This is why concepts are more important than tricks

[Snowfall]

I read this on a teacher's website. It's the teacher's explanation of a subtraction trick taught by Everyday Math. I'm not knocking the teacher for getting the answer wrong - I promise I'm not. My point is that this is just a prime example of why tricks are no match for good conceptual understanding. This one in particular seems extremely cumbersome, and it's really no wonder she got it wrong. I can't really understand why this was considered easier than explaining the concepts behind regrouping. lol

 

Here it is:

 

"The Everyday Math Program has lots of neat ways to teach kids how to subtract, other than the traditional way. They are really good, especially for those students who just can't do the regrouping way without making errors. My favorite method is what I call the Elevator Method. I begin by telling the students my "elevator story." When you go into the hospital to have some surgery, you climb into the elevator and head UP to the surgery floor. You're pretty nervous, so this is a NEGATIVE THING. GOING UP IS NEGATIVE. However, when you get out of the hospital, you climb into the elevator and head DOWN. You're happy that the surgery went well and you are feeling POSITIVE. GOING DOWN IS POSITIVE. Now let's subtract with the problem 807 - 294. Write the problem down with the 294 under the 807. Don't look at individual numbers, but look at place values. We'll start with the hundreds column. We have 8 hundreds and 2 hundreds. 800 - 200 = 600. Write that down under the problem. Put a PLUS in front of it, because we subtracted going DOWN, and GOING DOWN IS POSITIVE. Now look at the tens column. We have 0 tens and 9 tens. 90 - 0 = 90. Write that down under the 600, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at the ones column. We have 4 ones and 7 ones. 7-4=3. Write that down under the 90, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at what we wrote down: +600, -90, -3. 600-90=510 (mental math, counting by tens backward if needed). 510-3=507. 507 is the answer. No regrouping necessary, and students can learn to do this really, really quickly!

Wow! I hope that helps!"

 

Edit to add that I do think it's a cool trick, but I just don't see how it should be taught in place of good understanding of regrouping. It's a lot to remember, so certainly no easier than just explaining the concept, IMO.

Edited April 15, 2011 by Snowfall

[ChrissySC]

I was always in favor of the "number houses" for conceptual understanding, which aids in teaching the idea of regrouping. For first through third grade the first time I taught math, I used MUS. It used this idea.

 

Sometimes, you can lack a good foundation which causes struggles. We have not moved from multiplication as of yet for the simple fact that dd does not understand that you can use the distribution and communative properties with multiplication. :) She does not what the name is for waht she is doing, but I do. LOL Thus, we wait for mastery. Long division will stay in the book right where I left it!

[buram]

What? That is supposed to help kids! I am dizzy from all of the elevator rides. Thanks for sharing.

[Sew happily ever after]

Sounds similar to terry's subtraction method in Right Start. I must add in defense of RS that they show different ways to subtract so that students know that there is more than one way to solve a problem. My children never chose to use this method for subtraction. It can be easy, but sometimes it is actually harder! But it is interesting to know that there are many different ways to do a problem and still get the same answer. Sometimes all those choices confuse kids, tho!

[regentrude]

I read this on a teacher's website. It's the teacher's explanation of a subtraction trick taught by Everyday Math. I'm not knocking the teacher for getting the answer wrong - I promise I'm not. My point is that this is just a prime example of why tricks are no match for good conceptual understanding. This one in particular seems extremely cumbersome, and it's really no wonder she got it wrong. I can't really understand why this was considered easier than explaining the concepts behind regrouping. .

 

But that's precisely the point: instead of a straight forward algorithm, she confused HERSELF and muddled the signs. If anything, this should be a clear indication that this is not a good method - if even the teachers get confused.

 

I have my issues with the program anyway.

Conceptual understanding is one thing that is extremely important - but equally important is practice of a standard fast algorithm so that the student learns to do these problems automatically. Everyday math is severely lacking in that department, too.

[Aquinas Academy]

What? That is supposed to help kids! I am dizzy from all of the elevator rides. Thanks for sharing.

:iagree:That was so confusing.

