Savoir vs connaitre in Chinese and some thoughts on lingenierie didactique

The French near synonyms “savoir” and “connaître” cannot be distinguished in English, neither can the Chinese characters zhi (知) and shì (識). The author would like to discuss some mathematics educational thoughts developed recently in Taiwan with a French school of mathematics educators who have established, among other achievements, l'ingénierie didactique since 1980s. The Taiwanese ideas originated in 2013 in response to the needs of a guideline for the design of the literacy-oriented mathematics curriculum for the newly implemented 12-year compulsory education. Our key ideas are (1) think of mathematics as a language, (2) distinguish zhi and shì and the later one is crucial for literacy, and (3) the work and responsibility of an educator is more like an engineer than a scientist. Five years later, we realized that our thoughts might have been very similar to those well established by the Didactique scholars. Therefore, here we are to present our perspectives and to learn from the eminent colleagues.