Development for pre-service and in-service mathematics teacher training programs focusing on the process of thinking mathematically

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The aim of this research is to develop programs and materials focusing on the process of thinking mathematically in pre-service and in-service mathematics teacher training. For example, pre-service teachers had experiences of observing and writing down one child's mathematical activities through the video of mathematics class and interpreting them. By these programs they have become accurate in their records of children's activities in actual classroom observations. Then after actual classroom observations, they took the opportunities to discuss their interpretations of the children's activities each other. So they have understood the meanings of children's activities and have appreciated them.