Elements of Difficulty Level in Mathematics* - Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing - page 90

summations of the activity of individual components), and typically exhibits hier-
archical self-organization under selective pressures. (Joslyn and Rocha 2000)
Complexity subtending system has 2 types. These are “disorganized complexi-
ty” and “Organized complexity” (weaver 1948). Characteristic of disorganized
complexity is a number of variables, and characteristic of organized complexity is
emergence.
In this research, we categorized elements of difficulty level in mathematics 10
types. So, this is not “disorganized complexity” if our research is true. On the
other hand, we can't conclude about existence of emergence.
Robert et al. found out that “Microslips”, fluctuation of moving for ungraspable
consciously, is caused about one time a minute (Robert et al. 1990). If microslips
have an impact difficulty level in mathematics, it can be complex system.
In this research, we cannot conclude whether complex system or not. In the
future, we hope to research this theme.
5.2 Lack of Understanding
Hill et al. assembled various researches that effective teachers have unique
knowledge of students' mathematical ideas and thinking, and they called assem-
bled researches “Mathematical Knowledge for Teaching (MKT)” (Hill et al.
2008). Fig.5 shows MKT model. MKT model build for teachers and this research
build for learners.
Fig. 5 Mathematical Knowledge for Teaching (Hill et al. 2008)