Software We've Liked

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Software We've Liked

Richard Strausz
I got together with some old teaching friends recently and we talked about software that we liked. Some that I have used successfully are:

Green Globs (pre-algebra and algebra)
http://www.greenglobs.net/index.html

LOGO (geometry and introductory computer progamming)
http://www.softronix.com/logo.html

The Eyeballing Game (geometry)
http://woodgears.ca/eyeball/

Any other teachers have titles/sites they have used?

Richard
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Re: Software We've Liked

Richard Strausz
Pages 4 and 5 of the PDF below gives a lot more info on Green Globs. It is actually rather old technology, but I have found it to be motivational for many students.

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CCQQFjAB&url=http%3A%2F%2Fmath.buffalostate.edu%2F~it%2FWorkshop%2FTuesday%2FGreenGlobs.pdf&ei=12XpU5-hDsKgyQTuwIKYAg&usg=AFQjCNFkvZxRL1Ar8zIVS9x7-iuu8wi1rA

Richard
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Re: Software We've Liked

Richard Strausz
In reply to this post by Richard Strausz
One of my DACTM (Detroit Area Council of Teachers of Mathematics) suggests the excellent iPad app and website https://www.desmos.com/

'Graph functions, plot tables of data, evaluate equations, explore transformations, and much more – for free!'

Richard
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Re: Software We've Liked

Bishop, Wayne
Damaging the prospect of innocent kids'
opportunity for math-based careers (see that
Japanese study) is not without its downside.

Wayne

At 02:01 PM 8/12/2014, Richard Strausz wrote:
>One of my DACTM (Detroit Area Council of
>Teachers of Mathematics) suggests the excellent
>iPad app and website https://www.desmos.com/
>
>'Graph functions, plot tables of data, evaluate
>equations, explore transformations, and much more ­ for free!'
>Richard
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Re: Software We've Liked

Richard Strausz
In reply to this post by Richard Strausz
Wayne, is there any software you would like to add to the list? Feel free.

Richard
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Re: Software We've Liked

Robert Hansen

On Aug 13, 2014, at 6:32 AM, Richard Strausz <[hidden email]> wrote:

> Wayne, is there any software you would like to add to the list? Feel free.
>
> Richard

Do you understand the fallacy here? The assumption that software is even pertinent to teaching these subjects.

Bob Hansen
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Re: Software We've Liked

Bishop, Wayne
In reply to this post by Richard Strausz
I'm prejudiced because I like geometry but my favorite is Cinderella.  I don't know enough mathematics and not nearly enough physics to really appreciate its power but it's great.
It's never been expensive but I didn't know till right now that it soon will be free.
News http://www.cinderella.de/
The pro version of Cinderella is going to be free for everybody soon. This enables you to use all features, including physics simulation and scripting, without a license. You can still order a personal license at the reduced price of 10 US$ or 7,50 € that will personalize your copy of Cinderella and makes it possible to put a copyright on your constructions. You will find the free pro version of Cinderella in the download area soon, please allow a few days while we prepare it.
Dunno if pictures will come through the listserve filters but, if they do, here's the standard construction of the incircle of a triangle.  In case you're rusty, bisect 2 of the angles for the center and drop the perpendicular to a side to get the radius.  As always, the mathematics is to prove it but the picture is nice as well and, of course, "live" so if you "drag" a vertex of the triangle, the right stuff happens.  In case the picture doesn't come through, you can try your own for free.  Under the Views tab at the top, select Hyperbolic View, expand it, and click the Hyp tab at the bottom and follow your nose.

Another nice example that reinforces the algebraic reality is the unique quartic determined by 5 noncollinear points in the Euclidean plane.  Again, it's the "dragging" the 5th point that is enlightening even though you know what's supposed to happen.  Thanks for asking,

WayneEmacs!

At 03:32 AM 8/13/2014, Richard Strausz wrote:
Wayne, is there any software you would like to add to the list? Feel free.

Richard
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Re: Software We've Liked

Richard Strausz
In reply to this post by Richard Strausz
Thanks for the Cinderella example. You like it for many of the same reasons I like Geometers Sketchpad and Geogebra. These definitely fit on the list.

