The Complex Journey of William Doll, Teacher Educator
1. A fractal is a mathematical set that displays a self-similar pattern across different scales. It is generated by running nonlinear equations of complex numbers, reiterated countless times through computer programs. French mathematician Benoȋt Mandelbrot coined the term “fractal” in the 1970s to describe the complexity of the irregular shapes in nature (Capra, 1996). Nowadays, fractals have become more popular mathematical and artistic images. Doll uses a fractal as a metaphor for curriculum to convey its complexity, richness, fluidity, and iterative beauty. See Chapter 4 of this book for more discussion. For more details, see Doll’s (2005) co-edited book, Chaos, Complexity, Curriculum, and Culture: A Conversation.
2. In almost every chapter, I introduce an episode from the video transcription of Doll and Trueit’s team teaching as an example of Doll’s pedagogical approach. In the transcription, I use the last names of Doll and Trueit and the first names of students, mainly because students were referred in class conversations by their first names. However, there was one exception. Fu is a Chinese student’s last name, not his first name, but I followed class members’ references to him as Fu in the conversation to make it easier for readers to recognize the name.←23 | 24→ ←24 | 25→
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