# Learning-App: P(X)

The student is playfully introduced to the theory of probability. This is done by means of a graphical representation, which the user composes interactively.

This results in **probability distributions** as well as composite **events**. While the classical approach formally calculates probabilities of these events, for the first time, it is possible to graphically determine probabilities. The conventional calculation path can be derived from the resulting diagram, enabling the student to learn the conventional approach as well.

The diagrams visualize the mathematical structure of probability theory: sizes of symbols and their spatial arrangements play a role here. Since such a visualization can be more easily grasped by the students than a formula, the underlying mathematical structures get more clearer. In this way, they can be comprehended not only by the skilled mathematician but also by the layman.

- Diagrams replace mathematical formulas.
- These are constructed by simple rules.
- Diagram structures show formal relationships.
- Only correct connections can be realized.
- The derivation of formulas is explained visually.

## The Diagram-Computer

Any random experiments can be defined, for which probability calculations are to be performed.

Limits are set insofar only discrete random experiments are supported. Their extent is limited by the size of the screen. On the other hand, it is just the size of an iPad on which the presentation has been optimized.

#### Diagram-Computer

Visual description of tasks

#### Teacher

Generation of tasks

#### Students

Understanding of solutions

#### Fractions

Computations with rational numbers

#### Learning Modules

At one owns pace, step by step

#### Graphic learning

Understand complex relationships

## Theory modules

Each theory module explains a concept. For this purpose, a diagrammatic depiction of this term is shown. Its relationship to other terms is explained in the same diagram.

## Examples

Using simple examples, the theoretical concepts are deepened. In addition to classic textbook examples with cubes and urns, there are many practical examples. These aid in transferring to new real scenarios.

## Tasks

Based on short exercises, the student can verify his skills. To this end, the correct diagrammatic elements have to be selected and arranged. The system verifies the correct layout of the diagram and provides feedback to the learner. Errors are immediately recognized and can be immediately corrected.