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Old 11th December 2018, 09:35 AM   #1
rlopez2
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Emmanuel Schanzer: Why is algebra so hard?

// __ TEDxTalks (13:52): Why is algebra so hard? | Emmanuel Schanzer | TEDxBeaconStreet

https://www.youtube.com/watch?v=FbqnaoU-3VI

TEDx Talks: Published on Dec 13, 2016
Emmanual Schanzer thought that the way algebra was taught made no sense, and decided to do something about it. He turned a discipline that frustrates many students into a skill they could immediately apply. Watch his talk to learn how.
Dr. Emmanuel Schanzer is a CS-expat, having spent several years as a program manager and developer before becoming a high school teacher and middle school academic coach. He is the founder and creator of Bootstrap, which he first designed as a curriculum for his own students in Boston. He has long been involved in connecting educators and technology, connecting parties at the Computer Science Teachers Association, Google, Microsoft, Facebook and at universities across the country. He holds degrees in computer science and curriculum development, and is a Doctor of Education with a research focus on using programming to teach algebra.
This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at http://ted.com/tedx
~
Schanzer is trying to be too funny and advertising his thing as the latest, greatest instead of discussing a polemic issue complicated by too much politics and too many illusions:

* there is absolutely nothing "abstract" about functions: All you do in your life from cooking following a recipe or just fixing a sandwich, to making and saving money and changing a diaper, are functions:

a) based on well-known primitive operations;
b) to be performed as step-by-step procedures;
c) in a certain order;
d) all of them;
e) from a start to a sought end (in which their syntactic machinery gives we to the semantic aspects of communication).

Think of actions you do and how all those steps are followed and how and the kind of problems that could arise if they aren't. Even animals know and do "functions":

// __ Smartest Bird (the intelligent raven solves the puzzle)

https://www.youtube.com/watch?v=WYBATyILJD8
~
That corvid, quite functionally, indeed!, followed all the steps to get its food.

In Mathematics, functions are much easier:

a) as well-known primitive operations we used the 6 basic operations (the ER|MD|AS in "PERMDAS");
b) to be performed as step-by-step procedures (which a operations resulting in partial results);
c) in a certain order: going one way (say LTR) and from the inner most parenthesis out (the P in "PERMDAS");
d) all of them;
e) from a well-defined start (a given "independent" value) to the sought end (the dependent one, given the functional relationship: y=f(x)).

What makes algebraic functions immensely powerful is that using just those basic operations and following basic procedures they can be used as modeling devices for anything that can be and happen. Anything visually, graphically expressed (from your mom's face to your doctor's signature or the microscopic picture of an amoeba) can be algebraically represented through functions. Cars, buildings and airplanes are first modeled and -tested- using functions before they are physically produced and this is 100% safe as long as the model is a faithful representation of reality. Functions are used to effectively represent and simulate from Beyonce's booty dance to the "landing" of a rover on another planet:

// __ The Great Math Mystery - NOVA Documentary on Mathematics - Math Language of the Universe

https://www.youtube.com/watch?v=7iyIyoZbAfY
~
When you code, say, in the Java language (as well as in C and C++), e are the starting main(...) method the run-time environment looks after in order to start your program and the last one is the last contextually closing curly bracket of the operation you are performing. In order to achieve b, that is, to demarcate the steps, a semicolon: (, is used at the end of each statement. Compilers check that a is right by making sure that only well-known primitive operations are used in syntactically proper ways and any other defined operations are defined as functions in your own code or imported libraries.
~
* functions are not objects but describe relationships among two sets of "objects": they are kind of like Arithmetic ratios and proportions, like the price tags you see on the stands of street vendors. They are not equations because there is not "right" or "wrong" values. Depending on how much money you give you get a number of bananas, there is no "right" or "wrong" amount of money to get a fixed number of bananas. While coding, functions have a number of typed input parameters, a signature specifying the type and scope of the output and the output itself.
~
* in java as in any programming language (since computer hardware internally uses the binary system for numeric representation) you definitely and exactly can divide by any power of 2. All other Arithmetic operations in computers are approximations, but this is not a problem at all, because, since computers are first and foremost modeling devices, you can easily model an exact Arithmetic based on prime factorizations, repeating sequences, ... I have taught that to primary school students when they ask me why dividing 4 by 33, gives the repeating sequence 0.(12).
~
* I think he makes a good point when he uses the x = x + 2 example, I have always though that programming languages should use something like: "x := x + 2" to mean "add 2 to whatever value you have in x and use (the same) variable x to store the result". However, if you code and understand Math well, at some point that kind of "equal sign overloading" gets totally contextualized, so you don't get confused about it at all.
~
* It may politically "make sense" to him (that is, he may make some money out of it) but IMO that "Bootstrap" thing is nonsense. As with anything, there is a reason for both Math and "CS" to be what they are and, as with anything, there are cultural aspects to computer programming.