Richard
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Re: Software We've Liked

Richard Strausz
In reply to this post by Richard Strausz
>
> On Aug 13, 2014, at 6:32 AM, Richard Strausz
> <[hidden email]> wrote:
>
> > Wayne, is there any software you would like to add
> to the list? Feel free.
> >
> > Richard
>
> Do you understand the fallacy here? The assumption
> that software is even pertinent to teaching these
> subjects.
>
> Bob Hansen
Another of Robert's rules: Students must be goaded and software is not pertinent to teaching.
Richard

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Re: Software We've Liked

Richard Strausz
In reply to this post by Richard Strausz
> I got together with some old teaching friends
> recently and we talked about software that we liked.
> Some that I have used successfully are:
>
> Green Globs (pre-algebra and algebra)
> http://www.greenglobs.net/index.html
>
> LOGO (geometry and introductory computer progamming)
> http://www.softronix.com/logo.html
>
> The Eyeballing Game (geometry)
> http://woodgears.ca/eyeball/
>
> Any other teachers have titles/sites they have used?
>
> Richard

Based on other suggestions, I am adding on:

desmos.com

and

cinderella/geometer's sketchpad/geogebra

- ---------------

Any others anyone would like to suggest?

Richard
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Re: Software We've Liked

Robert Hansen
In reply to this post by Richard Strausz

On Aug 13, 2014, at 2:15 PM, Richard Strausz <[hidden email]> wrote:

> Another of Robert's rules: Students must be goaded and software is not pertinent to teaching.

What do you test your students on after they have played with the software?

Bob Hansen
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Re: Software We've Liked

Bishop, Wayne
In reply to this post by Richard Strausz
I could be wrong, but my guess is that some of our reasons are very different.  For example, I don't let students use any of these for work that I grade - I want them to formally construct their own where "formally" should be in quotes because I don't mean using a physical compass and straightedge.  A good sketch is what I'm after with no physical tools (other than a writing instrument) unless they can't even draw an approximation of a straight line free and where I tell them to use the edge of a book or fold a piece of paper a couple times.  Fold again at a right angle or the corner of a book if they can't "eyeball" a right angle but arcs of circles are supposed to look like their centers and radii are close to correct.  I do use Geometer's Sketchpad for that because (although not nearly so sophisticated) it allows much more control to demonstrate what I have in mind from the students.  For example, constructing a (yet to be proved, "the") perpendicular from a point to a line.

WayneEmacs!

At 11:10 AM 8/13/2014, Richard Strausz wrote:
Thanks for the Cinderella example. You like it for many of the same reasons I like Geometers Sketchpad and Geogebra. These definitely fit on the list.

Richard
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Re: Software We've Liked

gatupper
In reply to this post by Robert Hansen
Well, if you have used the software to graph say (y-x+3)(x-y^2)=0 or (y-|x|)(y+3)=0 & some similar such {exprA * exprB * exprC}=0 etc., then it would not be unreasonable to ask the student on a test to provide the equation of the '+' coordinate axes.

If the student has graphed y=|y| , (y^2 + (x-3)^2) = .001 etc., it would be appropriate to ask the student to provide an equation for the whole plane or the equation whose graph is the single point (9,-2).

Note that these examples are unlikely to be examined in the standard (pre-calc function-fixated) curriculum, but developing an interest in mathematics may not be equivalent to preparing for calculus.

Gary Tupper

Offence can only be taken, never given.

