In math and science lessons, teachers are often confronted with great differences in basic knowledge and experience among their students.

Fibonacci project aims at supporting students as individually as possible. This may lead to the disintegration of levels of achievement. Experience has proved that both demanding or expecting too much but also too little from a student may lead to his or her lack of motivation and consequently to a failure in learning. In order to avoid this problems should be developed which allow solutions on different levels of understanding.

Meaningful learning can also be achieved with different complexity. All students need good basic knowledge and also the basic capacity for understanding math and science problems which enable them to continue their studies.

It is not sufficient to acquire basic knowledge by just collecting individual elements and simply keep them ready for use. It is much more important for a student to be aware of the connection between these elements in order to create a network of their math and science knowledge. It is only then that basic knowledge can serve as a solid basis for creative processes and can initiate and support a problem-solving way of thinking.

Read more under basic pattern 5: Cumulative learning

Catalogues of basic knowledge are commonly known. Usually they summarize all the important contents of a subject for each school year according to the requirements of the curriculum. In their digital version they may serve as a basis for individual completion.

Alternatively these catalogues can be developed in the course of the school year. Thus the students get the chance to reflect on the contents more carefully and reduce them to their essential parts.

Writing and creative work support the individual learning process.

• Encyclopedic use: In case of a knowledge gap, these catalogues can be used as a kind of encyclopedia.
• File cards: Systematic revision can be achieved by using question and answer cards as in learning foreign languages.
• Revision and practice circle: Problem solutions at various degrees of difficulty, the mixture of old and new tasks, compulsory tasks and optional ones, make practice and revision circles a valuable means of differentiating the levels of capacity and individual support.
• Revision and practice worksheets: Similar to the tasks of a practice circle they are also useful. The students should be given free choice. Thus boredom and excessive demand can be avoided.