rlopez2
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Old 11th December 2018, 09:50 AM   #2
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Why is this in the conspiracy section?
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Old 11th December 2018, 10:10 AM   #3
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Thought I was getting the Rosetta Stone of algebra in 15 mins. Should'a known better.
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Old 11th December 2018, 02:21 PM   #4
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Notice how Conspiracy Kooks and Advocates of Crackpot Science seem to have a hatred of Mathmatics?
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Old 11th December 2018, 03:26 PM   #5
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I find algebra quite easy myself

[/end thread]
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Old 11th December 2018, 03:30 PM   #6
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Originally Posted by Hans View Post
Why is this in the conspiracy section?
Because there is a bird involved...

Birds have feathers and can fly, SO WHY CAN'T I !!! ELEVENTY!!!
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Old 11th December 2018, 03:44 PM   #7
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Tune in tomorrow, same Batshitcrazy-time, same Batshitcrazy-channel.
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Old 11th December 2018, 03:58 PM   #8
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But srsly, why is it so hard ? People say 'why is is so hard', but they don't really mean it. They don't really look for the reason. They don't think.
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Old 11th December 2018, 04:12 PM   #9
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Originally Posted by Hans View Post
Why is this in the conspiracy section?
Because there isn't a 'batpoop crazy word salad' section?
(have a look at the posters previous)

I think MikeG sums it up...

Originally Posted by MikeG View Post
I recognise the words. The grammar? Wow..........that's a work of art.
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Old 11th December 2018, 04:24 PM   #10
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Originally Posted by Whip View Post
I find algebra quite easy myself

[/end thread]

Yep, that and trigonometry. I never got what all the fuss was about.
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Old 11th December 2018, 04:51 PM   #11
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Originally Posted by Dr.Sid View Post
But srsly, why is it so hard ? People say 'why is is so hard', but they don't really mean it. They don't really look for the reason. They don't think.
the guy thinks using a quote feature is hard. glad I don't have to be near him after he drops a growler. wiping would make him pass out.
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Old 11th December 2018, 04:54 PM   #12
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Originally Posted by Dr.Sid View Post
But srsly, why is it so hard ? People say 'why is is so hard', but they don't really mean it. They don't really look for the reason. They don't think.
I was having this discussion with my nephew (a math whiz), and we agreed on this one point:

There are great math teachers, and lousy math teachers. If you hate algebra you probably had a lousy math teacher.
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Old 11th December 2018, 05:05 PM   #13
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Originally Posted by Axxman300 View Post
I was having this discussion with my nephew (a math whiz), and we agreed on this one point:

There are great math teachers, and lousy math teachers. If you hate algebra you probably had a lousy math teacher.
I had that problem in school. I think it had more to do with the content of the program than the quality of the teacher. In high school algebra seemed to be about memorizing rules that did not relate to anything, just to pass the test. The math didn't do anything useful.

Later, in the Air Force, I worked on analog flight simulators. Analog computers are formulae in physical form. Once I could see actual values the math made sense.

Last edited by Pope130; 11th December 2018 at 05:19 PM.
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Old 11th December 2018, 05:14 PM   #14
Dr.Sid
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Originally Posted by Axxman300 View Post
I was having this discussion with my nephew (a math whiz), and we agreed on this one point:

There are great math teachers, and lousy math teachers. If you hate algebra you probably had a lousy math teacher.
Nono .. teacher teach algebra. They don't make it. And I never said I hate algebra. If you think algebra is not hard, you just don't know enough. There is certainly algebra hard enough to be called hard.
But why ? Focus on the 'why'. You can say 'why wouldn't it be hard. But that's just another phrase. Think about the 'why'. Focus on it. Dive into it.
It's really cardinal question, don't you think ?
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Old 11th December 2018, 05:14 PM   #15
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Originally Posted by Pope130 View Post
I had that problem in school. I think it had more to do with the content of the program than the quality of the teacher. In high school algebra seemed to b about memorizing rules that did not relate to anything, just to pass the test. The math didn't do anything useful.

Later, in the Air Force I worked on analog flight simulators. Analog computers are formulae in physical form. Once I could see actual values the math made sense.
You may be confusing rules with identities.

These are the only rules for solving algebraic linear equations.

