[Maths-Education] review of interactive geometry software

[Walter Whiteley]

About buttons - but not action buttons - one of the features I really  
appreciate (I use GSP)  are the hide-show buttons.

When doing a demonstration, the capacity to refocus the viewer's  
attention by hiding portions of the diagram so that the viewer is  
looking at where I think the key events are happening is very  
powerful.  Then I can pull back to the whole after altering the  
viewer's perception/prior knowledge of the diagram.  Substantial  
visual reasoning involves refocusing attention, then pulling back to  
the whole.

My most powerful example was the standard problem  ' the maximum  
number of pieces you can cut a pizza into with n cuts' .  At one point  
reviewing some reasoning about seven lines, I hid everything except  
the last line and the points of intersection with the previous lines.   
The TA in the room noted there was a stunned silence - what was on the  
screen was not what anyone else in the room was looking at  or focused  
on - though it was what I was starting to reason with (the one- 
dimensional case), and what my words were trying to direct attention to.

This feature does let me make visible to others how my attention is  
shifting across a diagram, as I move through steps of reasoning.  So I  
consider it invaluable to have hide-show as a feature to switch from  
whole, to critical parts, and back to hole.   These shifts in  
attention are key and are awkwardly communicated if all I can do is  
wave my hands over the figure.


Walter Whiteley
York University, Toronto Ontario

On 13-Aug-10, at 7:59 AM, Douglas Butler (Argonet) wrote:

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> Kate, John and Dave
>
>
>
> An interesting thread, and it will be fascinating to read Kate's
> conclusions.
>
>
>
> I know Autograph is not really a DGS system, so not really in this  
> frame,
> but I would like to explore David's point about action buttons.  He  
> makes a
> good case for them, but I have never really felt the need. I worry  
> that that
> some students might see them 'magic', performing operations that  
> they have
> not been involved in setting up. I can see that it may well be time  
> for a
> rethink.
>
>
>
> The Autograph approach is quite different, expecting the teachers,  
> with full
> interaction from the students, or the students themselves, to set up  
> each
> situation from the bottom up, with judicious use of the slow plot and
> scribble tool.
>
>
>
> If anyone reading this would like to see the latest version of  
> Autograph
> (MAC or PC) just send me an email and I'll set you up. Or have a  
> browse
> through some items I have done recently for ATM and NCTM:
>
>   www.tsm-resources.com/videos.html
>
>
>
> Good luck with the project, Kate
>
> Douglas
>
>
>
> == from Douglas Butler < debutler at argonet.co.uk > ==
>
> Director, iCT TRAINING CENTRE (OUNDLE)
>
> PO Box 46, Oundle, Peterborough PE8 4EJ, UK
>
> T: +44 (0)1832 273444 F: 273529 M: +44 (0)7860 843462
>
> www.tsm-resources.com    www.autograph-maths.com
>
>
>
> -----Original Message-----
>
> From: maths-education-bounces at lists.nottingham.ac.uk
> [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of  
> John
> Mason
>
> Sent: 12 August 2010 08:10
>
> To: Mathematics Education discussion forum
>
> Subject: Re: [Maths-Education] review of interactive geometry software
>
>
>
> Hi Kate,
>
>
>
> I have been using cabri since it started, at least once every two or  
> three
> days. Recently I have started using Cinderella, because it has a  
> scripting
> language which enables me to make applets where the Mac version of  
> Cabri is
> a bit weak.  I haven't used Sketchpad for some time, largely because  
> I found
> the macro-construction clunky (it has probably
>
> changed) and talking to NickJ in Brazil, it sounds as though  
> Sketchpad is
> the most innovative and powerful of them all. That said, the macro
> construction in Cinderella is similar: it decides what is input and  
> what is
> output; but I am still learning how Cinderella works.
>
>
>
> I am like DaveH in that I use DGS for plenary work, displaying a  
> phenomenon
> and then getting people to make sense of what they have seen.
>
> So I too am using lots of buttons.  I aim to offer images, what  
> Gavrial
> Salomon called 'supplanted imagery' to enrich people's example spaces.
>
>
>
> Cinderella is not nearly as sophisticated as Sketchpad in being able  
> to move
> to different worksheets. Nevertheless I like being able to access  
> all the
> objects, as in Geogebra, to change the names and the labels, and so  
> on.
> Geogebra I use only when I need something for people familiar with it.
>
>
>
> I think you definitely should have some demo files like Dave's. I am
> developing one on eigenvalues but am not yet happy with it.  There  
> is a set
> of simple ones called Langrange & Tangents on my website
> (http://mcs.open.ac.uk/jhm3; go to Applets; look under Chordal  
> Studies).
>
>
>
> Is this part of the review that Ros Sutherland is involved in?
>
>
>
> Cheers
>
>
>
> J
>
>
>
> On 11/8/10 23:33, Kate Mackrell wrote:
>
>>
>
>> Thanks Dave.
>
>>
>
>> I wonder if perhaps instead of or as well as solving a problem in  
>> each
>
>> software I should design and make a pre-prepared file such as Dave
>
>> suggests?
>
>>
>
>> Kate
>
>> On 11-Aug-10, at 6:39 PM, Dave Hewitt wrote:
>
>>
>
>>>
>
>>> Excuse quick response.... I choose Sketchpad originally mainly due  
>>> to
>
>>> the power of the buttons. The buttons enable me to construct
>
>>> pre-prepared files which are designed to use as a teaching resource,
>
>>> mainly with an interactive whiteboard. I am not sure whether the
>
>>> description I have just written makes it clear enough as to how I
>
>>> tend to use sketchpad as a teacher and so I offer an example  
>>> attached
>
>>> along with reference to an article which gives a brief indication of
>
>>> how I might use it in a classroom (Hewitt, D. (2007), 'Canonical
>
>>> images', Mathematics Teaching, 205, pp. 6-11.). The fact that you  
>>> ask
>
>>> the second question you have in your email adds to my sense that few
>
>>> people seem to consider the opportunities sketchpad, in particular,
>
>>> offers as a teaching resource by way of carefully constructed
>
>>> pre-prepared files where the teacher might control what happens with
>
>>> the file initially as part of a whole class interactive engagement
>
>>> with mathematical questions which can lead quite directly towards
>
>>> some desired mathematical content. In the literature I tend to read
>
>>> about students being given a problem/task and using the software  
>>> as a
>
>>> tool to work on that task. This is, of course, one powerful way of
>
>>> using such software. however, personally I have found it  
>>> particularly
>
>>> powerful to use sketchpad as a pedagogic tool working with a whole
>
>>> class, and this seems to be rarely discussed in the literature.
>
>>>
>
>>> Hope this makes some sense!
>
>>>
>
>>> In haste,
>
>>>
>
>>> Dave.
>
>>>
>
>>>
>
>>> Dr Dave Hewitt
>
>>> School of Education
>
>>> University of Birmingham
>
>>> Edgbaston
>
>>> Birmingham
>
>>> B15 2TT
>
>>>
>
>>> Tel: +44 (0)121 414 4824
>
>>> Fax: +44 (0)121 414 4865
>
>>> ________________________________________
>
>>> From: maths-education-bounces at lists.nottingham.ac.uk
>
>>> [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Kate
>
>>> Mackrell [katemackrell at sympatico.ca]
>
>>> Sent: 11 August 2010 18:02
>
>>> To: maths-education discussion forum
>
>>> Subject: [Maths-Education] review of interactive geometry software
>
>>>
>
>>>
>
>>> I am currently writing a comparative review of Sketchpad/Cabri/
>
>>> Cinderella/Geogebra and would love to hear from anyone on the list
>
>>> concerning:
>
>>>
>
>>> a. their reasons for choosing to use a particular interactive
>
>>> geometry software.  Don't necessarily limit yourself to the ones
>
>>> above - I would possibly be open to including other softwares in the
> review.
>
>>>
>
>>> b. any geometry/algebra tasks that would provide a useful basis of
>
>>> comparison for the softwares.  I have a number of ideas, but I'm
>
>>> worried that I will automatically choose a task that works best with
>
>>> my own favourite software, which would not be quite fair!
>
>>>
>
>>> Thanks
>
>>>
>
>>> Kate Mackrell<Rotating dot.gsp>