[Spy Car]

The standard algorithm isn't the easiest way to solve 807 - 294.

 

Far easier to do it the Singapore mental math style where the subtrahend gets bumped up (+6) to 300. The minuend likewise gets bumped up (+6) and we have:

 

813-300=[ ]

 

Bill

[kchara]

OK, I tried to follow along... I wrote it down in a notebook.... I'm still not getting it. Am I the only one that thinks that maybe EM makes these problems intentionally difficult to understand? It just seems like they're setting kids up for failure.

[EJCMom]

I'm confused. I did it in my head and got 513. All the elevator stuff just confuses me. I've never been good in math though. I can't figure out how she got 507 at all.

[Tsutsie]

HUH???

[CatMomof3]

:001_huh: - that is all I can say

[kchara]

I figured it out!!! She meant to write 804-297, which does equal 507. Still an unnecessarily complicated way to do math, IMO.

[Halcyon]

I read this on a teacher's website. It's the teacher's explanation of a subtraction trick taught by Everyday Math. I'm not knocking the teacher for getting the answer wrong - I promise I'm not. My point is that this is just a prime example of why tricks are no match for good conceptual understanding. This one in particular seems extremely cumbersome, and it's really no wonder she got it wrong. I can't really understand why this was considered easier than explaining the concepts behind regrouping. lol

 

Here it is:

 

"The Everyday Math Program has lots of neat ways to teach kids how to subtract, other than the traditional way. They are really good, especially for those students who just can't do the regrouping way without making errors. My favorite method is what I call the Elevator Method. I begin by telling the students my "elevator story." When you go into the hospital to have some surgery, you climb into the elevator and head UP to the surgery floor. You're pretty nervous, so this is a NEGATIVE THING. GOING UP IS NEGATIVE. However, when you get out of the hospital, you climb into the elevator and head DOWN. You're happy that the surgery went well and you are feeling POSITIVE. GOING DOWN IS POSITIVE. Now let's subtract with the problem 807 - 294. Write the problem down with the 294 under the 807. Don't look at individual numbers, but look at place values. We'll start with the hundreds column. We have 8 hundreds and 2 hundreds. 800 - 200 = 600. Write that down under the problem. Put a PLUS in front of it, because we subtracted going DOWN, and GOING DOWN IS POSITIVE. Now look at the tens column. We have 0 tens and 9 tens. 90 - 0 = 90. Write that down under the 600, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at the ones column. We have 4 ones and 7 ones. 7-4=3. Write that down under the 90, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at what we wrote down: +600, -90, -3. 600-90=510 (mental math, counting by tens backward if needed). 510-3=507. 507 is the answer. No regrouping necessary, and students can learn to do this really, really quickly!

Wow! I hope that helps!"

 

Edit to add that I do think it's a cool trick, but I just don't see how it should be taught in place of good understanding of regrouping. It's a lot to remember, so certainly no easier than just explaining the concept, IMO.

 

I don't even understand what he's talking about. Too much talk, not enough math!

[Capt_Uhura]

807

-294

______

600 (800-200)

-90 (0-90)

+3 (7-4)

--------

513

 

Looks like she did 4-7 and got -3 instead of 7-4.

 

The whole elevator analogy is VERY, VERY confusing. I feel sorry for the poor kids taught with this method.

 

Yes, RS shows this method but it's instructive, not meant to teach this particular way of doing it, if I recall correctly. After DC has learned subtraction, it's introduced as "Look how Terry did this problem. Is this right? Can you explain why she did it this way?"

Edited April 15, 2011 by Capt_Uhura

[Supertechmom]

My 13 year old just pointed out that she has set them up for "epic fail" in number line. "Going up is negative and going down is positive." Thus the confusion when you learn that going up the number line is POSITIVE!

[AmericanMom]

What? That is supposed to help kids! I am dizzy from all of the elevator rides.

:iagree:

 

If someone had tried this on me when I was a kid, they would have lost me right after the bit about having surgery because I would have thought I wonder who's having surgery and when and why and where and how long will it take and will I have to go visit them because I don't like the way hospitals smell and it is cold in there and ....

