All this calculator use is misguided nonsense. in engineering school, everyone was proficient in their use, but they were of little value in finding the solution to problems. Of course, once you figured out the solution, calculators saved a lot of time manipulating the large multi-digit numbers and fractions and calculating the trig functions.

Most of the problems we solved had long multistep solutions and the calculator was mostly useless until the last step when you finally simplified everything to get the final answer (a single correct answer I might add). In fact, if you tried to use your calculator too early in the solution you would inevitably introduce rounding errors into your answer. Plus, the answer 2*sqrt2 usually conveys more about the nature of the answer than 2.828.

-- KDeRosa - 29 Sep 2005

good grief

-- CatherineJohnson - 29 Sep 2005

In my article in Ed. Next (An A-Maze-Ing Approach to Math) I put in a sidebar on Everyday Mathematics that includes the excerpt on long division from the teacher's manual that Carolyn quoted as well as the following that appears on EM's web site as well in other materials:

“In one study, only 60 percent of U.S. ten-year-olds achieved mastery of the algorithm using the standard regrouping (borrowing) algorithm. A Japanese study found that only 56 percent of 3rd graders and 74 percent of 5th graders achieved mastery of this algorithm.”

The sidebar talks about how I never got answers to my questions about this "research". I persisted after the article was published and contacted Andy Isaacs who said that he was unable to find the cite for such "research" and said that this statement would be removed (it's still there), since it's hardly rigorous to cite a vaporous study. (He was actually saying that to someone else at EM, and I was actually cc'd on the message!). He did defend his belief that the subtraction algorithm is difficult for students, blah blah blah.

Yes, EM relies on calculators to do many things. As I've pointed out somewhere on KTM previously, the Students Reference Manual has a discussion of equivalent fractions and talks about how to convert 1/5 and 1/4 to percentages or decimals, by multiplying numberator and denominator by 20 and 25 respectively, but when it comes to 5/8, their method is "use the calculator".

My daughter's school supplements EM, though it varies by teacher. Her current teacher uses EM alone; no supplements. Has them work in groups. The other day my daughter had three questions wrong on a worksheet, and yet she had the three preceeding questions correct--the same principle was involved for all of them. So I asked her why she couldn't do the last three. Her response: "Oh, those are the ones Libby did". Libby is her partner at the "group" table, since the teacher has them work in groups for science and math--the team approach. I told my daughter I expect her to do all the problems on the worksheet (of course to the extent she has been given instructioon on how to solve them but that's another issue).

I use Saxon and other texts at home to teach her what she isn't getting at school.

-- BarryGarelick - 29 Sep 2005

I mean the school specifically, as opposed to the state department of ed, or a consultant from E-Math-----

-- CatherineJohnson - 10 Jun 2005

. . . with my son, now three years later, they are drilling those math facts in the Everyday curriculum like there is no tomorrow . . .

GOOD

Do you know if the school decided this?

-- CatherineJohnson - 10 Jun 2005

I can tell you that my daughter had NO IDEA how to do division at the end of 5th grade. I thought that she didn't get it...

She also wasn't strong in the lattice method of multiplication. Honestly, there were so many addition steps that she was bound to make a mistake -- especially since drilling of any type of math fact was out of the question, although, with my son, now three years later, they are drilling those math facts in the Everyday curriculum like there is no tomorrow. I'm sure the math tests forced them to it (against their better teaching judgement, of course.)

-- KatherineProuty - 10 Jun 2005

Mastery of the intricacies of these algorithms is a huge undertaking, and one that experience tells us is doomed to failure for many students...."

Frankly, I am shocked to find a statement like that in a teacher's manual. And learning long division is a huge undertaking? Give me a break.

Me, too.

I see this constantly in constructivist books.

This stuff is too hard to teach, so let's not teach it.

Let's just understand it.

Well, understanding is easy, compared to doing.

I understand how to play the piano, for pete's sake.

But can I sit down and play a Mozart concerto?

No.

-- CatherineJohnson - 09 Jun 2005

This is absolutely horrifying. I had no idea.

Suddenly you're seeing a problem like 365/.5????

I'm speechless.

Writing this blog with you, I'm realizing that my own problems have been in a completely different category.

Christopher has been using SRA Math, which, one of our readers pointed out, is a very demanding curriculum. (I'll say.)

I don't know what I think about SRA; at first I hated it, mostly because I couldn't teach from it.

But then, again, I'm not a trained teacher, and I hadn't done grade school math in years.

I'd have to sit down and seriously go through the book to have an informed opinion----look at the sequence of topics, the level of repeated practice, etc.

