TI-Nspire: the latest snake oil

[Domenico Rosa]

Recently I received a letter announcing a one-day "exciting workshop on the new handheld, the TI-Nspire." The letter concludes with: "You'll be amazed at what this handheld can do for you and your students."

For almost two decades I have been truly amazed by what students can not do with their graphing calculators. Most of my current students, the majority of whom have been shamelessly pseudo-educated, possess one of the following models, which they were required to buy in high school:

TI83 Plus
TI83 Plus Silver Edition
TI84 Plus
TI84 Plus Silver Edition

As I correct their quizzes and examinations, I keep asking myself: "What on Earth were they doing in high school with these calculators?"

I can't wait to see the amazing things that future students will be able to do with the lastest snake oil.
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[Alain Schremmer]

On Apr 19, 2008, at 1:51 PM, Domenico Rosa wrote:

> Recently I received a letter announcing a one-day "exciting  
> workshop on the new handheld, the TI-Nspire." The letter concludes  
> with: "You'll be amazed at what this handheld can do for you and  
> your students."
>
> For almost two decades I have been truly amazed by what students  
> can not do with their graphing calculators. Most of my current  
> students, the majority of whom have been shamelessly pseudo-
> educated, possess one of the following models, which they were  
> required to buy in high school:
>
> TI83 Plus
> TI83 Plus Silver Edition
> TI84 Plus
> TI84 Plus Silver Edition
>
> As I correct their quizzes and examinations, I keep asking myself:  
> "What on Earth were they doing in high school with these calculators?"
>
> I can't wait to see the amazing things that future students will be  
> able to do with the lastest snake oil.

Yes, but there is a lot more money in selling calculators of any  
persuasion than paper and pencil.

What I find a bit more surprising, though, is that an otherwise  
respectable profession should give in to the pressure.

It is easy to circumvent. As Dienes used to say, instead of asking on  
a multiple-choice test, for instance,

2+3 =

7, 5, …

just put it in a way where calculators won't help:

2+3 is

between 7 and 9, less than 19, …

Regards
--schremmer
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[Ed Laughbaum]

Alain brings up a good point - that being that we
need to be smart enough to change our assessments
so that the graphing calculator is of little
help. I  usually include test items where the
graphing calculator gives the wrong answer - if I can.

This conversation brings me to a point I have
been promoting for years, and that is that the
graphing calculator is a teaching tool. Yet high
school and college faculty alike often use it as
a tool for doing the very math we teach.

I just taught a 2-day workshop for a high school
in Ohio, and I got the all-to-often response,
"Oh, we should use it as a teaching tool?" My
guess is that the thought had never occurred to
them because of the way they were taught to use
the GC - whether from colleagues, their teachers, TI, etc.

Best,

Ed
===========================
At 10:10 AM 4/21/2008, Alain Schremmer wrote:

>On Apr 19, 2008, at 1:51 PM, Domenico Rosa wrote:
>
>>Recently I received a letter announcing a one-day "exciting
>>workshop on the new handheld, the TI-Nspire." The letter concludes
>>with: "You'll be amazed at what this handheld can do for you and
>>your students."
>>
>>For almost two decades I have been truly amazed by what students
>>can not do with their graphing calculators. Most of my current
>>students, the majority of whom have been
>>shamelessly pseudo- educated, possess one of
>>the following models, which they were
>>required to buy in high school:
>>
>>TI83 Plus
>>TI83 Plus Silver Edition
>>TI84 Plus
>>TI84 Plus Silver Edition
>>
>>As I correct their quizzes and examinations, I keep asking myself:
>>"What on Earth were they doing in high school with these calculators?"
>>
>>I can't wait to see the amazing things that future students will be
>>able to do with the lastest snake oil.
>
>Yes, but there is a lot more money in selling calculators of any
>persuasion than paper and pencil.
>
>What I find a bit more surprising, though, is that an otherwise
>respectable profession should give in to the pressure.
>
>It is easy to circumvent. As Dienes used to say, instead of asking on
>a multiple-choice test, for instance,
>
>2+3 =
>
>7, 5, …
>
>just put it in a way where calculators won't help:
>
>2+3 is
>
>between 7 and 9, less than 19, …
>
>Regards
>--schremmer
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[Robert Kimball]

