Research On Nonlinear Dynamics Models Of Individual Learning

It is essential to apply modern techniques to train creative talents. It is the new demands of the society on education. At present, a large number of scholars are committed to the research on teaching reforms. They have proposed new teaching modes such as cooperative learning, organizational learning and group learning. All these are based on individual learning. Therefore, it is significant and important for us to investigate individual learning rules to make full use of modern education thoughts and education modes to cultivate high quality innovative talents.This paper studies the inhibiting factor and the promoting factor impacting individual learning based on the existing logistic models of individual learning, establishes IKGM model (Individual Knowledge Growth Model) that is a nonlinear dynamic model for individual learning and able to describe the plateau phenomenon, and analyzes the stability and bifurcation of equilibrium point of the model. Besides IKGM model, this work also explores and proposes an improved IKGM model, with adding the impacting factor of forgetting ?.With respect to IKGM model, this paper explores the nonlinearity of individual learning, analyzes parameters influencing individual learning, and respectively explores the influence of each parameter on individual learning. The following conclusions were drawn:(1) the main impacting factors are:?(ratio of inhibiting factors and promoting factors) and d (teaching difficulties).The factor ? has a significant impact on individual learning, while d has smaller influence on individual learning; (2) x0(initial knowledge), ?(ratio of inhibiting factors and promoting factors), and d (teaching difficulties) jointly determine whether the plateau phenomenon occurs or not during individual learning, but it mainly depends on ? whether students could break through the plateau when the plateau phenomenon exists.What's more, this paper constructs an improved model of IKGM with adding the impacting factor of forgetting ?. By analyzing dynamic features of the model and comparing it with the IKGM with experiments, we draw the conclusion on how the ? influences the individual learning as follow:(1) when a (the promoting factor), c (the inhibiting factor), and ? (the forgetting factor) simultaneously influence individual learning, the decrease of ? decreases the amount of students' final knowledge. When students' initial knowledge is less than final knowledge, the larger ? is, the quicker the rate of students' knowledge decreases. When students' initial knowledge is more than final knowledge, the larger ? is, the slower the rate of students' knowledge increases; (2) when a=0 and c=0, the change curve of individual knowledge conforms to the Ebbinghaus forgetting curve, that is, the decrease rate of individual knowledge increases with ? increasing, which refers to the lost rate of individual knowledge increases. However, the amount of knowledge will eventually decrease to the same value. Therefore, the change of ? only influence the changing rate of individual knowledge. From these results, this paper suggest that teachers should pay more attention to students' learning states. They should also improve the knowledge levels of students by helping students adjust their emotional states by themselves, stimulating students' learning motivation, and helping students find appropriate learning methods, rather than completely rely on the patterns of teaching materials and teaching modes. Moreover, teachers should take teaching difficulties into consideration when they design the teaching. To help students to get a better learning effect, they should design appropriately difficulties.