Weekly Math Updates

March 28, 2007


  • Goals
  • The Enron of Education
  • Brain Programming - A Simple Question
  • Utah's Real Math Scores
  • Weekly Comic - yeah, it's personal...that's me!


Hi all,

Remember the list of goals I had put together a year ago? A couple months ago someone asked me about them and I reprinted them. Well I think we can pretty much check off number 3 now even though not quite the way I'd hoped it would be.

1) Elect a solid school board member who understands the math concerns (Accomplished)
2) Get Utah to adopt CA's math standards (New "world class" standards coming)
3) Get ASD to choose 2 quality math programs to allow us to pick from (Accomplished--though the picks could have been better)
4) Split ASD into smaller sizes to rein in the power and restore local control (in process)

Regarding number 4, I think there are significant things in process that will cause this to happen in the future. Last weekend I met with several legislators in a brainstorming session on education reform ideas. It was a very productive meeting. I will tell you that besides smaller districts, my number one item was to pass a "Truth in Grading" act which would cause schools to be more responsible for the grades they pass out. No more straight A's for children that don't know the concepts but give a valient effort writing down the process. As it happens, this type of accountability is sort of in process with a couple of bills that passed last session, not directly addressing this, but will indirectly. More on this another time though.

The Enron of Education

As an accountant I watched Enron from a different perspective than non-accountants did. I knew wrong had been done and a penalty was paid by many including Arthur Anderson's collapse which caused the loss of thousands of innocent peoples' jobs. Corporate America now has a new set of regulations to abide by under SOX (Sarbaines Oxley) and I fully support it to better ensure the honesty and integrity of the system. What those accountants were missing was an NEA behind them which could have prevented those intrusive reforms. ;)

Just as corporate America denied there was a problem until it really blew up in their faces, today we have many facets of public education that could be considered early warning signs of their own "Enron." It's just not politically correct to point them out or stir the pot or you're labeled a number of things including biased, flawed, crackpot, and so on (and those are only the ones I have personal knowledge of being called :)).

When parents have no control over their child's education and start homeschooling or paying extra money for private schooling, the enormous growth of charter schools, the UEA actively enlisting the PTA's and fighting change to protect their dominion, etc..., you have all the signs of corporate corruption protecting it's turf and customers backing away from the very real problems they see. Customers don't usually open their mouths when there's a problem, they just quietly back off and find another vendor to meet their needs. Most problems companies have aren't known to them unless they have a really open feedback mechanism that actually listens to its customers and when customers see another customer chopped to pieces they are reticent to open their own mouths for fear of going through the same experience.

People invested in the corporation are often scared to become "whistleblowers" and risk their job or future opportunities, yet they can have a vital role in saving the company from major embarrassment or complete collapse.

Brain Programming - A Simple Question

A couple months ago I got some fascinating information about the brain that I knew I wanted to share with you but so much else has been happening I put it in the background till now.

I don't know how long ago this was, but researchers hooked up an MRI to several people's brains and monitored what happened when they exposed them to math problems. What happened surprised them. They knew there was a conscious center of thought that should light up, but they were surprised when 5 other areas of the brain known to be subconscious areas also lit up. They discovered that math isn't done consciously except what the person has to think about. Math is processed in parts of the brain that function on the order of 800 times faster than the consciousness.

Here's another fascinating thing, they put these people on sedatives and the conscious area lights went out on the MRI's but the subconscious didn't. You DO have cognitive thought at the subconscious level.

The research also showed that new connections can be made in the brain which leads to enhanced capacity and "plasticity". You can still learn and memorize even in old age.

So here's a little puzzle for you. In the world of computers, you have high and low level languages. Thankfully, billiant people have come along and done heavy programming work to make your life easier so you can write in a high level language and a "compiler" will translate it into language the machine understands. Here's an example using a simple program that prints "Hello World" to your computer screen in a high and low level language.

High Level--C Code (nice and short)

#include <stdio.h>

int main()
    printf("Hello World\n");

Lower Level--Assembly Code (a lot more work)

 .file "hello.c"
# GNU C version 4.1.1 (Gentoo 4.1.1-r3) (i686-pc-linux-gnu)
# compiled by GNU C version 4.1.1 (Gentoo 4.1.1-r3).
# GGC heuristics: --param ggc-min-expand=100 --param ggc-min-heapsize=131072
# options passed:  -mtune=pentiumpro -auxbase -fverbose-asm
# options enabled:  -falign-loops -fargument-alias -fbranch-count-reg
# -fcommon -fearly-inlining -feliminate-unused-debug-types -ffunction-cse
# -fgcse-lm -fident -finline-functions-called-once -fivopts
# -fkeep-static-consts -fleading-underscore -floop-optimize2 -fmath-errno
# -fpcc-struct-return -fpeephole -fsched-interblock -fsched-spec
# -fsched-stalled-insns-dep -fshow-column -fsplit-ivs-in-unroller
# -ftrapping-math -ftree-loop-im -ftree-loop-ivcanon -ftree-loop-optimize
# -ftree-vect-loop-version -fverbose-asm -fzero-initialized-in-bss -m32
# -m80387 -m96bit-long-double -maccumulate-outgoing-args -malign-stringops
# -mfancy-math-387 -mfp-ret-in-387 -mieee-fp -mno-red-zone -mpush-args
# -mtls-direct-seg-refs
# Compiler executable checksum: c5661af1fb414d3746241fc893b6891a

