A General Framework and Theoretical References -- The Chinese Written Language as Tool for a Possible Historical and Epistemological Reflections on the Mathematics and the Impact of Teaching/Learning of Mathematics -- The Meta-rules between Natural Language and History of Mathematics -- Common Sense and Fuzzy Logic -- The Experimental Epistemology as a Tool to Observe and Preview Teaching/Learning Phenomena -- Strategy and Tactics in the Chinese and European Culture: Chess and Weich’i -- Rhythm and Natural Language in the Chinese and European Culture -- Conclusions.

The book provides strong evidence that research on the cognitive processes from arithmetic thought to algebraic thought should take into consideration the socio-cultural context. It is an important contribution to the literature on linguistic structure in comparative studies related to Chinese student mathematics learning. This book not only makes a great contribution to research in mathematics education, the findings of this study also addressed insightful approaches and thoughts of understanding the development of algebraic thinking in cultural contexts for classroom teachers. Using written Chinese language from different theoretical references provided wonderful approaches for understanding student algebra cognitive development in a different way and calls educators for to pay special attention to an epistemological and linguistic view of algebraic development. The findings inform classroom teachers that the cultural context plays an important role in student learning mathematics. A typical analysis of the cognitive dimension involved in some in the historical and cultural contexts is a great resource for classroom teachers. I really enjoyed reading this book and learned a lot from its compelling analysis. Shuhua An, Associate Professor and Director of Graduate Program in Mathematics Education, California State University, Long Beach .