[Capt_Uhura]

My 13 year old just pointed out that she has set them up for "epic fail" in number line. "Going up is negative and going down is positive." Thus the confusion when you learn that going up the number line is POSITIVE!

 

I KNOW! That's where I got confused! Where is the shaking head icon?

 

My teacher friend said that for the first time, they have more kids in remedial math than in remedial English. This is b/c Everyday Math is so verbal, that before, kids who were struggling w/ English could still learn math. Now w/ math being so heavily word-based, those kids can no longer math. Then add to that, all the kids who are not struggling w/ English, are struggling w/ math b/c of all the verbiage and switching from topic to topic too quickly.

[FairProspects]

My 13 year old just pointed out that she has set them up for "epic fail" in number line. "Going up is negative and going down is positive." Thus the confusion when you learn that going up the number line is POSITIVE!

 

I KNOW! That's where I got confused! Where is the shaking head icon?

 

My teacher friend said that for the first time, they have more kids in remedial math than in remedial English. This is b/c Everyday Math is so verbal, that before, kids who were struggling w/ English could still learn math. Now w/ math being so heavily word-based, those kids can no longer math. Then add to that, all the kids who are not struggling w/ English, are struggling w/ math b/c of all the verbiage and switching from topic to topic too quickly.

 

:iagree:This is where I got confused too, after thinking - but what if you went downstairs for surgery?

 

I feel like Jerry Maguire - You lost me at hello!

[Halcyon]

My 13 year old just pointed out that she has set them up for "epic fail" in number line. "Going up is negative and going down is positive." Thus the confusion when you learn that going up the number line is POSITIVE!

 

 

This is exactly what I thought when I read the problem-I was thinking about number lines and I was like "Huh?"

[Guest mrsajoy]

This is exactly what I thought when I read the problem-I was thinking about number lines and I was like "Huh?"

 

I thought the same thing, and therefore couldn't get my head into it from the get go.

[Snowfall]

807

-294

______

600 (800-200)

-90 (0-90)

+3 (7-4)

--------

513

 

Looks like she did 4-7 and got -3 instead of 7-4.

 

The whole elevator analogy is VERY, VERY confusing. I feel sorry for the poor kids taught with this method.

 

Yes, RS shows this method but it's instructive, not meant to teach this particular way of doing it, if I recall correctly. After DC has learned subtraction, it's introduced as "Look how Terry did this problem. Is this right? Can you explain why she did it this way?"

 

Yeah, she (or he) did the last part backwards. She forgot that she subtracted down instead of up. That's what I assumed anyway. I do think it's a cool trick. I just think that a kid ought to be proficient enough at math to know that answer is wrong immediately (once they're 10 or so, I think) because there's no way you could subtract a # with 9 tens from a # with 0 tens and get a number with 0 tens. I didn't even have to do all the math to realize she was wrong, because her answer was impossible.

(*I just edited this, because I had originally said this about ones, but there were never zero ones in her answer. Not sure what I had typed that for. I think the whole thing confused me so much I forgot what I was saying. lol)

 

I also agree with those of you who didn't appreciate the "up is negative, down is positive" aspect of it. I HATE that part!

Edited April 17, 2011 by Snowfall

[The Governess]

Oh. Wow.

 

I think Singapore math has spoiled me. I didn't know it was possible to make such a simple problem so complicated. :001_huh:

[Miss Sherry]

My 13 year old just pointed out that she has set them up for "epic fail" in number line. "Going up is negative and going down is positive." Thus the confusion when you learn that going up the number line is POSITIVE!

:iagree:

[BabyBre]

Ugh! I'm sorry, but repetition of the phrase "GOING UP IS NEGATIVE" is just far too ironic when you're talking about reform math! I would be ROFL, but I know how serious our math problem is, and it's because of programs like EM. "Counting backward if necessary..." God, help us.