Ed,
The visuals that can be displayed with N-Spire
(or with Fathom, or with Excel, or with the TI-84, or with Casios ...)
are so helpful when used appropriately to aid learning and deepen understanding.
The task of providing meaningful and appropriate professional development to teachers is daunting! But we must continue and we have to succeed!
Thanks for all you've done.
Rob



Robert L Kimball (rlkimball@...)
Department Head, Mathematics and Physics
919-866-5960
www.waketech.edu/~rlkimbal
www.waketech.edu/math

>>> Ed Laughbaum <elaughba@...> 4/21/08 10:46 am >>>

Alain brings up a good point - that being that we
need to be smart enough to change our assessments
so that the graphing calculator is of little
help. I  usually include test items where the
graphing calculator gives the wrong answer - if I can.

This conversation brings me to a point I have
been promoting for years, and that is that the
graphing calculator is a teaching tool. Yet high
school and college faculty alike often use it as
a tool for doing the very math we teach.

I just taught a 2-day workshop for a high school
in Ohio, and I got the all-to-often response,
"Oh, we should use it as a teaching tool?" My
guess is that the thought had never occurred to
them because of the way they were taught to use
the GC - whether from colleagues, their teachers, TI, etc.

Best,

Ed
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[Alain Schremmer]

On Apr 21, 2008, at 10:46 AM, Ed Laughbaum wrote:

> Alain brings up a good point - that being that we need to be smart  
> enough to change our assessments so that the graphing calculator is  
> of little help. I  usually include test items where the graphing  
> calculator gives the wrong answer - if I can.
>
> This conversation brings me to a point I have been promoting for  
> years, and that is that the graphing calculator is a teaching tool.  
> Yet high school and college faculty alike often use it as a tool  
> for doing the very math we teach.
>
> I just taught a 2-day workshop for a high school in Ohio, and I got  
> the all-to-often response, "Oh, we should use it as a teaching  
> tool?" My guess is that the thought had never occurred to them  
> because of the way they were taught to use the GC - whether from  
> colleagues, their teachers, TI, etc.

1) It seems to me—indeed here I am a bit uncertain—that in using  
calculators and computers in teaching, the risk is in the tail  
wagging the dog. What I fear is that, ipso and de facto, it assents  
to and ratifies the "topics" approach as, right now, a chain of  
environments in which a subject could be developed and learned by  
interaction, a kind of flight simulator if you will, would seem to be  
over the horizon. Moreover, it would probably be based on some  
programmed branching and here again, if only for simplicity's sake,  
the underlying theory would likely wind up being behaviorism.

2) Learning any subject starts with grappling with very simple and  
very powerful concepts. The important thing at this point is not to  
avoid the battle and to have time personally to come to terms with  
these concepts, to make one's peace with them, to make them one's  
own. The process here is mainly one of internalization and I am  
indeed leery, at this point, of any obtrusive interface: while I am  
doing most of the composing of the magnum opus on the screen, when  
something is recalcitrant, I wind up picking up paper and pencil.

3) But beyond that there comes Thurston's compression. And then we  
can use technology to investigate things previously unreachable. The  
best example I know is that of Dynamical Systems which really took  
off exactly when phase portraits became easily available.

For example, we need to think long and hard about 2+3 but then we can  
use technology to do 123456789.987654321+ 987654321.123456789. But if  
we don't think long and hard about 2+3 we will not be able to  
understand the result that the technology gives us.

For another example, we should first struggle with understanding  
where does the "quadratic formula" comes from and then we can use  
technology for solving   -3873,045 x^2 + …  And then, going back to  
paper and pencil, we could investigate, say, how to attack the  
problem of discussing the solutions of (m-1)x^2 +(m+1)x – m = 0 and  
then use technology to investigate what happens for a whole range of  
values of m. And then back to paper and pencil to think about what  
kind of functions of m as coefficients of the quadratic equation in x  
will produce this or that effect. And then on to technology perhaps  
to check one's intuition before one attempts a proof. Etc

Regards
--schremmer
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[Beth Hentges-2]

The radius of convergence of this series is R=1.