> On Aug 13, 2014, at 3:12 PM, Robert Hansen <[hidden email]> wrote:
>
>
>> On Aug 13, 2014, at 2:15 PM, Richard Strausz <[hidden email]> wrote:
>>
>> Another of Robert's rules: Students must be goaded and software is not pertinent to teaching.
>
> What do you test your students on after they have played with the software?
>
> Bob Hansen

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Re: Software We've Liked

Richard Strausz
In reply to this post by Richard Strausz
>
> On Aug 13, 2014, at 2:15 PM, Richard Strausz
> <[hidden email]> wrote:
>
> > Another of Robert's rules: Students must be goaded
> and software is not pertinent to teaching.
>
> What do you test your students on after they have
> played with the software?
>
> Bob Hansen

I test them on the relevant course content that we are doing

Richard
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Re: Software We've Liked

Bishop, Wayne
In reply to this post by gatupper
At 04:14 PM 8/13/2014, [hidden email] wrote:

>If the student has graphed y=|y| , (y^2 + (x-3)^2) = .001 etc., it
>would be appropriate to ask the student to provide an equation for
>the whole plane or the equation whose graph is the single point (9,-2).
>
>Note that these examples are unlikely to be examined in the standard
>(pre-calc function-fixated) curriculum, but developing an interest
>in mathematics may not be equivalent to preparing for calculus.

Oh my yes!  This will help develop an interest in mathematics!!  The
non--calculus bound students will be ecstatic!!!  Wanna buy my bridge?

Wayne
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Re: Software We've Liked

gatupper
In reply to this post by Bishop, Wayne


On Wednesday, August 13, 2014, Wayne Bishop <[hidden email]> wrote:
I could be wrong, but my guess is that some of our reasons are very different.  For example, I don't let students use any of these for work that I grade - I want them to formally construct their own where "formally" should be in quotes because I don't mean using a physical compass and straightedge.  A good sketch is what I'm after with no physical tools (other than a writing instrument) unless they can't even draw an approximation of a straight line free and where I tell them to use the edge of a book or fold a piece of paper a couple times.  Fold again at a right angle or the corner of a book if they can't "eyeball" a right angle but arcs of circles are supposed to look like their centers and radii are close to correct.  I do use Geometer's Sketchpad for that because (although not nearly so sophisticated) it allows much more control to demonstrate what I have in mind from the students.  For example, constructing a (yet to be proved, "the") perpendicular from a point to a line.

WayneEmacs!

And the follow up exercise: note that P & Q are on opposite sides of AB - can you, the student, do a similar construction wher P & Q are on the same side?
And another: note that PQ perpendicularly bisects AB - can you do a similar construction whereby PQ bisects  AB but not perpendicularly. (All with proofs)

Gary Tupper
 
At 11:10 AM 8/13/2014, Richard Strausz wrote:
Thanks for the Cinderella example. You like it for many of the same reasons I like Geometers Sketchpad and Geogebra. These definitely fit on the list.

Richard
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Re: Software We've Liked

GS Chandy-2
In reply to this post by Richard Strausz
Robert Hansen (RH) posted Aug 13, 2014 6:28 PM (http://mathforum.org/kb/message.jspa?messageID=9556737):

>
> On Aug 13, 2014, at 6:32 AM, Richard Strausz
> <[hidden email]> wrote:
>
> > (Richard Strausz): Wayne, is there any software you
> > would like to add to the list? Feel free.
> >
> > Richard
>
> (RH): Do you understand the fallacy here? The assumption
> that software is even pertinent to teaching these
> subjects.
>
> Bob Hansen
>
"Fallacy" ?  What fallacy??

"pertinent" - see definitions below, just above my signature.

Notwithstanding the lack of exposure that RH believes I suffer from to 'American' English poetry, and the  consequent inadequate understanding of the subtleties concealed within Robert Hansen's exposition, I observe that, in his post heading this thread, Richard Strausz had actually asked the following:

>> "I got together with some old teaching friends
>> recently and we talked about software that we liked.
>> Some that I have used successfully are: ..."  (Aug 11, 2014 3:30 PM, http://mathforum.org/kb/message.jspa?messageID=9552400).

I believe he was seeking to find out whether any software could be useful in helping his students to 'learn' and possibly appreciate some math, including, perhaps, geometry, etc. (That is, could some of the software "CONTRIBUTE TO" his [Richard Strausz's] and other school students to understand/appreciate math?)

On constructing a couple of models using the 'One Page Management System' (OPMS), I'd tend to believe the answer in general is, "Software COULD certainly contribute to student learning of math" - but there are also a couple of quite serious difficulties (brought about by reason of the 'unthinking use' of software), which may come 'in the way' of effective learning.  