I do think that it's a hard book to teach from even if you are trained and have experience; every teacher I've discussed it with at our school has said so immediately. And I've found it's quite difficult for me to learn, or re-learn, concepts from the books.

Still, it's nothing like fuzzy math.

Everything is taught in SRA Math, everything. (And taught FAST.)

We've been struggling around here for a completely different reason.

-- CatherineJohnson - 09 Jun 2005

EverydayMathEpilogue

In which I finally get to graduate from Everyday Math.

I guess I'm just slow on the uptake. I finally figured out why I ended up teaching so much of what I consider basic math to my son in the last two years; it wasn't that he spaced out and missed it, it was that it never was taught at all.

What threw me off was that problems using these skills cropped up in the text anyway. When Ben came home with homework he was unable to do, I assumed he'd just failed to get it.

It turns out, though, that the kids were just supposed to use calculators. Duh.

Ben graduated from elementary school last night, in a two-hour tear-jerking ceremony to end all ceremonies. Every kid got a special award with his diploma: the Math Wizard award, the Most Encouraging award, the Future Leader award, the Social Butterfly award. Ben got the Energizer Bunny award. He really did.

And today I found this discussion of excerpted material from the Everyday Math Teacher's Reference Manual, grades 4-6. It explained so much.

When discussing the Fraction-Addition Algorithm, the authors state: "It is important to note that Everyday Mathematics does not support the traditional emphasis on finding a least common denominator. This approach is excessive, too formal, and without much meaning for many people. In fact, implying the least common denominators are the only permissible denominators is probably harmful to later learning in algebra."

Will someone please explain to me why there is so much fear, in math education, of the harm that learning things might do? How about the damage done when you don't learn things?

The Everyday Mathematics curriculum displays a clear preference for the partial-products algorithm for multiplication, which is extraordinarily cumbersome for all but simplistic calculations, requiring n time m intermediate, or partial, products instead of min(n,m) as required by the standard algorithm. (The numbers n and m represent the number of digits in each number.)

Actually, there is something to Everyday Math's claim that the partial-products algorithm has value because of its similarity to an algorithm taught in high school for multiplying binomials. Remember having to multiply expressions like (x+y)(a+b), using a method that was acronymized as FOIL (first, outer, inner, last)?

To get the result, you first multiply the first factors (x and a), then the outer ones (x and b), then the inner ones (y and a), then the last (y and b). That's the algebraic version of what Everyday math calls the partial products method: 53 times 36 gets multiplied as (50+3)*(30+6)= 50*30 + 50*6 + 3*30 + 3*6.

The problem with using this algorithm for multiplying numbers is that you end up adding 4 terms together, instead of the two you could have if you used the standard algorithm, which is a lot more efficient. If you use the partial-products algorithm to multiply two three-digit numbers, you'll get 9 summands to add instead of 3; but the Everyday Math Teacher's manual would never recommend that you do that. It would tell you that smart people -- sensible people -- use a calculator.

But I really believe in the value of teaching an efficient algorithm. Kids who are growing up to be engineers, computer scientists, physicists, mathematicians, chemists, analysts, statisticians and finance experts need to learn to appreciate efficiency in algorithms.

"The authors of Everyday Mathematics do not believe it is worth the time and effort to fully develop paper-and-pencil long division algorithms for all possible whole number, fraction, and decimal problems. Mastery of the intricacies of these algorithms is a huge undertaking, and one that experience tells us is doomed to failure for many students...."

Frankly, I am shocked to find a statement like that in a teacher's manual. And learning long division is a huge undertaking? Give me a break.

Anyway, this explains why I suddenly found problems like 365/.5 in Ben's homework, without any preamble whatsoever, or any explanation of the meaning of dividing by a decimal. To me, it represented a whole new requirement for understanding and skill; to Everyday Math, it was just an extra keystroke on a calculator. Anyway, I swung into action the night we found that problem, and gave Ben a crash course in decimal division; it was one of my finer moments of reactive teaching.

"It simply does not seem wise to invest 100 hours or more on instruction and practice of algorithms that some students will succeed at doing slowly on paper, with uncertain results, while nearly anyone can quickly and accurately find a quotient with a calculator."

Concerning accuracy and calculators, see GirlVsCalculator.

"This said, the practical needs of students to succeed on outdated standardized tests may require you to teach long division algorithms."

Not to mention their practical needs for passing algebra, calculus and physics later on in their lives.


AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

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• Posted by: CarolynJohnston
• LogDate: Jun 08, 2005 @ 23:47