I'm having trouble justifying for myself whether or not it converges at each endpoint:
x=-1
x=1

Thanks,
Beth in MN
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[wmackey]

Exactly!!!  All you have to do is ask them a question instead of  
instructing them to do an algorithm.

wayne

Quoting Alain Schremmer <schremmer.alain@...>:

>
> On Apr 19, 2008, at 1:51 PM, Domenico Rosa wrote:
>
>> Recently I received a letter announcing a one-day "exciting  
>> workshop on the new handheld, the TI-Nspire." The letter concludes  
>> with: "You'll be amazed at what this handheld can do for you and  
>> your students."
>>
>> For almost two decades I have been truly amazed by what students  
>> can not do with their graphing calculators. Most of my current  
>> students, the majority of whom have been shamelessly  
>> pseudo-educated, possess one of the following models, which they  
>> were required to buy in high school:
>>
>> TI83 Plus
>> TI83 Plus Silver Edition
>> TI84 Plus
>> TI84 Plus Silver Edition
>>
>> As I correct their quizzes and examinations, I keep asking myself:  
>> "What on Earth were they doing in high school with these  
>> calculators?"
>>
>> I can't wait to see the amazing things that future students will be  
>>  able to do with the lastest snake oil.
>
> Yes, but there is a lot more money in selling calculators of any
> persuasion than paper and pencil.
>
> What I find a bit more surprising, though, is that an otherwise
> respectable profession should give in to the pressure.
>
> It is easy to circumvent. As Dienes used to say, instead of asking on a
> multiple-choice test, for instance,
>
> 2+3 =
>
> 7, 5, …
>
> just put it in a way where calculators won't help:
>
> 2+3 is
>
> between 7 and 9, less than 19, …
>
> Regards
> --schremmer
> ****************************************************************************
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> * To unsubscribe, email the message "unsubscribe mathedcc" to
> majordomo@... *
> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
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[wmackey]

Of course they didn't think to use them as a teaching tool.  They have  
been "trained" to teach algorithms, not math, and when you give them a  
calculator, they teach calculator algorithms or if you give them  
computers and MML, guess what they teach.

wayne

Quoting Ed Laughbaum <elaughba@...>:

>
> Alain brings up a good point - that being that we need to be smart
> enough to change our assessments so that the graphing calculator is of
> little help. I  usually include test items where the graphing
> calculator gives the wrong answer - if I can.
>
> This conversation brings me to a point I have been promoting for years,
> and that is that the graphing calculator is a teaching tool. Yet high
> school and college faculty alike often use it as a tool for doing the
> very math we teach.
>
> I just taught a 2-day workshop for a high school in Ohio, and I got the
> all-to-often response, "Oh, we should use it as a teaching tool?" My
> guess is that the thought had never occurred to them because of the way
> they were taught to use the GC - whether from colleagues, their
> teachers, TI, etc.
>
> Best,
>
> Ed
> ===========================
> At 10:10 AM 4/21/2008, Alain Schremmer wrote:
>
>
>> On Apr 19, 2008, at 1:51 PM, Domenico Rosa wrote:
>>
>>> Recently I received a letter announcing a one-day "exciting
>>> workshop on the new handheld, the TI-Nspire." The letter concludes
>>> with: "You'll be amazed at what this handheld can do for you and
>>> your students."
>>>
>>> For almost two decades I have been truly amazed by what students
>>> can not do with their graphing calculators. Most of my current
>>> students, the majority of whom have been shamelessly pseudo-  
>>> educated, possess one of the following models, which they were
>>> required to buy in high school:
>>>
>>> TI83 Plus
>>> TI83 Plus Silver Edition
>>> TI84 Plus
>>> TI84 Plus Silver Edition
>>>
>>> As I correct their quizzes and examinations, I keep asking myself:
>>> "What on Earth were they doing in high school with these calculators?"
>>>
>>> I can't wait to see the amazing things that future students will be
>>> able to do with the lastest snake oil.
>>
>> Yes, but there is a lot more money in selling calculators of any
>> persuasion than paper and pencil.
>>
>> What I find a bit more surprising, though, is that an otherwise
>> respectable profession should give in to the pressure.
>>
>> It is easy to circumvent. As Dienes used to say, instead of asking on
>> a multiple-choice test, for instance,
>>
>> 2+3 =
>>
>> 7, 5, ?
>>
>> just put it in a way where calculators won't help:
>>
>> 2+3 is
>>
>> between 7 and 9, less than 19, ?
>>
>> Regards
>> --schremmer
>> ****************************************************************************
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>> * To unsubscribe, email the message "unsubscribe mathedcc" to  
>> majordomo@... *
>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
>> ****************************************************************************
>
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[wmackey]