It would all depend, I should think, on how the teacher approaches his/her task of 'guiding' his students through the math.

I observe that Wayne Bishop has suggested a software called "Cinderella", and that Richard Strausz already  has "Geometer's Sketchpad", etc, etc, on his list.

During my own school days there were no computers in 'math education' at all, and looking back now I feel that a whole lot was mainly up to the way the teacher guided his/her wards. Which is precisely the situation now.

I do believe a good many of my classmates who got to 'fear and/or loathe' math - mainly because of the way it was 'taught to them' - MAY well have learned to appreciate math a bit if they'd had access to some good 'math learning software' - BUT of course only IF to begin with they were guided by a sensitive, empathetic teacher who himself or herself actually liked/loved math!

In other words, the situation was then much the same as it is now - it depends entirely on the 'math education system', which a good teacher with the above-noted qualities can do much to help make *effective*.

How 'pertinent' is math software?  

I'd guess it would depend to a great extent on the 'math education system', which, in turn, would greatly depend on the 'education system' as a whole.  

I believe that good 'math learning software' could certainly help both teachers and students a good bit.  Such software is just a tool, though it IS one with a great many IMPLICATIONS hidden within its use.  However, I'd guess it's a great deal up to the teacher in question to make it 'pertinent' and, in fact, to make 'math' itself pertinent to the students' real lives and careers.

'pertinent':
- --Having logical precise relevance to the matter at hand (Free Online Dictionary, Farlex).

- -- Relevant or applicable to a particular matter; apposite (Oxford Dictionaries)

- -- relating to the thing that is being thought about or discussed  (Merriam-Webster online dictionary)

I'd guess - notwithstanding any 'American' English poetry - that the real questions to be asking should ONLY be:

Could 'math learning software' "CONTRIBUTE TO" the student learning/appreciating math, to the teacher guiding his/her wards into math?

I do tend to  wonder what might be the 'fallacy' that Robert Hansen found Richard Strausz had perpetrated in asking  his question.  (I wonder whether a quick course in 'American' English poetry might help me?  Only some minor 'sarcasm' here).

GSC
("Still Shoveling!, etc, etc")
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Re: Software We've Liked

Gary Tupper
In reply to this post by Bishop, Wayne
On 13/08/2014 7:00 PM, Wayne Bishop wrote:

> At 04:14 PM 8/13/2014, [hidden email] wrote:
>
>> If the student has graphed y=|y| , (y^2 + (x-3)^2) = .001 etc., it
>> would be appropriate to ask the student to provide an equation for
>> the whole plane or the equation whose graph is the single point (9,-2).
>>
>> Note that these examples are unlikely to be examined in the standard
>> (pre-calc function-fixated) curriculum, but developing an interest in
>> mathematics may not be equivalent to preparing for calculus.
>
> Oh my yes!  This will help develop an interest in mathematics!! The
> non--calculus bound students will be ecstatic!!!  Wanna buy my bridge?
>
> Wayne
Calculus-bound students will also hopefully find some interest in such
topics. Am I the only teacher who has attempted to find a reference to
"truth" in the index of a math text & come up short? Is there any reason
why a text would not state that solving is essentially a search for truth?

Or is the word politically incorrect?

Gary Tupper
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Re: Software We've Liked

Bishop, Wayne
In reply to this post by gatupper
At 07:59 PM 8/13/2014, Gary Tupper wrote:

On Wednesday, August 13, 2014, Wayne Bishop <[hidden email]> wrote:
I could be wrong, but my guess is that some of our reasons are very different.  For example, I don't let students use any of these for work that I grade - I want them to formally construct their own where "formally" should be in quotes because I don't mean using a physical compass and straightedge.  A good sketch is what I'm after with no physical tools (other than a writing instrument) unless they can't even draw an approximation of a straight line free and where I tell them to use the edge of a book or fold a piece of paper a couple times.  Fold again at a right angle or the corner of a book if they can't "eyeball" a right angle but arcs of circles are supposed to look like their centers and radii are close to correct.  I do use Geometer's Sketchpad for that because (although not nearly so sophisticated) it allows much more control to demonstrate what I have in mind from the students.  For example, constructing a (yet to be proved, "the") perpendicular from a point to a line.

