# Laboratory on Mathematics and Mathematics Education/Logo

About Turtles and Stars

## Logo
### Task 1: Exploring Logo

* Install the English version of MSW Logo on your computer. (Please use the English version, because the Portuguese version uses other commmands.) If you are not allowed to install software on your computer, I will give you MSW Logo on a flash.
* Try to create a regular triangle, pentagon, and hexagon by interactively directing the turtle.
* Teach the turtle a new word "regpolygon" with the number of edges and the length of the sides of the regular polygon as parameters. For example, the command "regpolygon 5 100" should paint a regular pentagon with side length 100.
* Write a procedure "rectangle :width :height" which paints a rectangle with the given width and height.
* Paint a circle.

### Task 2: Be creative!

* Teach the turtle a new word "star" which paints a star.
* Teach the turtle to paint a house.
* Teach the turtle to paint the skyline of a city. Therefore, use your house command.
* Teach the turtle to paint flowers.
* Be creative! Just paint!
Please copy and paste your code snippets into our results page!

### Task 3: Why Logo?

* Find some arguments why Logo should be used in schools. Think about learning objectives and learning philosophies.
* Collect your arguments in the group (active plenum).

### Task 4: Add the images

Add the resulting Logo images to our results page.
* Save the image as gif file on your hard disk or flash (choose "Bitmap/Save" and then select "gif").
* Upload the image to wikiversity (use the "Toolbox/Upload file" option on the left side).
* Put the image link on our results page.

### Task 5: Traditional ethnic patterns of Mozambique

* Write procedures which paint different beautiful traditional ethnic patterns of Mozambique.
* Copy and paste your code into our results page.
* Upload the image and make a link on the results page.

### Task 6: Introduction to Logo in Schools

How can Logo be introduced in schools, especially to students at very young ages in primary school? Collect your ideas!
* Your results

## Bruner's EIS principle
### Task 7: Logo and EIS

* Create an idea how Logo can be introduced with regard to Bruner's EIS principle in school (e.g. on grade level... 1!).
* Present your ideas.
For those who are fast: Think about how the EIS principle can be used in the field of learning to calculate with fractions.

## The Power of Recursion
### Task 8: Be recursive with numbers!

* Write a procedure which calculates the factorial of a given natural number.
* Write a procedure which calculates the n-th Fibonnacci number.
* Write a procedure which calculates the greatest common divisor of two natural numbers.

### Task 9: Be recursive with graphics!

Paint one of the following images: recursive graphics

### Task 10: Recursion and EIS

How can the EIS principle be realized within the context of recursion? Collect ideas!

## Links and Materials

* The Logo Philosophy
* MSW Logo
* Image of the first turtle robot
* Logo Philosophy and Implementation - Text about Logo and its implementation in different countries (e.g. Argentinia, Brazil, and Thailand)
* Videos about Logo: Video 1 Video 2
* Seymour Papert about teaching thinking
* Introduction to Bruner's EIS principle