I've done things like this in college algebra, not quite getting to  
the relations between m and the solutions per se, but still into some  
concepts.  It is a lot more fun than teaching them to factor and get  
credit for factoring even if they don't have a clue as to what a  
solution to a quadratic equation is.

wayne

Quoting Alain Schremmer <schremmer.alain@...>:

>
> On Apr 21, 2008, at 10:46 AM, Ed Laughbaum wrote:
>
.....

>
> For another example, we should first struggle with understanding  
> where does the "quadratic formula" comes from and then we can use  
> technology for solving   -3873,045 x^2 + …  And then, going back to  
> paper and pencil, we could investigate, say, how to attack the  
> problem of discussing the solutions of (m-1)x^2 +(m+1)x – m = 0 and  
> then use technology to investigate what happens for a whole range of  
>  values of m. And then back to paper and pencil to think about what  
> kind of functions of m as coefficients of the quadratic equation in  
> x will produce this or that effect. And then on to technology  
> perhaps to check one's intuition before one attempts a proof. Etc
>
> Regards
> --schremmer
> ****************************************************************************
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> majordomo@... *
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[Alain Schremmer]

On Apr 21, 2008, at 6:24 PM, wmackey wrote:

> Exactly!!!  All you have to do is ask them a question instead of  
> instructing them to do an algorithm.

I note with relish that you didn't say "… to push a button".

Regards
--schremmer
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[Alain Schremmer]

On Apr 21, 2008, at 6:36 PM, wmackey wrote:

> I've done things like this in college algebra, not quite getting to  
> the relations between m and the solutions per se

Wait a minute, I never said I did that. All I ever did was to suggest  
a line of enquiry!

> , but still into some concepts.  It is a lot more fun than teaching  
> them to factor and get credit for factoring even if they don't have  
> a clue as to what a solution to a quadratic equation is.

In fact, it is a lot more instructive to consider the function f_m(x)  
= (m-1)x^2 +(m+1)x – m

In any case, after the students reset themselves, they too have a lot  
more fun.

The only trouble, usually, is the lack of time and for that we can  
blame the semester-based course—as opposed to the year-based course  
which prevents the exponential character of the learning curve to  
become effective.

Regards
--schremmer

> Quoting Alain Schremmer <schremmer.alain@...>:
>
>>
>> On Apr 21, 2008, at 10:46 AM, Ed Laughbaum wrote:
>>
> .....
>>
>> For another example, we should first struggle with understanding  
>> where does the "quadratic formula" comes from and then we can use  
>> technology for solving   -3873,045 x^2 + …  And then, going back  
>> to  paper and pencil, we could investigate, say, how to attack  
>> the  problem of discussing the solutions of (m-1)x^2 +(m+1)x – m =  
>> 0 and  then use technology to investigate what happens for a whole  
>> range of  values of m. And then back to paper and pencil to think  
>> about what  kind of functions of m as coefficients of the  
>> quadratic equation in  x will produce this or that effect. And  
>> then on to technology  perhaps to check one's intuition before one  
>> attempts a proof. Etc
>>
>> Regards
>> --schremmer
>> *********************************************************************
>> *******
>> * To post to the list: email mathedcc@... *
>> * To unsubscribe, email the message "unsubscribe mathedcc" to
>> majordomo@... *
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>> *******
>
>

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[Martha Haehl]

Well put. One of the many things I recognized years ago when I was first
able to use graphing calculators is that most students did not connect
roots to factors to x-intercepts (if the roots are real). They would use
the quadratic formula, for example, get real roots, graph the related
parabola which had no x-intercepts and have not clue that they had to
have made a mistake somewhere. That was enlightening to me that students
who had not used technology had learned some procedures but not a bigger
picture of what the procedures yield.