WayneEmacs!

And the follow up exercise: note that P & Q are on opposite sides of AB - can you, the student, do a similar construction wher P & Q are on the same side?

Who says P & Q are on opposite sides of the line?  Obviously, they must be distinct points but anything else?

And another: note that PQ perpendicularly bisects AB

But AB was not given, only that  A be (almost) any point of the line and  B  constructed from it so arbitrary in terms of the original problem where only perpendicularity makes sense.  My experience has been that week geometry students treat "perpendicular bisector" as one word whether the perpendicular makes sense or, in other contexts, the bisector (midpoint) makes sense.

 - can you do a similar construction whereby PQ bisects  AB but not perpendicularly. (All with proofs)

My students can't, even very good ones, so I do include one just to try (too often in vain) to get students not to use the words meaninglessly.  Here it is with the proof included.
  Emacs!
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Re: Software We've Liked

GS Chandy-2
In reply to this post by Richard Strausz
Robert Hansen (RH) Aug 13, 2014 6:28 (http://mathforum.org/kb/message.jspa?messageID=9556737):

>
> On Aug 13, 2014, at 6:32 AM, Richard Strausz
> <[hidden email]> wrote:
>
> > (Richard Strausz): Wayne, is there any software you
> > would like to add to the list? Feel free.
> >
> > Richard
> >
>
> (Robert Hansen): Do you understand the fallacy here?
> The assumption that software is even pertinent to
> teaching these subjects.
>
> Bob Hansen
>
I have already  responded to this - the messasge has not yet appeared.

There are, I believe, a couple of points that it may be worth further clarifying:
 
1) Robert Hansen's wrong notions of "how a learner learns math"; as well as

2) Robert Hansen's wrong notion of the meaning the 'American' English and 'English' English word "fallacy".  

The meaning of the word is provided for reference below, just above my signature, along with some useful background about it, a 'list of fallacies', etc, etc.

The first wrong notion of Robert Hansen's is that there is ONLY the teacher 'teaching", as it were.  

This is profoundly incorrect (apart from being a 'technical fallacy' as I shall try to make clear in the following).  

The heart of the matter involves:

First, foremost and primarily the "learner learning" - from a person (say, a "teacher") or, from a "book", from "life", etc, etc.

In case the learner is learning from a book, I guess the author of the book is taking the role of the "teacher".  In any case, the  "learner learning" is fundamental, NOT "the teacher teaching"!  (Except in the case of "life itself", which  is always fundamental).

The 'fallacy', if any, is that Robert Hansen has omitted the heart of the matter, namely, the issue of the "learner learning" - he assumes it is only a matter of the "teacher teaching".  

WRONG!  

It's the "learner learning" that is fundamental and crucial.  The "learner can learn" without the 'teacher teaching" - but there's no use at all the "teacher teaching" unless there's at least one "learner learning"!

I repeat:  If there is no "learner to learn", then there is really no point in the "teacher teaching".  

To use a rather loose analogy, there is no point in pouring water into a vessel that isn't there at all!  If one wishes to teach anything (be it math or be it the piano or cooking), one needs to have a "learner" to DO the "learning", "learn" what is being "taught".

The second wrong notion is the meaning of the word "fallacy".  

As will be observed from the quotations/ excerpts from various sources quoted below, the word means more or less the same in both 'American' English and in 'English' English.  (In case anyone is interested, the  word also means more or less the same in 'Indian' English as well).

