Examples of designed software (Th!nklets)
is tool for building and manipulating 3d block buildings on the screen.
This tool is used in an enviroment:
with all kinds of tasks and problems for young children to develop spatial abilities.
Building with three views
Building with two views
Building with silhouets
are collections with more difficult problems that can be used in secondary education.
Programs for building
is developed for secondary education. In this enviroment students can build structures by using commands in a formal language. By using variables, student can build much more efficiently. In this way they can experience the power of variables and get insight in the 3d coordinate system.
On a basic level the th!nklet
can be used to perform a calculation by making a chain of operations between an input box and an output box.
One of the ideas that played an important role in the development of this applet is that constructing an arrow chain to perform a calculation
is a means to shift the attention from carrying out a calculation procedure to representing it.
The task for the student is to construct the arrow chain representation. The th!nklet then carries out the calculations.
Chain representations foster the view on a calculation process as something independent from the specific numbers in the
input box and thus prepares for the concept of formula and function.
The th!nklet has other options that can support further steps in learning the concepts variable, formula and function.
Word variables or letters can be used as input. In that case the result is a word expression or a formula:
If the input box is empty or contains a word or a character, it is possible to represent this variable input by a single table
of numbers. It's possible to make graphical representations as well.
has similar options, but works with with tree structures to overcome the limitations of the arrow chains.
Both th!nklets can be modelling tools in problem solving activities, but they can be used for investigating the structure of algebraic expressions as well.
Algebra Arrows Problems 1
Algebra Arrows Problems 2
are designed for the this second application. Student have to find arrow chains for a given formula or to change one formula to another.