Similarly, students did not know that the process of multiplication or
factoring (or any other algebraic manipulation of one expression to
another) yields an identity. That was something that became easier to
get across with graphing technology. Do the manipulation, graph the two
forms of the expressions, and if the graphs are not identical, you did
not get an identity from your process--i.e., you made a mistake. Find
it!

The lack of teaching depth in mathematics extends far before graphing
technology was accessible to students.

Interestingly, a few years ago I heard a talk by an math professor from
Kansas State University who is quite the math historian. He noticed in
his research that around the time of the Black Plague that European
mathemmaticians who had done many arithmetic calculations with
manipulatives (a bag of different sizes of rocks used in a manner
similar to an abacus). During that era mathematicians transistioned to
pencil and paper calculations. He hypothesized that  the deaths during
the Plague created an abundance of old clothes that were turned into
rags then into paper, making paper affordable for the first time in
history.

In that transition, much was lost and much was gained--using
manipulatives could help better understand arithmetic structure, but
pencil and paper was much more portable. There was resistence to the
change.

I suspect with technology, much will be lost and much will be gained in
the transition. But there will be a transition. It is up to us to
redefine the study of mathematics and keep it rich through this
transition. I would beat all odds if I live for another 50 years, but it
will be interesting to see where this all lands--but it will land
someplace that does not look like 1950. Ah, the interesting times we
live in!!

Martha

Martha Haehl,
Ph.D., Education & Urban Leadership
Mathematics Instructor
816-759-4221
martha.haehl@...
Metropolitan Community College-Penn Valley
3201 S.W. Trafficway
Kansas City, MO 64111

>>> wmackey <wmackey@...> 4/21/2008 5:36 pm >>>
I've done things like this in college algebra, not quite getting to  
the relations between m and the solutions per se, but still into some

concepts.  It is a lot more fun than teaching them to factor and get  
credit for factoring even if they don't have a clue as to what a  
solution to a quadratic equation is.

wayne

Quoting Alain Schremmer <schremmer.alain@...>:

>
> On Apr 21, 2008, at 10:46 AM, Ed Laughbaum wrote:
>
......
>
> For another example, we should first struggle with understanding  
> where does the "quadratic formula" comes from and then we can use  
> technology for solving   -3873,045 x^2 + …  And then, going back to  

> paper and pencil, we could investigate, say, how to attack the  
> problem of discussing the solutions of (m-1)x^2 +(m+1)x – m = 0 and
 
> then use technology to investigate what happens for a whole range of

>  values of m. And then back to paper and pencil to think about what  

> kind of functions of m as coefficients of the quadratic equation in  

> x will produce this or that effect. And then on to technology  
> perhaps to check one's intuition before one attempts a proof. Etc
>
> Regards
> --schremmer
>
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> majordomo@... *
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>
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[Alain Schremmer]

On Apr 21, 2008, at 7:28 PM, Martha Haehl wrote:

> The lack of teaching depth in mathematics extends far before graphing
> technology was accessible to students.

That is certainly true. The question, though, is why don't we  
recognize it?

> Interestingly, a few years ago I heard a talk by an math professor  
> from
> Kansas State University who is quite the math historian. He noticed in
> his research that around the time of the Black Plague that European
> mathemmaticians who had done many arithmetic calculations with
> manipulatives (a bag of different sizes of rocks used in a manner
> similar to an abacus). During that era mathematicians transistioned to
> pencil and paper calculations. He hypothesized that  the deaths during
> the Plague created an abundance of old clothes that were turned into
> rags then into paper, making paper affordable for the first time in
> history.

You wouldn't, by any chance, recall the name of the lecturer?