Fallacy:
A: from Dictionary.com (http://dictionary.reference.com/browse/fallacy)
+++++
 1. a deceptive, misleading, or false notion, belief, etc.: That the world is flat was at one time a popular fallacy.
2. a misleading or unsound argument.
3. deceptive, misleading, or false nature; erroneousness.
4. Logic. any of various types of erroneous reasoning that render arguments logically unsound.
+++++
B: From 'Merriam-Webster: (http://www.merriam-webster.com/dictionary/fallacy)
+++++
1 a obsolete :  guile, trickery
b :  deceptive appearance :  deception

2 a :  a false or mistaken idea <popular fallacies>
b :  erroneous character :  erroneousness

3 :  an often plausible argument using false or invalid inference

C: Internet Encyclopedia of Philosophy (http://www.iep.utm.edu/fallacy/)
+++++
Fallacies

A fallacy is a kind of error in reasoning. The alphabetical list below contains 209 names of the most common fallacies, and it provides brief explanations and examples of each of them. Fallacies should not be persuasive, but they often are. Fallacies may be created unintentionally, or they may be created intentionally in order to deceive other people. The vast majority of the commonly identified fallacies involve arguments, although some involve explanations, or definitions, or other products of reasoning. Sometimes the term “fallacy” is used even more broadly to indicate any false belief or cause of a false belief. The list below includes some fallacies of these sorts, but most are fallacies that involve kinds of errors made while arguing informally in natural language.

An informal fallacy is fallacious because of both its form and its content. The formal fallacies are fallacious only because of their logical form. For example, the slippery slope fallacy has this form: Step 1 “leads to” step 2. Step 2 leads to step 3. Step 3 leads to … until we reach an obviously unacceptable step, so step 1 is not acceptable. That form occurs in both good arguments and fallacious arguments. The quality of an argument of this form depends crucially on the probabilities that each step does lead to the next, but the probabilities involve the argument’s content, not merely its form.

The discussion that precedes the long alphabetical list of fallacies begins with an account of the ways in which the term “fallacy” is vague. Attention then turns to the number of competing and overlapping ways to classify fallacies of argumentation. For pedagogical purposes, researchers in the field of fallacies disagree about the following topics: which name of a fallacy is more helpful to students’ understanding; whether some fallacies should be de-emphasized in favor of others; and which is the best taxonomy of the fallacies. Researchers in the field are also deeply divided about how to define the term “fallacy” itself, how to define certain fallacies, and whether any theory of fallacies at all should be pursued if that theory’s goal is to provide necessary and sufficient conditions for distinguishing between fallacious and non-fallacious reasoning generally. Analogously, there is doubt in the field of ethics regarding whether researchers should pursue the goal of providing necessary and sufficient conditions for distinguishing moral actions from immoral ones.

(continues - http://www.iep.utm.edu/fallacy/)

D: Wikipedia (has a quite useful entry at https://en.wikipedia.org/wiki/Fallacy)

E: Wikipedia has something most useful under "List of Fallacies" (https://en.wikipedia.org/wiki/List_of_fallacies).

F: Logical Fallacies (http://www.philosophicalsociety.com/logical%20fallacies.htm)

G: Informal Logic (Stanford Encyclopedia of Philosophy - http://plato.stanford.edu/entries/logic-informal/)

H: Stanford Encyclopedia of Philosophy
Abridged Table of Contents (http://www.sycamoreprojects.com/I_Base/Literature/Aesthetics_files/Stanford%20Encyclopedia%20of%20Philosophy.pdf)

It is well worth studying as much as possible about 'fallacies' etc, as it is, I believe, amongst the aims of math-teach to improve math education in US schools - and I've been observing that fallacies have in fact been bedevilling us plenty here at Math-teach.  For instance, those famous 'slogans' are definitely fallacies ('sarcastically' intended though some of them may have been on occasion).  

(I am here primarily in order to learn something that could perhaps use to help us improve a thing or two from the valuable efforts you're making to improve math education in the USA.  Even if  your efforts haven't yet yielded much except in the way of the 'slogans' about which I've commented on occasion, at least some of yu are making the effort, and I may be be able to learn something - and perhaps I might even be able to provide a couple  of useful ideas on occasion).

I do want to take this opportunity to assure Robert Hansen that I haven't missed any of the 'subtleties' of his ideas because I've not read 'American' English poetry.  I have of course not read anywhere near as much as I would like to, but I definitely have read read quite enough to understand all the 'subtleties' of RH's  postings, splendid 'sarcasms' and all.

Fallacies as well.

GSC
("Still Shoveling!, etc, etc")
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