The following steps provide a good method to use when solving linear equations.
Simplify each side of the equation by removing parentheses and combining like terms.
Use addition or subtraction to isolate the variable term on one side of the equation.
Use multiplication or division to solve for the variable.

Last edited by bknight; 11th December 2018 at 05:17 PM. Reason: Added rules
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Old 11th December 2018, 06:24 PM   #16
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Originally Posted by Axxman300 View Post
I was having this discussion with my nephew (a math whiz), and we agreed on this one point:

There are great math teachers, and lousy math teachers. If you hate algebra you probably had a lousy math teacher.
I had a great math teacher Mr. Reynolds & Mrs Kukora but guess what I STILL hate math. I learned it and had to teach it at times at the college level and for the Army (good old ballistic gunnery with book tables, two forks and slide rules before the Tacfire and BCS systems)....guess what I still hate it. When I was in a position to hire people for teaching positions anyone saying they thought 'math was fun' got little sympathy from me.

End math rant

What is the thread for anyway?
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Old 11th December 2018, 06:34 PM   #17
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Originally Posted by Hans View Post
I had a great math teacher Mr. Reynolds & Mrs Kukora but guess what I STILL hate math. I learned it and had to teach it at times at the college level and for the Army (good old ballistic gunnery with book tables, two forks and slide rules before the Tacfire and BCS systems)....guess what I still hate it. When I was in a position to hire people for teaching positions anyone saying they thought 'math was fun' got little sympathy from me.

End math rant

What is the thread for anyway?
You were in the field artillery?
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Old 11th December 2018, 06:58 PM   #18
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... in which their syntactic machinery gives WAY to the semantic aspects of communication ...

the actual sign seems to have been eaten after: "the steps, a semicolon"
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Old 11th December 2018, 07:03 PM   #19
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Al Gerbil gnawing on your colon? that would explain alot.
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Old 11th December 2018, 08:01 PM   #20
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Originally Posted by Whip View Post
I find algebra quite easy myself

[/end thread]
I may have jumped the gun here.......I sometimes struggle with fibromyalgebra
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Old 11th December 2018, 08:42 PM   #21
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Originally Posted by bknight View Post
You were in the field artillery?
OUAT
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Old 11th December 2018, 08:51 PM   #22
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Originally Posted by Hans View Post
I had a great math teacher Mr. Reynolds & Mrs Kukora
apparantly not
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Old 11th December 2018, 10:33 PM   #23
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Originally Posted by Horhang View Post
apparantly not
WELL, I could make up a story about Mr R becoming Mrs K but no I shall admit a grammar error!
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Old 11th December 2018, 11:18 PM   #24
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Originally Posted by Pope130 View Post
I had that problem in school. I think it had more to do with the content of the program than the quality of the teacher. In high school algebra seemed to be about memorizing rules that did not relate to anything, just to pass the test. The math didn't do anything useful.

Later, in the Air Force, I worked on analog flight simulators. Analog computers are formulae in physical form. Once I could see actual values the math made sense.
In high school they split algebra into two year-long classes (Algebra AB/CD), and my teacher was more concerned with how neat my notebook was than how well I did on tests, and I never did any better than a C- in the class.

I liked the subject.

In 2011 I was back in college and had to start from basic mathematics and work my way up. I had attempted Algebra in 2008 with no prep hoping my 30 year gap wouldn't be a problem, and I was wrong. I had the highest grades ever in the mathematics and pre-algebra classes. My pre-algebra class was taught by a young guy who could walk everyone through the steps as clearly as possible.

Then things got interesting. Algebra is still broken into two classes. My first algebra class was a blast, but the first quarter was all review of basic mathematics, and we barely got to Quadratics by the end of the semester.

The next level algebra class was where I ran into trouble. My first teacher barely spoke English, and he had us do our homework online through what I felt was a scam educational outlet that used an outdated program for content. Instead of studying, most of us just picked multiple choice questions until we got the right answers. There was NO WAY TO PRACTICE GRAPHING, and even if you did the math and entered the coordinates the program didn't recognize the answer. We tested this in the Math Learning Center where most of us did our homework, and even the tutors (who were math teachers) couldn't get it to work.
So the next year I re-took it, making sure I got a teacher who used a book, and not a computer, and I did better. Even so the first quarter of the semester for advanced algebra class focused on basic mathematics instead of picking up at the quadratics.

