-forgive my ignorance, folks, I did this exercise in math club, and I had difficulty with it then and still don't "get it" now. Sometimes I need a sense of purpose or a reason for doing something to understand what I am doing. Can someone enlighten me about what I could do with this exercise? Is this a way of enlarging a figure in a predictable fashion? Feeling Like I missed Something aka Kalli |
2 0
0 2
3 0
0 3
0 1
1 0
-1 0
0 1
Try your own variations of "diagonal" matrices. You will notice what
matrices produce flips, stretches or rotations. After this,
predictability comes.
In the software, the "Init" button (for "initial") resets everything.
Let us know what you discover with matrices!
--
Cheers,
MariaD
Make math your own, to make your own math.
http://www.naturalmath.com social math site
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Don,
The problem with 1s is that kids don't necessarily see multiplication
by 1 as multiplication! It is a good example of learning paradoxes.
Once kids are strong on multiplication, they find multiplying by 1 the
easiest thing in the world. However, when they are still
conceptualizing multiplication, or a new instance of it like
multiplication of matrices, examples involving 1s may confuse. Such
examples don't clearly express any multiplicative action (e.g.
grouping or stretching) - so they are more abstract than
multiplication by other numbers. I hope it makes sense, and if not, I
can describe it some more. In the same spirit, I try not to introduce
addition via adding 0, and can't introduce sets starting with either
empty set or the set of all objects in your space.
I eventually told kids to pick whole numbers less than three.
Interestingly, 1s were picked by the most advanced kids in the groups
who already had some algebra and figured out it will be the easiest
thing to try!
> This activity goes back to my work with Bob Davis (EXPLORATIONS IN
> MATHEMATICS - a text for teachers, by Bob Davis; Addison-Wesley 1967, out of
> print), further back to A Path to Modern Mathematics by W.W. Sawyer 1966,
> and further back to On Growth and Form, by D'Arcy Thompson, originally
> published in 1917! I have a 1961, abridged ed. published by Cambridge U
> Press; no matrices, but lots of tranformations in animals, fish, honeycombs,
> and shells (equiangular spirals-The Nautilus!). And invariants.
> I guess I try to make things simple for kids, Maria.
> Keep up the fine work you are doing!!!
> Don
>
> On Sun, Apr 26, 2009 at 9:29 AM, Maria Droujkova <drou...@gmail.com>
> wrote:
>>
>> This is an activity designed by Don Cohen the Mathman, in his book
>> "Changing Shapes with Matrices." You can find some sample book problems
>> here, and follow links to other Don's materials:
>> http://www.mathman.biz/html/probcswm.html
>>
--
Cheers,
MariaD
Make math your own, to make your own math.
http://www.naturalmath.com social math site