[Stratford]

Ack! Everyday Math is one of the many reasons we are taking DS out of PS for 2nd grade. After reading that, I'm completely confused. If I started talking about elevators, DS would think I'd lost it. A friend of mine has a 2nd grader and had to email the teacher recently to ask how they teach subtraction....parents couldn't figure out how to help their kids with homework. In the 2nd grade. Heaven help us.

 

That said, I'm really excited about homeschool. I'm looking forward to helping my kids understand the basics (the real basics, not the phony-baloney-elevator-trick-math basics.)

[lionfamily1999]

Edit to add that I do think it's a cool trick...

I disagree. A cool trick would be one that (at least) the adult who knows it could use to get the correct answer. That was a total mess.

 

It would be far easier to teach math correctly in the first place.

:iagree:

Oh. Wow.

 

I think Singapore math has spoiled me. I didn't know it was possible to make such a simple problem so complicated. :001_huh:

Me too. I was thinking... just count up!

[Snowfall]

I disagree. A cool trick would be one that (at least) the adult who knows it could use to get the correct answer. That was a total mess.

 

Well, that's true. lol I think her (his?) problem was that she got too confused typing it all out. MY problem is that I think she'd likely get just as confused doing it in class, since she doesn't even have a written record there. Anyway, how can a kid keep up with all of that, if they don't even understand what's happening in the first place? I honestly don't think the teacher even had a good grasp of regrouping, since the other explanation in the rest of the post was the old "go to your neighbor and borrow a one," and this was the best the person could come up with in response to a question about kids who didn't understand regrouping in subtraction. I feel her pain. I didn't really understand it until I started teaching dd, and I was a straight A student throughout most of my school years. <blush> If we were using Everyday Math, I'd probably never have figured it out either.

 

While I completely understand why the teacher might be confused (inadequate math education with teachers that never properly explained it to her/him) I do think it's a travesty that we let people teach math when they don't seem to understand it, using a curriculum that doesn't make up for their lack of understanding. If the curriculum were better, the teacher would understand it. At least, that's been my experience, working through math all over again as an adult (which is absolutely embarrassing, but at least I put the effort in). It's just as bad that we make teachers teach math with a curriculum that makes it so darn confusing and convinces everyone that the kids don't need to understand it because they know 5 different tricks for each type of problem.

[lionfamily1999]

Well, that's true. lol I think her (his?) problem was that she got too confused typing it all out. MY problem is that I think she'd likely get just as confused doing it in class, since she doesn't even have a written record there. Anyway, how can a kid keep up with all of that, if they don't even understand what's happening in the first place? I honestly don't think the teacher even had a good grasp of regrouping, since the other explanation in the rest of the post was the old "go to your neighbor and borrow a one," and this was the best the person could come up with in response to a question about kids who didn't understand regrouping in subtraction. I feel her pain. I didn't really understand it until I started teaching dd, and I was a straight A student throughout most of my school years. <blush> If we were using Everyday Math, I'd probably never have figured it out either.

 

While I completely understand why the teacher might be confused (inadequate math education with teachers that never properly explained it to her/him) I do think it's a travesty that we let people teach math when they don't seem to understand it, using a curriculum that doesn't make up for their lack of understanding. If the curriculum were better, the teacher would understand it. At least, that's been my experience, working through math all over again as an adult (which is absolutely embarrassing, but at least I put the effort in). It's just as bad that we make teachers teach math with a curriculum that makes it so darn confusing and convinces everyone that the kids don't need to understand it because they know 5 different tricks for each type of problem.

:iagree: completely. That was my point, if it was so easy then they could have gotten it right. That mess was not easy and I agree, I doubt they could have gotten it right on the board.

 

On a lighter note, by neighbor across the street teaches 5th grade math at a ps. She uses Singapore on the sly ;) Sure, the curriculum is that new math, but she teaches Singapore :D

[nmoira]

Sounds similar to terry's subtraction method in Right Start.

It's not a bad mental technique for multi-digit subtraction questions, provided the student can do simple calculations lightning fast; however, its not our preferred technique. We practice going up to the next 100, 1000, 10000 until the calculation is almost instant. Then we chop and add.

