Most people seem to hate (or at least do not like) mathematics. I think that the roots of this are in the bad school education. As a teacher I already had the opportunity to work in several classes with the 4th and 5th grade in the Waldorf School of Rastatt. I was very surprised to notice that even those small kids already hated maths.
Mathematics is not only very interesting and useful, but it is also a good way to spiritual development. Rudolf Steiner calls it “a way to spiritual awareness”. Mathematics helped him a lot in order to have some soul experiences and create his anthroposophy. My spiritual way and believe in God also appeared because of my mathematics studies.
So, I want to create an interesting, lively, inner-experience-based and stress-free approach of teaching mathematics.
The concept includes the following:
1. No exams and tests. From time to time there will be a mock exam in order to learn how to perform good in exams.
2. No homeworks. Who wants can do some exercises, but it is up to the students.
3. Two extra consultation hours per week for help and explanation, so students can ask personally much more questions and obtain answers.
4. 20% free time in class. This means that in this time we will do something else than maths. Most of the topics will consider personal evelopment and ideas of the students.
5. 20% absence from the classes. Every student has the freedom not to come in 20% of the classes. The reason could be told to the teacher, but it must not be. If someone is missing more than 20%, some extra studies at home and exams will be needed.
6. Students may have to make small presentations from time to time.
7. Every student have to choose each term (September to January and February to June) a project. There is a big freedom in choosing the topics. The teacher will create a list with at least 120 possible topics. The project should be done alone or in small groups (2-3 students). It should be written down in about 50 pages (preferably in English) and presented after that to the group. As you can see it is s very serious work, but it will prepare the students for the future and develop in them a lot of new and useful skills. And it is also very important for the mathematics education and for the personality to learn to learn alone (or in teams) and to delve into a specific topic. This will be a kind of meditation and concentration for the spirit. Everything should be written on a computer and delivered on a digital medium. After that it will be uploaded in internet, so everyone can use it. In this way we will manage to create our own living textbooks and collect a big amount of high quality learning materials. Our dream is to create a lot of nice waldorf learning books in maths.
8. At the end of every epoch the students should write a small summary what they had learned. They also have to write a characteristic of the teacher. And also give a personal feedback. The teacher has to do the same.
9. There is no point to have less than two hours maths at a stretch. The programme should be made in such a way, so we have always two hours. Sometimes it can be useful to have even four hours (for example for presentations or mock exams), but normally more than two hours is too much. There is no need of a pause between the two hours. Thus students can go 10 minutes earlier.
10. Classes should be mixed from time to time, this means that students from different ages and classes will come together.
11. Parents, other teachers and external guests are always welcome to take a vivid part in the classes.
12. Also interesting guest presentations are welcome. The teacher should try to organise at least to guest presentations per term.
13. Cooperation with other math teachers and schools are more that welcome. At the end there should be a lively maths, teaching and learning community.
14. Visits and lectures outside the school are also very important.
15. The teacher and the students have to introduce theirselves, both written and oral. It is also very important to understand who knows already what. Also, how is the overall attitude towards mathematics and what the students really want to learn. The material should be interesting, useful and practical.
16. And last, but not least – students are taking an active part in the learning process.
Rhythm is everywhere and in everything. People also need rhythm, especially in education. That’s why it is so important to establish such a rhythm in the class.
I suggest the following rhythm for a two-hours-lesson:
– greeting per handshake
– morning saying / prayer / meditation / singing, for example this one:
Ich schaue in die Welt,
in der die Sonne leuchtet,
in der die Sterne funkeln,
in der die Steine lagern.
Die Pflanzen lebend wachsen,
die Tiere fühlend leben,
in der der Mensch beseelt
dem Geiste Wohnung gibt.
Ich schaue in die Seele,
die mir im Innern lebt,
der Gottesgeist, er webt
im Sonn- und Seelenlichte,
im Weltenraum da draußen,
in Seelentiefen drinnen.
Zu dir, o Gottes Geist,
will ich bittend mich wenden,
dass Kraft und Segen mir
zum Lernen und zur Arbeit
in meinem Innern wachse.
More than one is possible.
– a small lecture and discussion in an interesting topic, not necessary a maths one.
– some math assignments will be done in the head, for example mental arithmetic
– a student will make a review of the material from the last lesson(s)
– questions and discussions about the topic
– further teaching on the topic (this is the main maths part). May be through some experiments.
– some assignments for individual work.
– résumé of the lesson
– some possibilities for further exercise and reading
– short omen about the next lesson
– saying goodbye with a handshake