 .section .rodata
 .string "Hello World"
.globl main
 .type main, @function
 leal 4(%esp), %ecx #,
 andl $-16, %esp #,
 pushl -4(%ecx) #
 pushl %ebp #
 movl %esp, %ebp #,
 pushl %ecx #
 subl $4, %esp #,
 movl $.LC0, (%esp) #,
 call puts #
 addl $4, %esp #,
 popl %ecx #
 popl %ebp #
 leal -4(%ecx), %esp #,
 .size main, .-main
 .ident "GCC: (GNU) 4.1.1 (Gentoo 4.1.1-r3)"
 .section .note.GNU-stack,"",@progbits

Lowest Level--Machine Language (did people actually do this at one time?)

This is where everything above is translated down to 1's and 0's. I'm not going to reproduce the actual code here but it would be a lot longer than the above text and consist of just a lot of this kind of stuff:

1001010110101001011010110101110001010110100101001011001010 (repeat this about 1,000 times)

Now here's the question...which would you want to program in?

Your brain functions at the lowest levels way in the background so you don't have to consciously think about what it's processing. If someone asks you what 5 * 8 is, if you don't have that hard coded into your brain's subconscious by having mastered it, then your conscious brain has to think about it and try to calculate it. Your brain is crippled because the machine and perhaps assembly languages are what your conscious mind has to work with.

Investigations and other fuzzy math programs goal is to get kids to do critical and higher level thinking. The problem is they skip the steps that put the machine and assembly language programming into the subconscious where the power of the mind is most efficient. They hand kids what they say is a "C" language program routine without ever giving the kids a compiler that knows the lower levels, so that routine has to be processed completely in the conscious and slower mind.

Let me state this another way. Kids that use Saxon and other strong programs which require fact practice and mastery of procedures, are given the internal programming that is needed to free the conscious mind up to do higher level programming (thinking). The geniuses of our time are not the people that walk around with a calculator to do math problems, they're the ones that disciplined their mind to master low order skills early on to free up their minds to make lightning fast connections when confronted with a problem in a real world high-level setting. Kids that don't get that deep programming of fact mastery will never achieve higher order thinking because the low order thinking wasn't drilled into their subconscious to the point of automaticity and their "CPU cycles" are wasted by having to do low level processes consciously.

Marsh Kaminsky made early childhood development his 2nd career (after his CPA days) and wrote a book I've previously talked about called "Wonderkidz." I went to Chicago last November to meet him and I have previously spoken about his efforts and knowledge. His research showed that most brain development happens by age 5. The earlier the start in "programming" kids to know the alphabet and number skills, the more neural development happens inside the brain to further it's intelligence and ability to later process new information. This is why people say it's best to teach children foreign languages when they're very young...the brain is more pliable and ready to establish vast 3-d traffic lanes for greater speed and processing power later on. The IQ of a child is raised by giving them early stimulus instead of waiting for it to all happen in school.

Is there a problem along the way telling the student, "by the way, there's higher orders for you to use later once you've got the basic compiler routines down"? Absolutely not, but shortchanging the student by teaching them higher order thinking (if you can even associate Investigations and the other "new math" programs with that) will never address the failure of the system to provide a solid compiler full of the lower level routines that will then know what to do with higher order commands later.

Singapore and Saxon math are perfect examples of balanced math.  They program the mind to know how to do math as well as asking appropriate questions to ensure children understand math.

Utah's Real Math Scores

Utah's math scores are above national average right? That's what we keep hearing. The other thing we keep hearing is Alpine School District's scores are above Utah's average. Wrong on at least one account. Members of the state school board have recognized that Utah's demographics are artificially inflating our scores.

The missing piece of this puzzle comes in understanding that Utah is home to more White kids than most other states. White kids have higher test scores than Blacks and Hispanics, typically, and Utah's 82% White population is weighing in at a higher factor when compared to other states with lower white populations.

The real picture if you take all the scores from all the states is that Utah's Whites are in the bottom third of the nation.

http://nces.ed.gov/nationsreportcard/states/profile.asp (Utah's profile and scores)

As for ASD being above Utah and above the national average, that's actually up in the air without knowing exactly where ASD comes in on NAEP scores. I don't know if those figures are available, but Utah at least has a bit of room for improvement.

Weekly Comic

I'm sorry to say, but last week's comic was short lived as my favorite. I know most of you don't know what I look like, but that's yours truly in our superintendent's dream. :) I did send him an autographed copy of this comic and have been informed that he laughed "loud and hard" when he saw it.

Archive: http://www.weaponsofmathdestruction.com

Till next week,

Oak Norton


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