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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 32   Last Post: Jul 7, 2013 9:03 PM

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Robert Hansen

Posts: 7,569
From: Florida
Registered: 6/22/09
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 5, 2013 7:41 PM
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On Jul 5, 2013, at 2:14 PM, Joe Niederberger <niederberger@comcast.net> wrote:

> Just caught my eye:
> http://www.oercommons.org/authoring/1364-basic-wff-n-proof-a-teaching-guide/view
>
> "In the past, studies show that rigorous play and applications can affect IQ scores of 21 points. Problem-solving, improved order thinking and reasoning skills are heightened."
>
> That's quite a claim! I skeptical, but it just caught my eye as I said.
>
> Cheers,
> Joe N


I could see a 20 point delta if I had taken an IQ test prior to 8th grade rather than after. It wasn't that I learned anything specifically in school that would affect an IQ test. But when we moved and I attended a middle class school with real classes and peers, as opposed to the previous impoverished one, the mental challenge was altogether a different experience. It was like turning on the light. That would be rare though.

I do believe we need more rigor in school if that is what you are after. I do believe that our college bound students are mostly suffering a very poor example of what we enjoyed academically and took for granted in our day. Come to think of it, a poor example of what we enjoyed vocationally as well (remember shop). I do believe that while our average middle class high school of the 70's wasn't a Stuyvesant, it still offered a lot of challenge to college bound (brighter) students. That is mostly gone now. When a student says they took Algebra 2 or Calculus in school and liked it, I am almost too afraid to ask them what they liked. I had a candidate once that majored in mathematics and I, not knowing any better, made the mistake of asking her what her favorite courses were.

Some, well, mainly Lou, have questioned my hypothesis that there has been a decline. Although, I think he means a decline in student ability, not a decline in the quality of mathematics education. I recall being exposed to so many derivations in my classes and producing many of them myself. Those are mostly gone today. Sure, I remember that many of my fellow students back then passed the class without deriving any of the trig sum and difference identities. But they didn't score as highly as those of us that could. And I don't recall seeing those same students continuing on in the more advanced subjects or worse yet, majoring in mathematics. Those derivations were there and need to be there for the aspiring students.

Do you realize that the majority of "good" honors courses teach from reprints of textbooks that are 30 years old. I am talking about high school algebra that is nearly as complete in principle and practice as what used to be known as college algebra, which is itself extinct. That is pretty scary when you think about it. Why are there so few (if any) books being created for the students that have actual ability with these subjects and so many books being created for those that do not? It's pretty crazy. As a parent you have to really shop around to find the authentic courses amidst all the fraud.

We have a school similar to the school your son attends. A public, semi selective (but not as selective as yours) junior/senior high school. Unfortunately, it is filled by a lottery and not by test scores, but because it espouses academic rigor, that does seem to be a somewhat effective filter and the average SAT scores (for the school) are in the low 1200's which is 200 points above the average SAT score. But all I can do is prepare my son and hope that he wins the lottery. If that fails then I will probably go with a nearby private school. The public school system has proven that they can produce rigorous schools that are as good as the best private schools. What keeps them from expanding this model?

Bob Hansen


Date Subject Author
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Clyde Greeno
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Jonathan Crabtree
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy

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