The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Education » mathedcc

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Re: memorizing Math facts
Replies: 35   Last Post: Sep 2, 2009 10:04 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robert Hansen

Posts: 11,345
From: Florida
Registered: 6/22/09
Re: memorizing Math facts
Posted: Aug 23, 2009 10:41 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"A developmental course like Alain's is perfect for this approach."

Have you actually read Alain's book?

I cannot find any subset of students to which this treatment of arithmetic is applicable. And maybe I just don't know how developmentally challanged some students are. But if I had this much trouble following it, then I would suppose that it would be hopeless for a weak student to follow it. And I am using the term "follow" loosely. I was not actually able to follow most of it, or at least place it into mathematical reasoning.

The ontology is the most convoluted and complicated presentation of arithmetic I have ever witnessed. It reminds me of my tensor calculus book.

It is wrong on so many levels that it will probably take me a week to discuss its "wrongness".

I have to be honest here, this is an absolutely unintelligible treatment of arithmetic. I know it's title says algebra but it never even gets to algebra. This is probably due to its introductory statement being so far off the mark...

"To put it as briefly as possible, Arithmetic and Algebra are both about developing procedures to figure out on paper the result of real-world processes without having to go through the real-world processes themselves."

That is a definition of computation. Math is about REASONING not procedure.

Arithmetic is about understanding addition, subtraction, multiplication and division. It doesn't matter if we are talking about 6 dollars divided into 4 equal groups of 6 billion dollars divided into 4 equal groups. Once you recognize the DIVISION, the problem is solved. There is no reasoning left from the original problem of arithmetic, it is now a problem of computation.

As a rule of thumb, once you have reduced any problem to a procedure, the reasoning is OVER. However, you must understand the reasoning behind the procedures in order to be able to reduce a problem to a procedure. Thus, for students to use a procedure like long division, they must first develop it in the classroom.

This book isn't developing anything. It seems more interested in obfuscating simple arithmetic with a strange ontology and vocabulary. It is trying to equate mathematical reasoning to english statements, and is so over the top in this aspect that it even makes simple and intuitive concepts like "counting" incomprehensible.

I would really like to see someone that thinks that this is a "perfect" approach show me how a student of this book would get ANY questions right in the SAT math section. Show me where the algebraic reasoning was even developed in any section of the book to actually do algebra.


As I said before, I am totally clueless on what the purpose of this book is. I guess that leaves the possibility that there is another "math" out there that is incomprehensible by mathematicians but is still valid. Obfuscate the entire essence enough and you almost feel like you are discussing the existence of god.

Well, thank god we have authentic problems of algebra to test against.


Date Subject Author
8/22/09
Read Re: memorizing Math facts
Wayne Mackey
8/23/09
Read Re: memorizing Math facts
Jonathan Groves
8/23/09
Read Re: memorizing Math facts
Robert Hansen
8/23/09
Read Re: memorizing Math facts
Alain Schremmer
8/26/09
Read Re: memorizing Math facts
Alain Schremmer
8/27/09
Read Re: memorizing Math facts
Robert Hansen
8/27/09
Read Re: memorizing Math facts
Alain Schremmer
8/28/09
Read Re: memorizing Math facts
Alain Schremmer
8/28/09
Read Re: memorizing Math facts
Jonathan Groves
8/30/09
Read Re: memorizing Math facts
Alain Schremmer
8/30/09
Read Re: memorizing Math facts
Alain Schremmer
8/30/09
Read Re: memorizing Math facts
Jonathan Groves
8/30/09
Read Re: memorizing Math facts
Robert Hansen
9/2/09
Read Re: memorizing Math facts
Alain Schremmer
9/2/09
Read Re: memorizing Math facts
Alain Schremmer
8/30/09
Read Re: memorizing Math facts
Jonathan Groves
9/2/09
Read Re: memorizing Math facts
Alain Schremmer
8/23/09
Read Re: memorizing Math facts
Robert Hansen
8/24/09
Read Re: memorizing Math facts
Jonathan Groves
8/25/09
Read pace of college courses
Beth Hentges
8/25/09
Read Re: pace of college courses
dradcliffe@gmail.com
8/26/09
Read RE: pace of college courses
Beth Hentges
8/26/09
Read FW: pace of college courses
Bruce Yoshiwara
8/26/09
Read RE: pace of college courses
Mowers, Kathy \(Owensboro\)
8/28/09
Read Re: pace of college courses
Jonathan Groves
8/30/09
Read Re: pace of college courses
Alain Schremmer
8/30/09
Read Re: pace of college courses
Jonathan Groves
9/2/09
Read Re: pace of college courses
Alain Schremmer
8/30/09
Read Re: pace of college courses
dradcliffe@gmail.com
8/30/09
Read Re: pace of college courses
Alain Schremmer
9/1/09
Read Re: pace of college courses
Wayne Mackey
9/1/09
Read Re: pace of college courses
Phil Mahler
9/1/09
Read Math Porfolio
Jodi Cotten
9/2/09
Read Re: pace of college courses
Alain Schremmer
8/31/09
Read Re: memorizing Math facts
EllysePerry
9/2/09
Read Re: memorizing Math facts
Alain Schremmer

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.