Who said that computation is boring?
Hands up!
This question has arisen in many schools and it is time to answer it with
foundation.
Since 2003 the schoolchilds of my village have in their
desks Tablet PC donated by the computer magnate,
they are the masters of the keyboard and the homework!
Who would have said in one of the areas in Spain that are becoming depopulated
soon be our grandchildren who have the last and better resources. Now what
remains is to give content to these PCs and, not only with
the Bill Gates Windows, making them attractive to schoolboys and schollgirls, because what they
hate most is monotony and do not like math because are a
"real bore" but you can animate it a little.
But that is going to end if they are taught to do calculations that are not
boring (before we had to learn to use the tables of logarithms and calculate
cube roots by hand) and the best way is to present them graphically with the
tools at our disposal, or either with
"animate" Excel spreadsheets,
what will be a more entertaining that the schoolchilds are close to the
mathematical calculation, without neglecting the formulas and equations that
make data come alive, do you like my waves?
What is important is that the teachers, in nursery, primary and secondary
schools, approach to computers without fear, thinking about computers as
allies instead of enemies, and receive support and computer classes in their
curriculum, whether science as letters, because nowadays, who does not know
how to use a computer is seen as an
illiterate of XXI century
can not be effective educators and their students either, as they are advanced
users of new technologies, both for study and for work.
One way of bringing mathematics to the students is teaching them with computer
programs and spreadsheets are a good ally because need equations to calculate,
graphic spreadsheets and, why not, animate them!
How to make "animated" calculations and graphics in Excel?
Nothing better than an example, inventing the wheel again, or rather creating
bubbles in the waves of this blog.
I'll use the circumference formula to calculate the coordinate points on the
axes X and Y. Solving the unknown Y in relation to the radius R of the circle
and the values of X, we obtain:
To do that,
open a new Excel spreadsheet and write in the following
cells:
Cell L6 - Radius R with number format without decimals.
Range K11:K211 - Integer values of x' consecutives from -100 to
+100.
Range L11:L211 - Integer values of x being equal to R (with the sign of
x if x ' > R) or equal to x', according to the formula:
Range M11:M211 - Value +y obtained from the formula for the
circumference:
Range N11:N211 - Value -y changing +y sign:
Range O11:O211 - Random value between negative and positive values of
y:
Columns P, Q and R as L, M and N but with a half circle of radius R /
2.
So far the calculations are based on the formula for the circumference of the
column M. (If you want to know why ROUND is used to calculate the square root
as explained in an article on
Linear Equations here
as it is a solution to the
frequent calculation bugs)
To graph these
two circles on a spreadsheet named "Waves" (Ondas in
Spanish) follow these steps:
1) Insert a
scatter graphic with straight lines.
2) Select data, adding
5 series: +y, -y, +y/2, y/2 and the series of
random values (see steps 3 through 7)
3) Add the series +y for the positive values of the first circle:
Series name:
Series X values:
Series Y values:
4) Add the series -y for the negative values of the first circle::
Series name:
Series X values:
Series Y values:
5) Add the series +y/2 for the positive values of the second circle:
Series name:
Series X values:
Series Y values:
6) Add the series -y/2 for the negative values of the second circle:
Series name:
Series X values:
Series Y values:
7) Add the series of random bubbles:
Series name:
Series X values:
Series Y values:
We already have the graph to which you can remove all but the series,
eliminating the axes, titles, gridlines, etc., only to see that the graphics
are stopped by now.
To animate the graphics we need to create an Excel macro to be launched by a
button that will start changing the radius R values to change the circles in
real time, but I will explain in another article that this is already long
enough.
As an aperitif, to modify the radius R you could add a scrollbar to the
spreadsheet, following the instructions on
this link (personally I like the form controls)
Download Pedro Waves
You can download the animated graphic from here:
To view the animation you must
enable macros and press Play.
Traducción al español
aquí.
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