way of introducing a conceptual understanding. Working the standard argorithm (what they are calling stacking) does not necessarily equate to fully understanding the place-value relationships the pictorial method in the video is seeking to advance.

 

The condescending tone and injected comments make me think very poorly of the video makers.

 

Bill

[LucyStoner]

FYI : I was not ridiculing it.

 

 

No, you were not. But the video is and that is what I was addressing when I said I grow weary. I hear people get all hot and bothered over non-standard algoritms and then they proceed to recommend math curriculums which build understanding through alternate algoritms. Singapore is very popular and it asks kids to do multidigit arithmetic many different ways. IIRC including counting boxes or other representations of thousands, hundreds, tens and ones.

[Farrar]

I think a lot of people conflate two totally different issues. One, that many schools (or "new math" of any sort) teaches non-traditional algorithms. Two, that teachers don't always do a very good job of teaching math or make "rules" about it (like, no stacking allowed) that don't necessarily help kids learn. The first issue is not a problem and the second one is. If you have teachers teaching an algorithm they don't get or if they can't explain fully the connections between what they're doing and why they're doing it, then I think they end up with a lot of "just do it this way!" and then kids and parents never get it and they turn against good tools, like using manipulatives or learning different methods.

 

To me, that's what it sounded like has happened in the case of this video. If you did have kids spending half their math year doing this type of addition, then I would sadly not be surprised and I also would not be surprised that the mom had turned snarky about it.

[regentrude]

I was not able to discern if the child understood WHY she should draw the 1000 as a cube and so on - it looked like a memorized procedure to me, and I fail to see the advantages of this memorized procedure over another.

I love math and have nothing against creative ways of problem solving, but I question whether putting much emphasis on this will lead the student to computational fluency, which, in addition to conceptual understanding, is absolutely essential. As a college instructor, I see students all the time who are not proficient in arithmetic; if these are the new teaching methods, they are apparently not helping, as the math skills of the students continue to decline.

 

And I get really angry when I hear "we are not allowed to use (whatever method) at school"!

 

Btw, this sort of math curriculum was the reason we pulled our kids from public school. While we agree with the importance of conceptual understanding (after all, both DH and I are theoretical physicists), we consider these methods as not useful in a standard classroom where they are implemented by teachers who don't know why half the stuff works, and where average students get bogged down in these methods and don't learn to actually compute an answer quickly and accurately because of all the drawing and cutting (fraction strips, anyone?)

 

ETA: I do not understand the whole debate about "place value". The student in the video was a 3rd grader. Surely, place value has been cemented by 3rd grade?

[MeaganS]

I agree with Bill on this one. I also tend to think that not allowing the child to use other methods can be a reasonable thing, assuming it is for the sake of forcing them to see the problem from a different direction. If the child knows the easy algorithm, they may never understand it as deeply as a child "forced" to approach the problem from many different angles. I don't know if that was the case here or not, but I don't think "we're not allowed to do stacking at school" is necessarily a condemning comment.

 

I was bored stiff in school, especially elementary school math. That boredom led me to my decision to homeschool, but I definitely think there is a place for not allowing the child to do the math the easy way.

[PachiSusan]

I agree with Bill on this one. I also tend to think that not allowing the child to use other methods can be a reasonable thing, assuming it is for the sake of forcing them to see the problem from a different direction. If the child knows the easy algorithm, they may never understand it as deeply as a child "forced" to approach the problem from many different angles. I don't know if that was the case here or not, but I don't think "we're not allowed to do stacking at school" is necessarily a condemning comment.

 

I was bored stiff in school, especially elementary school math. That boredom led me to my decision to homeschool, but I definitely think there is a place for not allowing the child to do the math the easy way.

 

I would agree with this except for one issue: Let's say a child can only understand what she's doing with Method A. The classroom she is in is being taught Method A is wrong, and bad and not effective, but that is how she understands Math. She is forced to use Method B and Method C that just, no matter how hard she tries, does not make sense to her.

 

Should this little girl be failed in her Math expression because she didn't fit the mold of what "should" be happening? Why can't she be allowed to use the method that works best for HER? What kind of "Why am I so stupid??" feelings would be brought up in her.

 

Lattice/Ladder Multiplication is one such idea. If I hadn't taught Lattice to my daughter in conjunction with traditional methods, she'd still be struggling with the concept of multiplication. Putting the two together was the best method for her and made the light go on for her.

 

To have a teacher FORBID the use of one of the tools does not sit well with me. We will have to disagree on this one. No argument put forth has made any impression that forcing a certain way is a good thing.

 

To me, the goal is understanding why you are doing what you are doing and then being able to show you know what to do. Forcing someone into a particular standard EITHER WAY is not helpful to some children.

 

I do not see how THIS method is superior. It's different. Stacking isn't superior. It attacks the problem a different way. Stacking may not be the "easy way out" for a child. It may be the way that child thinks.

 

It seems to me that the prevailing goal is for a child to understand and achieve - not to punish them because they don't understand things the way the latest teaching method is being taught to them.

[PachiSusan]

I felt this as well. She could not explain EITHER method's whys...simply HOW to follow a formula to get an answer.

 

I was not able to discern if the child understood WHY she should draw the 1000 as a cube and so on - it looked like a memorized procedure to me, and I fail to see the advantages of this memorized procedure over another.

