Turtle Pythagoras 2

A proof of Pythagoras' theorem in Turtle Art


Cannot get the colour fill as above though





The following may be a better representation. Student challenge, program the following:

Image http://en.wikipedia.org/wiki/Mathematical_beauty

See also Turtle Pythagoras
See also implementation in Game Maker

To do: Python block does not accept box(theta) as input

Turtle e

Calculation of e using the Taylor series

http://en.wikipedia.org/wiki/E_(mathematical_constant)#Complex_numbers

(Turtle Art seems to now only display one decimal point at V83 so I have scaled up by 10^12 to show decimal places, Previous example of Pi showed decimal places)

Student challenge: calculate square roots with the Taylor series

http://en.wikipedia.org/wiki/Methods_of_computing_square_roots

File:Turtle_e.ta

En español
Cálculo de correo utilizando la serie de Taylor

(Turtle Art muestra limitada decimales por lo que han ampliado en un 10 ^ 12 para mostrar más cifras decimales, el ejemplo anterior de Pi mostraron cifras decimales)

Estudiantes desafío: calcular raíces cuadradas con la serie de Taylor

Turtle Art - collapsed stacks and numeric input

Turtle Art now has the ability to collapse a stack of blocks, shown expanded above and collapsed below.
That, along with copy and paste, allows you to develop a handy set of stacks, like subroutines, for later reuse, which do not complicate program readability or use screen space.

The stack above captures a multi digit integer from the keyboard and returns with it in Box1 when enter is pressed. The digits 0-9 have a key value of 48 to 57. The enter key has a value of 13.

Turtle_Art_getnumber.ta

En español
septiembre 2010

Turtle Art tiene ahora la posibilidad de contraer una pila de bloques, que se muestra ampliada por encima y por debajo se derrumbó.

Eso, junto con copiar y pegar, le permite desarrollar un conjunto útil de las pilas, como subrutinas, para su uso posterior, que no se complican la legibilidad del programa o espacio en la pantalla uso.

La pila por encima de captura un número entero de varios dígitos desde el teclado y vuelve con él en el Cuadro n º 1 cuando se pulsa ENTER. Los dígitos 0-9 tiene un valor de clave de 48 a 57. La tecla Enter tiene un valor de 13.

Turtle Art - higher ceiling

A good learning environment for self-directed learning has a low entry, wide walls and high ceiling. That is, it is easy for beginners, can facilitate a wide range of creative efforts and is unrestricted in top end complexity.

Turtle Art for the Sugar operating system started out as a nice little, Logo like, drawing package
for young learners. Its Turtle and Pen pallets allowed young learners to draw geometric shapes, solve problems and learn a bit about geometry and logic.

Its Scratch like interlocking program blocks made programming foolproof.

Maybe a year ago, Walter Bender introduced the Portfolio pallet, which allows the integration of multimedia into this simple programming language. This extended the use of Turtle Art into literacy activities.

Python programmable blocks were also added, this extended the ceiling, there was no effective limit to the top end functionality. There is however a big leap from drag and drop progam blocks to object oriented Python which limits the usefulness of these blocks.

Recently Walter and Raúl Gutiérrez Segalés have done a major rewrite of Turtle Art, the pre-release version (at the time of writing), version 83 is here. Variable names and block stack (subroutine) names are now themselves variables. These variables can be numeric or string and the + operator can concatenate both data types. This greatly increases the power of Turtle Art while staying with familiar drag and drop block programming.

The program shown above above creates a 10x10 array of variables. The variable "index" contains a string RnCm where n and m are the row and column. The variable "index" is used to name 100 variables named R1C1 to R10C10 which have the value Row x Column stored in them.

A variable "subroutine" or stack name is also used. On the first pass, "runarray" calls stack "doit" to create the array and initialise the array values on the second pass it calls stack "printit" to display the array values.

Now a wide range of sophisticated programming is possible. For example, Turtle Art could compute fractals but the slow execution of the underling Python interpreted language is a major limitation.

Maths Wars

http://commons.wikimedia.org/wiki/File:Euler%27s_formula.png

"Maths Wars" refers to the tension between instruction and construction in teaching/learning

The following interesting quote came via Artichoke

"Many of those wanting to build relational understanding with students assume that spending time on rote procedural knowledge is an important precursor for developing deeper conceptual understanding. This seems like a common sense approach – a let’s keep a foot in both camps kind of approach. However, research findings in math education suggest otherwise (Pesek and Kirshner 2000). It seems more likely that, in maths education at least, time spent building prior instrumental understanding is an interference to, not an aid to, developing relational understanding."

Interesting because Australia schools at least seem to spend a lot of time on rote procedural knowledge in mathematics.

More on Pesek and Kirshner 2000

"Students who received the procedural instruction prior to the conceptual instruction learned less than did students who received only the conceptual instruction. Somehow, exposure to routine application of formulas inhibited or interfered with students' subsequent conceptual learning."

It still seems likely to me that the best teaching will incorporate both solid procedural knowledge and problem solving in authentic and relevant contexts. This study does not destroy that belief, but it does sound a warning that you can't just mix a bit of both and always get good results.