I do like algebra. I feel that taking the class allowed me to finish my first novel because the subject trains your brain to see systems, and cause & effect clearly, and solve mysteries (find for X).
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Old 12th December 2018, 06:49 AM   #25
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Originally Posted by Hans View Post
OUAT
?????
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Old 12th December 2018, 08:13 AM   #26
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nvm

Last edited by theprestige; 12th December 2018 at 09:43 AM.
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Old 12th December 2018, 08:34 AM   #27
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Originally Posted by bknight View Post
?????
Sorry 'OUAT' means 'once upon a time'.
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Old 12th December 2018, 08:38 AM   #28
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****.
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Old 12th December 2018, 09:05 AM   #29
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Originally Posted by Hans View Post
Sorry 'OUAT' means 'once upon a time'.
Ah, I was also in FA in the early 70's training fadac operators.
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Old 12th December 2018, 12:24 PM   #30
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Originally Posted by Hans View Post
Sorry 'OUAT' means 'once upon a time'.
Ah. I thought it was a phonetic spelling of WHAT or WAT. Like Kewl or Hai.
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Old 12th December 2018, 12:31 PM   #31
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Originally Posted by Hans View Post
I had a great math teacher Mr. Reynolds & Mrs Kukora but guess what I STILL hate math. I learned it and had to teach it at times at the college level and for the Army (good old ballistic gunnery with book tables, two forks and slide rules before the Tacfire and BCS systems)....guess what I still hate it. When I was in a position to hire people for teaching positions anyone saying they thought 'math was fun' got little sympathy from me.

End math rant

What is the thread for anyway?
Not artillery, but my understanding of algebra and calculus is directly related to marksmanship - when other kids complained it wasn't necessary to learn those subjects I kind of laughed internally.

For an unfortunate to air their delusions.
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Old 12th December 2018, 12:49 PM   #32
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Originally Posted by BStrong View Post
Not artillery, but my understanding of algebra and calculus is directly related to marksmanship - when other kids complained it wasn't necessary to learn those subjects I kind of laughed internally.

For an unfortunate to air their delusions.
I made my Algebra teacher's day when I showed him the US Army Ranger Handbook section on explosives where the formula to calculate minimum safe distances, and amount of charge needed per size of obstacle are listed.
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Old 12th December 2018, 01:49 PM   #33
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Originally Posted by Hans View Post
Sorry 'OUAT' means 'once upon a time'.
Another ex Redleg here...
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Old 12th December 2018, 01:50 PM   #34
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Originally Posted by Axxman300 View Post
I made my Algebra teacher's day when I showed him the US Army Ranger Handbook section on explosives where the formula to calculate minimum safe distances, and amount of charge needed per size of obstacle are listed.
There reasons why Cadets have to take so much math at West Point.
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Old 13th December 2018, 08:17 AM   #35
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Originally Posted by dudalb View Post
Another ex Redleg here...
Hey there son of Saint Barbara - good to know there are other here who know how to keep their bubbles level and their powder dry.
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Old 13th December 2018, 08:20 AM   #36
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Originally Posted by bknight View Post
Ah, I was also in FA in the early 70's training fadac operators.
I was one of the first TACFIRE fire support guys FIST and later Bn. & Bde FSO. We took it to the national training center for a couple of rotation to see if it would work in the field - it did - kinda.

I REALLY hated Freddy FADAC!
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Old 13th December 2018, 08:24 AM   #37
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Originally Posted by bknight View Post
You were in the field artillery?
He's not the only one.

There are several of St. Barbara's Chosen on these boards.
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Old 13th December 2018, 11:41 AM   #38
Wolrab
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Algebra is hard because be was starring at acute triangle.
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"Such reports are usually based on the sighting of something the sighters cannot explain and that they (or someone else on their behalf) explain as representing an interstellar spaceship-often by saying "But what else can it be?" as though thier own ignorance is a decisive factor." Isaac Asimov
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Old 13th December 2018, 11:45 AM   #39
Hellbound
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Originally Posted by Axxman300 View Post
I made my Algebra teacher's day when I showed him the US Army Ranger Handbook section on explosives where the formula to calculate minimum safe distances, and amount of charge needed per size of obstacle are listed.
Similar to FM 5-34, the Engineer's Bible:
http://www.enlistment.us/field-manua...eld-data.shtml

I was a trained as a combat engineer. Turning big things into lots of smaller, higher-velocity things was a core piece of the job description
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Old 13th December 2018, 12:50 PM   #40
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Originally Posted by Hans View Post
I was one of the first TACFIRE fire support guys FIST and later Bn. & Bde FSO. We took it to the national training center for a couple of rotation to see if it would work in the field - it did - kinda.

I REALLY hated Freddy FADAC!
LOL, that was all that was available in the early 70's.
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