## Abstrakt

This master thesis is motivated by the fact that examples often are used to ease the teaching and learning of mathematics. On this basis it is investigated what the functions and importance of examples when teaching and learning mathematics is, and whether it is possible based on didactics of mathematics to design examples which supports student’s learning of mathematical concepts. The thesis has found that there has not been conducted research on this topic within didactics of mathematics. On the other hand, within the field of psychology of learning there has been conducted research on »learning by induction« and »learning by examples«. These research have been included in this thesis to illustrate to what extent »learning by examples« has been researched before. Furthermore, It has also been necessary to define when something can be defined as an example. The thesis has included a wide range of theories from the didactics of mathematics. The purpose of these theories is to provide a basis for designing a course, and particularly for designing mathematical examples. There are a total of four different courses designed for four different high school classes, respectively, an A-level class and three B-level classes. Each of the courses spans for two days with a total of 4 lessons, and each course deals with a different mathematical topic. The courses have been implemented and executed, and it is the collected data that serves as the underlying for the analysis and discussion. The thesis concludes that is it possible to design examples that supports the student’s learning of mathematical concepts based on theories from the didactics of mathematics. At the same time, it is not possible to design examples without also designing the context in which they occur, and in this context the learning objective becomes particularly important. It can also be concluded that it is not possible to design examples that support reification, but that it instead is possible to design examples that have a reification potential. Furthermore, it can be concluded that examples are essential for the teaching and learning of mathematics. Regardless of how the examples are designed, they will always shape the student’s learning, by for example managing the learning focus among other things. Examples quickly become the subject of a teacher’s teaching, and it is possible with examples to promote specific learning goals. As such, it becomes important for the teacher to be able to design and analyze examples in a way that ensures the use of examples that promote the appropriate learning objectives. Failing to use the »right« example for a specific learning objective, may result in a derailment of the intended learning process.

Uddannelser | Matematik, (Bachelor/kandidatuddannelse) Kandidat |
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Sprog | Dansk |

Udgivelsesdato | 15 jun. 2011 |

Vejledere | Morten Blomhøj |

### Emneord

- Sfard
- Læringteori
- Eksempler
- piaget
- Tall
- Formidling
- Skovsmose
- brousseau
- Winner