 

1562-628 = 562 + 372 = 934 (chop at 1000)

4562-1628 = 2562 + 372 = 2934 (chop at 2000)

 

The master skill here is adding. It's a hold over from our Right Start days. DD the Elder does these like lighting, so the practice certainly paid off.

 

I'm on a phone. I hope I typed all that in right. :tongue_smilie:

Edited April 16, 2011 by nmoira
Typo

[ChrissySC]

(I didn't get my quote to post, but I am referring to Bill's post.)

 

 

I totally agree. This is much like most curricula's mental math (Saxon's name for these approaches.)

[Surfside Academy]

Someone needs to send this teacher a copy of Liping Ma's book! :D

[lindsrae]

Our local ps uses enVision Math...does anyone know if this kind of shenangins goes on in this math curriculum?

[Spy Car]

Our local ps uses enVision Math...does anyone know if this kind of shenangins goes on in this math curriculum?

 

My son's school also uses enVision. He is only in 1st Grade but it doesn't seem to be a bad program. It wouldn't be my choice, but it doesn't resemble what I've seen of Everyday Math.

 

Bill

[MrsMe]

HUH???

 

 

My thoughts exactly. Not a cool trick. It's stupid and time-consuming.

[BBarnes]

Now I get it! My ds has been unsuccessfully trying to subtract like this and I could never understand why. He attended ps K-3 and they taught Everyday math. I'm still trying to break this habit of subtracting up and down.

 

I hated Everyday math, and it's one of the reason I decided to homeschool.

[jewellsmommy]

The standard algorithm isn't the easiest way to solve 807 - 294.

 

Far easier to do it the Singapore mental math style where the subtrahend gets bumped up (+6) to 300. The minuend likewise gets bumped up (+6) and we have:

 

813-300=[ ]

 

Bill

 

 

:thumbup::hurray: for Singapore (and other none crazy maths :tongue_smilie:).

[Spy Car]

:thumbup::hurray: for Singapore (and other none crazy maths :tongue_smilie:).

 

With you!

 

Bill

[MrsMe]

Right here is where my eyes glazed over.

 

 

:lol::lol: Me too! And all that for such an easy problem! Can you imagine standing in line waiting for your change back while the kid goes through this scenario in his head? Good grief! I hate to think what happens when they get into Algebra.

 

Twisted.

[cellocoffee]

Growing up in Taiwan where I learned my basic math(even I wasn't mathy,

I actually enjoyed arithmetic drills)

Such method for a simple question is shocking to me.

It's confusing, inefficient. So glad we r hs-ing and feel sorry

for teachers who have to follow this method.

 

Thanks for sharing, (still in shock)

Edited April 16, 2011 by cellocoffee

[Joyofsixreboot]

Sounds similar to terry's subtraction method in Right Start. I must add in defense of RS that they show different ways to subtract so that students know that there is more than one way to solve a problem. My children never chose to use this method for subtraction. It can be easy, but sometimes it is actually harder! But it is interesting to know that there are many different ways to do a problem and still get the same answer. Sometimes all those choices confuse kids, tho!

 

:iagree:

[Snickerdoodle]

:

If someone had tried this on me when I was a kid, they would have lost me right after the bit about having surgery because I would have thought I wonder who's having surgery and when and why and where and how long will it take and will I have to go visit them because I don't like the way hospitals smell and it is cold in there and ....

 

 

Oh my goodness. You've described one of my kiddos to a T.

 

:lol:

[Tammyla]

Basic math skills are much less complicated and necessary in the long run imo.

[Researcher]

:thumbup::hurray: for Singapore (and other none crazy maths :tongue_smilie:).

 

 

:iagree:

 

 

Sadly, Everyday Math is used in all the public schools here as well as many of the private schools.

[mommycheryl]

It's not a bad mental technique for multi-digit subtraction questions, provided the student can do simple calculations lightning fast; however, its not our preferred technique. We practice going up to the next 100, 1000, 10000 until the calculation is almost instant. Then we chop and add.

