“From the very first day the teacher must emphasize: What I want you to do is not just to answer correctly, but show that you are thinking,” says Yukiko Asami-Johansson, researcher at the University of Gävle.
The Japanese method accentuates the fact that learning will increase with the help of problem solving. That the teacher chooses problems that are appropriate for the lesson to be learned and then anticipates how the students will solve them.
The problem is presented, and the students think it through themselves, the teacher does not go through it with them initially. Let them guess, first individually and then in a group.
“In the Swedish model only the problem-solving ability is emphasized,” says Yukiko Asami-Johansson.
What is crucial is that the teacher plans the lessons moment by moment and creates appropriate problems. Using appropriate problems only now and again does not work. One has to plan everything from day one. In the first lesson then this problem is appropriate and at the next lesson that problem, and so on, the whole year.
“The actual problem is very important and must include:
“In Japan one does not do this work alone – one collaborates with other teachers and then it is much easier and more enjoyable.”
From the beginning the teacher must emphasize again and again: “What I want you to do when you solve the problem is to show how you have been thinking!” So that the students realise that the making of an estimate leads on to rational thinking.
“And besides, if one has estimated an answer, one wants to know if one is right or wrong, and each problem leads to the next key problem. One achieves a completely different attitude to tackling problems.”
If one observes a Japanese teacher in a lesson there is a lot of acting.
The teacher pretends the whole time that he is no authority. “Oh, is that what you think…” “Is it true…?” “But look, this seems to work…”
“One plays down one’s own knowledge in order to allow the students to discuss the solutions among themselves.”
Because the method requires of the teacher that they understand which method the student is really using, this also makes demands on the teacher.
“Unfortunately what happens here with us is that, perhaps mainly in the lower grades, teachers that do not really want to teach mathematics are forced to do so.
Then the teacher does not have much motivation to investigate the different methods one can use to reach a certain goal.
If Kalle has his own ingenious method, that the teacher does not understand, perhaps he/she will force Kalle to discard his method. “No Kalle, I think you should use my method.” And then one kills the joy of solving mathematical problems.”
In Japan the teachers are forced to do a so called “Open lesson”. They plan a lesson together and then one teacher uses it in a class and the other teachers observe.
Even teachers from other schools in Japan can come and observe.
Then, after the lesson one discusses what worked well and what didn’t work well. Afterwards the lesson plan is rewritten by the group of teachers and then used again in another class.
“Then one discusses that lesson, it is a cyclical process. And one becomes a better teacher and it is fun. Japanese mathematics teachers have their own network so there is a large social element too.”
Yukiko Asami-Johansson has been a teacher of mathematics at the upper secondary level and is now a researcher lecturing future teachers at the University of Gävle.
“I have myself used this method and seen the potential and possibilities. What I am trying to convey to my teaching students is that they should learn this method and cooperate with other teachers.
I want to try and show them that this is not something that perhaps only works in Japan, or in a certain classroom, but it works all over the world because it is universal.”
The plan is to do a PhD on this topic, on how Japanese teachers use the Japanese model and Swedish teachers use their model with practical mathematics lessons.
Yukiko collaborated with a teacher when she did her study. The teacher learnt the whole method and they planned all the assignments.
“She thought through the students’ possible problem-solving approaches. If someone comes up with such and such an answer, how should I react? She planned every lesson in detail, which was vital.”
When Yukiko later interviewed the students they said it was such fun to think about problems. “Mathematics is now my favourite subject because I realised the lessons are not just about getting correct answers, but about thinking, and that is fun.”
“To be successful with this method social norms in the classroom are very important. The students must feel confident about expressing themselves.
If you don’t feel confident in the classroom, if someone should laugh at you or react negatively to your thoughts, then one gives up.”
These strategies for solving problems have been attributed to the Hungarian mathematician George Pólya.
His book, written in 1945, about actual problem-solving - “How to solve it” - has sold over a million copies. Pólya’s hypothesis was: "Learning is letting the students think for themselves, to estimate first..."
“Many countries throughout the world have adopted these ideas, Japan is one of them,” concludes Yukiko.
For further information, please contact:
Yukiko Asami-Johansson, researcher at the University of Gävle
Tel: 026-64 87 87
Text: Douglas Öhrbom