Sunday, June 10, 2007

Making Good Choices (remix)


I like having a choice. For example, it’s nice to know that I can read what I want, wear what I want, and go where I want, all within reason of course. I really think that for the most part, choice is a good thing.

But when it comes to adding, subtracting, multiplying and dividing, is it always that wonderful? I mean, do we really need 15 algorithms to add, subtract, multiply, and divide? In Everyday Math there are at least 15 ways taught to perform 4 operations (+,-,x,%). Actually, when you add the remaining 3 STANDARD operations (they do teach to add using a standard algorithm), that makes 18 ways to do 4 operations, doesn't it? I feel sick already....

The funny thing is that only 1 of the 15 algorithms is a standard operation in Everyday Math… and that’s the algorithm for addition that Everyday Math calls the “fast method”. I'm not really sure why you would even want to do one that was slow, tedious or inefficient. When it comes to the other 3 STANDARD operations (subtraction, multiplication, division) they just didn’t make the Everyday Math algorithm cut, I suppose. Maybe 18 algorithms is a few too many even for the folks at EM. Of course, the all powerful long division didn’t even make the "final fifteen” at all. And as for borrowing and carrying, who needs that nonsense when you can 'trade first' or use 'partial sums' instead? You could also count backwards on the number chart and of course, there's always a calculator!

According to the publisher “Research has shown that teaching the standard U.S. algorithms fails with large numbers of children, and that alternative algorithms are often easier for children to understand and learn. For this reason, Everyday Mathematics introduces children to a variety of alternative procedures in addition to the customary algorithms.”


I would love to know which research they are referring to. They certainly aren’t talking about my children or most of the children I know. They are perfectly capable of understanding and learning to use standard algorithms quite well, thank you.

The many algorithms of Everyday Mathematics are described in detail by Bas Braams here:
http://math.nyu.edu/~braams/links/em-arith.html

And by the Everyday Mathematics publisher here:
http://everydaymath.uchicago.edu/educators/Algorithms_final.pdf

Here’s a quick summary:

Addition
1. partial sums* (focus algorithm)
2. column addition
3. fast method (standard/traditional addition)
4. opposite change rule

Subtraction
1. trade first* (focus algorithm)
2. left to right subtraction
3. counting up
4. partial differences
5. same change rule
**Standard subtraction method is not part of Everyday Mathematics

Multiplication
1. partial products method* (focus algorithm)
2. lattice method
3. short method
4. Egyptian method
**Standard multiplication algorithm is not part of Everyday Mathematics curriculum

Division
1. partial quotients method* (focus algorithm)
2. column division

**Standard method of long division is not part of Everyday Mathematics curriculum.

Everyday Math has these “focus algorithms” that they expect all students to learn at some point although “as always in Everyday Mathematics, students are encouraged to use whatever method they prefer when they solve problems.” (Algorithms in Everyday Mathematics)

These focus algorithms are supposed to be “for those students who do not achieve proficiency using other algorithms” and yet there are no pre-assessments to see what algorithms the students already bring to the table because the EM folks don't really care what you already know. You had better learn the 15 algorithms though, because the homework, class work, and tests require you to show your work using the algorithm d’jour. Which I repeat, does not include long division. Even the “left to right subtraction” method for subtraction and the “short method” for multiplication are a variation of the standard method. Apparently, in Everyday Mathematics, nothing is sacred.


Take a look at how Everyday Mathematics handles division here: http://www.youtube.com/watch?v=eKld7lQHKRg



The funny thing is, I'm thinking even the authors seem understand how ridiculous this is. They constantly reiterate, “students are encouraged to use whatever method they prefer when they solve problems" and yet they contradict themselves when the homework consists of showing multiplication work using the “lattice method” and the test requires students to show their work in this way as well. What happened to that opportunity to choose something a little more efficient or that you’re simply more comfortable with?

Even teachers are given a way out of this ‘madness’ by the authors of Everyday Mathematics who state, “a teacher who has developed an effective strategy for teaching algorithms, and who feels that the focus algorithm approach is unnecessary or compromises that strategy, is not obliged to adopt the focus algorithms approach.”

Of course, there may be students who choose to use the focus algorithms or any of the other unconventional algorithms mostly because they haven’t learned to use the more efficient ones. For some students, Everyday Math is all they know. While some classmates are busily drawing a lattice, my child has completed at least four equations. Correctly and with understanding. Is it so impossible to believe that some children actually love math? That some if not most, can gain understanding using standard algorithms presented in context and by a well prepared teacher who hopefully also loves math? That some children are actually encouraged to have a work ethic that propels them to seek greater and greater challenge?

Standard algorithms really deserve a fair shake before being discarded for less efficient ones. After all, there is something to be said for the "fabulous four" standard operations that have withstood the test of time and continue to be the preferred choice of the majority of the math and science community and at least one first grader and one fourth grader I know very well.

1 comment:

Dom Rosa said...

Everyday Mathematics is part of our system of pseudo-education that Andrei Toom exposed in his landmark article, "A Russian Teacher in America," which was published in the Journal of Mathematical Behavior, and is reproduced at:

http://www.inform.umd.edu/EdRes/Colleges/ARHU/Depts/CompLit/cmltgrad/JSchaub/ta_main/toom.html