> In that transition, much was lost and much was gained--using
> manipulatives could help better understand arithmetic structure, but
> pencil and paper was much more portable. There was resistence to the
> change.

I find this rather intriguing and would like to read more about it.

> I suspect with technology, much will be lost and much will be  
> gained in
> the transition. But there will be a transition. It is up to us to
> redefine the study of mathematics and keep it rich through this
> transition. I would beat all odds if I live for another 50 years,  
> but it
> will be interesting to see where this all lands--but it will land
> someplace that does not look like 1950. Ah, the interesting times we
> live in!!

Yes and no. I think that the situation  we have now—and I mean in  
mathematics education—is much a direct consequence, if not a part, of  
something well documented in Paul Krugman's The conscience of a  
Liberal. (It should be noted that "He is among the 50 top economists  
in the world according to IDEAS/RePEc." Wikipedia.)

Regards
--schremmer

> Martha
>
> Martha Haehl,
> Ph.D., Education & Urban Leadership
> Mathematics Instructor
> 816-759-4221
> martha.haehl@...
> Metropolitan Community College-Penn Valley
> 3201 S.W. Trafficway
> Kansas City, MO 64111
>
>>>> wmackey <wmackey@...> 4/21/2008 5:36 pm >>>
> I've done things like this in college algebra, not quite getting to
> the relations between m and the solutions per se, but still into some
>
> concepts.  It is a lot more fun than teaching them to factor and get
> credit for factoring even if they don't have a clue as to what a
> solution to a quadratic equation is.
>
> wayne
>
> Quoting Alain Schremmer <schremmer.alain@...>:
>
>>
>> On Apr 21, 2008, at 10:46 AM, Ed Laughbaum wrote:
>>
> ......
>>
>> For another example, we should first struggle with understanding
>> where does the "quadratic formula" comes from and then we can use
>> technology for solving   -3873,045 x^2 + …  And then, going back to
>
>> paper and pencil, we could investigate, say, how to attack the
>> problem of discussing the solutions of (m-1)x^2 +(m+1)x – m = 0 and
>
>> then use technology to investigate what happens for a whole range of
>
>>  values of m. And then back to paper and pencil to think about what
>
>> kind of functions of m as coefficients of the quadratic equation in
>
>> x will produce this or that effect. And then on to technology
>> perhaps to check one's intuition before one attempts a proof. Etc
>>
>> Regards
>> --schremmer
>>
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[Joan Kessler]

 Last week in Calc 2 I was teaching a section on Polar conics and gave the
class the general formula to explore. The graphing Calculator didn't do a
great job, so they asked me to use my "other" program on my computer (via a
projector) so they could explore the graphs. What if we use sine instead of
cosine? Before I graphed it on a 5ft. screen, I asked how the functions were
related and how they graphed differently in polar, parametric,  and
rectangular. We discussed it for a few minutes, then the nice color graph
came up and they were so pleased with themselves- not only did they see the
differences, but understood why it happened. We explored the eccentricity
and the difference between plus and minus in the formula and, the class got
so much more out of it than just using the theorems in the text or just
hitting buttons on a calculator themselves. Their learning was guided. There
is nothing better to teach with than Visualizations done right. Of course,
done right, is the key expression here. Unfortunately new teachers are not
being taught how to use these technology tools to their best advantage in
the classroom. Some have not even been exposed to graphing calculators in
college, let alone how to teach with them.  And we all know that in the CC's
effective use of technology  is rare.

With respect to the TI Inspire. I went to a workshop last summer and was not
excited about it at all. Very steep learning curve and higher price - it
would take years of regular use to become spontaneous with it the way I am
with an 84 or my "other" math software.

 On another note. If anyone is moving to Southeast Florida, or knows someone
who might be, I have knowledge of a fantastic full time opening for a
qualified math person starting in August.  Serious inquiries only- please
send me an email privately.


Joan Kessler, NBCT
Mathematics Department
College Academy @ Broward Community College Central
3501 SW Davie Road
Ft. Lauderdale, FL 33314
Phone: [phone]  x 2012



 or joan@...
www.distancemath.com


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