[PachiSusan]

I think a lot of people conflate two totally different issues. One, that many schools (or "new math" of any sort) teaches non-traditional algorithms. Two, that teachers don't always do a very good job of teaching math or make "rules" about it (like, no stacking allowed) that don't necessarily help kids learn. The first issue is not a problem and the second one is. If you have teachers teaching an algorithm they don't get or if they can't explain fully the connections between what they're doing and why they're doing it, then I think they end up with a lot of "just do it this way!" and then kids and parents never get it and they turn against good tools, like using manipulatives or learning different methods.

 

To me, that's what it sounded like has happened in the case of this video. If you did have kids spending half their math year doing this type of addition, then I would sadly not be surprised and I also would not be surprised that the mom had turned snarky about it.

 

I think this is a great point. It sounds to me, after reading the responses here, that the teacher might not really understand the applications of this method and didn't impart to the students that it was for learning the concepts and with such great numbers, to use a different method.

[musicianmom]

I think the alternate methods, when used improperly and for too long, can impede learning as much or more than simply using the old-fashioned algorithm. A subpar teacher isn't going to get all the nuances of how to teach math this way, he/she will probably latch on to "okay, this is how we do addition now" and teach it in the same rote way as the old algorithm was taught.

 

For some reason I am reminded of my senior English class in high school. We had weekly vocabulary quizzes, which were easy and required only a 5-minute glancing over the words in homeroom for me. But then my teacher watched some video about study skills. Rather than teaching us the concepts from the video, she latched onto one suggestion from the video, using flash cards to study. For the rest of the year, we were required to make flash cards of our vocabulary words (copying words and definition) and show them for a grade. What a waste of time and index cards!

 

 

[PachiSusan]

I think the alternate methods, when used improperly and for too long, can impede learning as much or more than simply using the old-fashioned algorithm. A subpar teacher isn't going to get all the nuances of how to teach math this way, he/she will probably latch on to "okay, this is how we do addition now" and teach it in the same rote way as the old algorithm was taught.

 

Yes!!!! I think that might have been what was going on here. I just wanted to give that little girl a hug. She was so adorable and smart!!

[EKS]

This is how I taught my children addition. Then I taught them the standard algorithm.

[Farrar]

 

It appears to me that many are arriving in kindy without preschool math skills, so they don't catch up and develop an understanding of place value until after 3rd grade.

 

I taught sixth grade math for the kids who were behind for a couple of years and I can say that for a number of them a lack of understanding of place value was one of the biggest issues. It particularly came up with large number multiplication and division, though I met kids who also simply couldn't round numbers to given place values - even if I had a chart in front of them to remind them of the place value names (thousands, ten thousands, etc.). I think this is obvious to a lot of people, but there are definitely kids who don't get it and never figure it out with direct remediation.

[PachiSusan]

No, you were not. But the video is and that is what I was addressing when I said I grow weary. I hear people get all hot and bothered over non-standard algoritms and then they proceed to recommend math curriculums which build understanding through alternate algoritms. Singapore is very popular and it asks kids to do multidigit arithmetic many different ways. IIRC including counting boxes or other representations of thousands, hundreds, tens and ones.

 

I have no issue with manipulatives or other methods to get the understanding of Math. I DO have a problem with forbidding a student to use a method that works for them and make an edict about that method. There is nothing wrong with any of the methods - as long as they work for the student.

[PachiSusan]

Honest question here: I may be totally reading into this, and if I am, I am sorry. I get the feeling that the prevailing attitude is that "stacking" can't teach the concept as well as these other types. Is that what people are saying?

 

If so, I truly don't get it. Melissa knows place value. She knows that when she borrows from the 10 column, she's adding 10 ones to the ones she already has, or when adding, she's grouping 10 tens and bringing one group of tens over to the tens column, etc...She's never been taught the type of math in this video at all and we've never used manipulatives...well check that. When we were first starting out we used "My LIttle Pony" math to show the concept of adding and subtracting. LOL :laugh:

[Farrar]

I think if there's good teaching and explanations along with teaching a child the traditional stacking algorithm, that of course they can learn to understand the concepts involved. But I think some kids will zone out of the explanations and even kids who "get it" would benefit from being able to do it another way. I think most kids would benefit from starting with manipulatives. I think one of the true tests of understanding math is whether you can look at a different method and understand it. I think this is why some people (maybe SWB as well?) suggest giving children a different math program's test from the one you're using every once in awhile - to make sure it's not just the teaching style, the one algorithm, etc. and that the child can get the concepts involved as well.

[Farrar]

Okay, I know it's spam and I reported it. But now I'm picturing getting fat from doing too much math. Math is so carby. I'd rather do history, it's got a better vitamin profile! Or grammar has more protein!

[PachiSusan]

Okay, I know it's spam and I reported it. But now I'm picturing getting fat from doing too much math. Math is so carby. I'd rather do history, it's got a better vitamin profile! Or grammar has more protein!

 

ha ha ha !! That totally made me laugh!!

[PachiSusan]

I think if there's good teaching and explanations along with teaching a child the traditional stacking algorithm, that of course they can learn to understand the concepts involved. But I think some kids will zone out of the explanations and even kids who "get it" would benefit from being able to do it another way. I think most kids would benefit from starting with manipulatives. I think one of the true tests of understanding math is whether you can look at a different method and understand it. I think this is why some people (maybe SWB as well?) suggest giving children a different math program's test from the one you're using every once in awhile - to make sure it's not just the teaching style, the one algorithm, etc. and that the child can get the concepts involved as well.

 

That's a great idea!! I do use a more Singaporey type of Math in the Summer Bridge activities and the first time she did them she was all "HUH????" Now she can do it knowing it's a different approach. I was so proud to see that aha moment!!!!