 

1562-628 = 562 + 372 = 934 (chop at 1000)

4562-1628 = 2562 + 372 = 2934 (chop at 2000)

 

 

This makes no sense to me. (sorry, but I have no experience with RS math) Is the idea of "chopping" to basically find the difference for each number from the 1000? I am seeing the first probelm as

1562 - 628 turning into

562 (because that is the difference from 1000) + 372 (difference from 628 to 1000). That is the mental math, finding the difference to the number you chop at? Then adding those together?

[Veritaserum]

The standard algorithm isn't the easiest way to solve 807 - 294.

 

Far easier to do it the Singapore mental math style where the subtrahend gets bumped up (+6) to 300. The minuend likewise gets bumped up (+6) and we have:

 

813-300=[ ]

 

Bill

 

Math Mammoth teaches this as well. MM also teaches the standard algorithm. Oy, the elevator talk was confusing!

[IsabelC]

Sounds insane to me. Maybe it would be fun for the more advanced kids who need something to occupy them, "Oh, look at this different way of solving it, I wonder can you figure out why exactly it works", but how the heck could a child who can't master basic subtraction the 'normal' way possibly understand this?

[Capt_Uhura]

Sounds insane to me. Maybe it would be fun for the more advanced kids who need something to occupy them, "Oh, look at this different way of solving it, I wonder can you figure out why exactly it works", but how the heck could a child who can't master basic subtraction the 'normal' way possibly understand this?

 

Exactly! That's how it is used RS.

[Snowfall]

Exactly! That's how it is used RS.

 

I also agree with Hotdrink, and I'm glad to hear that's how it's used in RS. I have RS C and have looked through every lesson, but I didn't remember this method being one of the ways subtraction was first introduced, so I couldn't comment.

 

Editing because I just thought about something. Is there even a logical way to demonstrate that method with manipulatives? I'm sure there is, but can someone explain how it would be done? I'm just curious now. It seems like it wouldn't make sense, since you'd have to be subtracting the minuend from the subtrahend, and how would you show that with manipulatives? My poor, manipulative-deprived math education won't let me picture it. lol

Edited April 16, 2011 by Snowfall

[nmoira]

This makes no sense to me. (sorry, but I have no experience with RS math)

Addition's being the master skill comes from Right Start, but this particular technique DD chose had is genesis in Right Start as well. Subtraction is introduced only briefly in Level B (we dropped RS not too far into C, so we never did get to its version of subtraction from the left), and IIRC only as counting up, as in making change. She saw how easy it was to go to the next 10, 100, etc. and then add. This technique she settled on for working with larger numbers is no different than making 10s in Singapore or MEP and works for her because her mental addition skills are very strong. Basic facts have to be rock solid to be good at mental math, and after that you choose the techniques that play to your strengths.

 

Is the idea of "chopping" to basically find the difference for each number from the 1000? I am seeing the first probelm as

1562 - 628 turning into

562 (because that is the difference from 1000) + 372 (difference from 628 to 1000). That is the mental math, finding the difference to the number you chop at? Then adding those together?

Yes, it's like counting up in chunks. Edited April 16, 2011 by nmoira

[Oak Knoll Mom]

 

My teacher friend said that for the first time, they have more kids in remedial math than in remedial English. This is b/c Everyday Math is so verbal, that before, kids who were struggling w/ English could still learn math. Now w/ math being so heavily word-based, those kids can no longer math. Then add to that, all the kids who are not struggling w/ English, are struggling w/ math b/c of all the verbiage and switching from topic to topic too quickly.

 

Thank you so much for this. I have a child who has difficulty with language processing. Although he shows flashes of genius with math, he still struggles with it too. I couldn't wrap my mind around why he struggled despite seeming to understand math. The quoted part above helped me realize that RightStart, even though it is a wonderful program, is too verbal for him. Light bulb!

 

I bought Math Mammoth Blue series (grouped by topic) and am going to spend the rest of this school year and summer filling in the holes left by RightStart and start him on grade level next fall. (Next fall's program TBD.)

 

Thank you, thank you, thank you!

Edited April 18, 2011 by Oak Knoll Mom
clarification