My dad figured this out years ago.

The string method work for all matrices, and it is at least ten times quicker to “do” than to “write about”.

My dad figured this out years ago.

The string method work for all matrices, and it is at least ten times quicker to “do” than to “write about”.

Filed under algebra, education, math, teaching, transformations, Uncategorized

Optional, yet optimal…..

Dear Assistant Superintendent MacGuffin:

Thank you for your interest in partnering with aggravatED, the education consultant-management education consulting firm, and for so thoughtfully completing our preliminary readiness screening tool, the Partner, Initiative, & Stakeholder Survey (PISS™).

Our consultant-management consultants looked with great interest at your PISS™, and they concluded definitively that your district would benefit from our innovative, strategic, and accountability-focused guidance.

As you may remember from our informational materials, our initial PISS™ analyses categorize participating schools/districts into four categories describing overall focus and consistency: Laser, Inconsistent, Diffuse, and Without Tangible Focus (WTF).

According to this scale, our initial analysis — which included a study of historic district performance and engagement data — identified your district’s PISS™ as just at the division between ‘Diffuse’ and ‘WTF’. Below are a few noteworthy — and seemingly competing — initiatives/partners that helped us reach these conclusions:

- Partnership with disruptED, ed-tech firm facilitating district’s…

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I was pondering the reality of negative numbers and after figuring out that a sequence of dots on a line can be extended in each of the two directions, and then arbitrarily selecting one dot as “the zero”. The line can be further labelled as 1, 2, 3, … to one side and -1, -2, -3, … on the other side.

(better to label the 1, 2, 3, … as +1, +2, +3, … and consider the lot as “signed numbers”)

Soon proceeding towards arithmetic I concluded that 7-3 is 4, and also 8-4 is 4, and therefore 13-9 is 4, and then 3-7 is -4, and -2-2 is -4. It was then observed that if a-b=c then a-y-(b-y) is also equal to c, regardless of the signs of the specific numbers involved.

This of course is stunningly obvious when looking at the signed difference of the first and the second number as an extended number line diagram.

The outcome of all this was an arithmetic for 0, 1, 2 modulo 3, and the signed difference x-y is a binary operation diff(x,y) with table:

…x … 0 1 2

y

0 0 1 2

1 2 0 1

2 1 2 0

Example: 1-2 is -1, which is 2 modulo 3

So a non abelian, non associative algebra with a not quite identity satisfies the conditions, where A=1, B=2 and C=0

—————————————————–

There are three objects and an operation called “doesn’t have a name”.

Two are similar, and the third is a bit different

They are paired to yield a single object as follows:

AA = BB = CC = C

AB = BC = CA = B

AC = CB = BA = A

Notice that BC and CB are different, so non-abelian.

Worse is that (AC)A = C and A(CA) = B are different, so non-associative.

And consequently A and B and C are different.

—————————————————-

Interestingly, and maybe separately, the minus sign behaves very differently from the plus sign:

a-(-b) is a+b, but there is no way of writing a-b using only addition.

This means that all expressions can be written with “minus” alone.

Filed under abstract, algebra, arithmetic, Uncategorized

This is a challenge !!!!!

There are three objects, A, B, and C, and an operation called “doesn’t have a name”.

Two are similar, and the third is a bit different

They are paired to yield a single object as follows:

AA = BB = CC = C

AB = BC = CA = B

AC = CB = BA = A

Notice that BC and CB are different, so non-abelian.

Worse is that (AC)A = C and A(CA) = B are different, so non-associative.

And consequently A and B and C are different.

Your job is to identify (model, in current jargon) the objects and the operation.”

The next post will be “the solution”.

Filed under abstract, algebra, Uncategorized

The video is scary:

Back in 1977, Superintendent James Guines of Washington D.C. explained his district’s competency-based education pilot program like this:

“The basic idea is to break down complicated learning into a sequence of clear simple skills that virtually everyone can master, although at different rates of speed.If you can train a pigeon to fly up there and press a button and set off a bomb, why can’t you teach human beings to behave in an effective and rational way?”

“We know we can modify human behavior. We’re not scared of that,” he added. “This is the biggest thing that’s happening in education today.”

HA! Those crazy 70’s! Boy did they have some crazy ideas back then.

But wait…

Now check out this recent video from Angela Duckworth and Katherine Milkman:

Here’s what Milkman has to say:

“If you repeatedly reward good behavior, and pair it with memorable cues, positive routines become…

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Try this for size:

Filed under arithmetic, critical thinking, math, Uncategorized

I have to go along with this.

You can get the conclusion, but the rest is quite compelling.

“In conclusion, it would be wonderful to be able to get all students competent in Excel and arithmetic, and a little bit of algebra, statistics and programming. Higher mathematics should be offered and taken by those who need it, or want it; but never required of all students.”

https://fee.org/articles/the-greatest-myth-about-math-education/?utm_medium=popular_widget

The article is from the “Foundation for Economic Education”

Filed under math, Uncategorized

Nice one!

I’ve been on book tour for nearly a month now, and I’ve come across a bunch of arguments pushing against my book’s theses. I welcome them, because I want to be informed. So far, though, I haven’t been convinced I made any egregious errors.

Here’s an example of an argument I’ve seen consistently when it comes to the defense of the teacher value-added model (VAM) scores, and sometimes the recidivism risk scores as well. Namely, that the teacher’s VAM scores were “one of many considerations” taken to establish an overall teacher’s score. The use of something that is unfair is less unfair, in other words, if you also use other things which balance it out and are fair.

If you don’t know what a VAM is, or what my critique about it is, take a look at this post, or read my book. The very short version is that it’s…

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Kids need hammers.

Denis Ian warns that “competency based education,” online teaching and assessment, spells the end of education and of childhood. It is not just a threat to public education. It is a mortal threat to education of any kind.

He posted this comment:

Competency based education isn’t a mirage anymore. It’s here.

Beyond the view of skirmishes now underway across an array of states, is an emerging reality that … in a very short while … this destroying reform will have razed an American institution to a mound of rubble.

And in its place … for as far as the eye can see … will stand drive-thru learning centers offering kiosk-educations from a B. F. Skinner touch-screen that will supply the finger-pointer with all they need to succeed in a life of rich monotony.

That’s what your now titling schools are going to look like. And that’s your child’s purgatory. Dante…

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The parallel equally spaced lines

and the desired length HI, of ribbon, wood, anything non-elastic.

DONE !

Filed under fractions, Uncategorized