Comments on: Augends, Addends and Commutative Property of Addition

By: The Math Mojo Chronicles » Learning Multiplication by Rote is a Disease

The Math Mojo Chronicles » Learning Multiplication by Rote is a Disease — Sun, 30 Mar 2008 04:15:13 +0000

[...] for visiting!Today a concerned reader took issue with what he understands my methods to be. (See comment #4 at Augends, Addends and the Commutative Law of Addition.) Fair enough, but I think he may have misunderstood my [...]

By: Al Aunchman

Al Aunchman — Sat, 29 Mar 2008 17:00:06 +0000

After all these years (30) of struggling to teach children math, I finally realize why it is so difficult. A brief perusal of some of the mathematical girations you go through to multiply two numbers together explains a lot of why kids are poor at math. Commutative and associative properties are more easily understood when you have the basic tools to work with without adding zeros then subtracting the number from your cousins name on your mother’s side of the family. Teach the basics by rote then progress to the more abstract. Simple to complex seems to work.

Professor Homunculus sez:

Al, I’m sorry you’ve come to that conclusion. If you’ve been teaching math for 30 years, you surely have some insights. But I can’t see see how you’d say, “simple to complex” seems to work. May I ask where it seems to work? And if it does, why is it a struggle for you, and why is it so difficult? Have you been teaching with the “girations” (sic) you say I use to make it so frustrating?

I’m not quite sure I understand the logic of your position.

I’m not being facetious (facetious would be, “… subtracting the number from your cousins name on your mother’s side of the family…”).

I’ve thought a lot about what you said here, and will add more to this reply at my next posting (probably today, Mar. 28, ‘08)

(Caveat - Although I’m not being facetious here, the post will be pretty facetious. Please don’t take it personally. It’s a sickness.)

By: blackhawkmath

blackhawkmath — Wed, 05 Mar 2008 06:22:18 +0000

There are no such things as secondary or tertiary subtrahends. This is because subtraction is a binary operation, it only works with two inputs. So when there is more than one operator, you must identify the principal operator, which is:
*the last one performed
*the only one outside of grouping symbols (parentheses) when all possible grouping symbols are used to help indicate the correct order of operations intended.

So, in your example, “8-3-2″ which is the minuend and which is the subtrahend is determined by which operator (subtraction sign or dash) is the principal operator.

If we put in parentheses that correspond to the correct order of operations, then ‘(8-3)’ is the minuend and ‘2′ is the subtrahend. The minuend also happens to be an indicated difference (which is just another way to write the number 5).

If we insert parentheses thus: ‘8 - (3 - 2)’ we get a completely different problem and answer, since subtraction is not associative. In this expression, 8 is the minuend and ‘(3 - 2)’ is the subtrahend.

The four operations (+, -, *, and /) are all binary, and so each operator should be considered separately after its two inputs are determined, regardless of how many other operators the inputs contain. One should always be aware of the correct order of operations, as this can be very difficult in some cases!

Professor Homunculus sez:

Thanks so much for a clear and informative answer, Blackhawk!

By: Richard Masoner

Richard Masoner — Mon, 03 Mar 2008 20:25:46 +0000

I’m glad you like the photo and thanks for the attribution! I’m a math nerd — I’ll have to check out your blog.

By: Mark Schooley

Mark Schooley — Sat, 01 Mar 2008 18:52:22 +0000

Are you saying that’s Augie Doggie? How do you know it’s not Doggy Daddy? ;)

Brian Sez:

Well, Hallelujah! Someone got it! The big picture is Doggy Daddy, but if you look at the door train, Augie is about to get on. Daddy is running for the train.
I just sent you an e-mail asking you which booklet you’d like.

Thanks for playing “Quiz the Whiz”