The Study On Teaching And Learning Of Statistics Concepts Based On The History Of Mathematics

With the implement of new curriculum, statistics teaching and learning has an important position in the primary and secondary schools, and has attracted people’s attention. In recent years, the development of HPM is burgeoning, and create the necessary conditions for history of mathematics integrate into mathematics teaching and learning. It is feasible and is of great significance that the history of mathematics integrate into teaching and learning of statistics concepts.This study presented an experiment research that the history of mathematics integrated into teaching and learning of statistics concepts such as mean, median and mode. We used the methods of pretest and posttest in the single group in the eighth grade. We put forward a triangle trigon model of teaching and learning based on the teaching of the history of mathematics, in which the history of mathematics activity is the center, and teachers, students and mathematics content formed a trinity in order to explore the classroom teaching, students’ cognitive process and teacher’s professional development. The research object is two teachers and their students in two classes in a good secondary school in a city of western region.According to the genetic "moments" in the history of mathematics, this study designed the activities on the history of mathematics and combined with the teaching content, and put into practice. On quantitative research, the students’ understanding level of the statistics concepts was divided into original meaning, choose to use, and problem-solving. On qualitative research, the students’ cognitive level is divided into six levels, that is: unistructural level (U), multistructural level (M), transitional level (T), relational level (R), application in one complex task (A1), and application in two complex task (A2). We measured students’ understanding level of statistics concepts before and after the experiment, and selected six students as cases in order to explore their cognitive development. We used hermeneutic circles model to explain teacher’s professional development and investigate their "statistical knowledge for teaching"(SKT) through listening to the teacher in class and interview them.The following conclusions can be found in the study:(1) there were3approaches to design activities of the history of mathematics, i.e., addition, duplication, and accommodation approaches, in which the most amount of them was accommodation approaches. These activities were of correspondence with the history of mathematics, activity background for more personal and public common sense. Most of the students agreed that the instruction in their class was different from their past mathematics instruction, and supported to use the history of mathematics in mathematics instruction, and preferred to take a mathematics course that integrated into the history of mathematics in the future.(2) The result of quantitative analysis of showed that the history of mathematics integrated into statistics concepts instruction could enhance students’understanding on statistical concepts. From the point of understanding level, the two class students existed significant differences in the original meaning, choose to use, and problem-solving. From the point of learning content, students existed significant differences on understanding of median, but not significant differences on the understanding of the mean. Through case studies of six students showed that five of the six participants notably strengthened their understanding of statistics concepts. One moved an entire cognitive level, and another one did little growth. The result come from the changes in students understanding demonstrated that historical integration in the class is important for some students to move from one level of understanding to another.(3) After HPM involved in instruction, two teachers changed from single hermeneutic circle to double ones on integration of the history of mathematics. A teacher could better understand the teaching subject knowledge on history of mathematics, but too much pay attention to the orientation of the history of mathematics, and the connection of PCK was not quite close together so that the integration of the history of mathematics was mechanical, not natural. While another teacher used her PCK advantages, pay attention to combine mathematical history with textbooks and students’cognitive so that her could smoothly integrate the history of mathematics into mathematics instruction. Teachers’statistical knowledge for teaching (SKT) had improved. Missed opportunities of knowledge were further explored in the stimulated recalled discussions, which could impact negatively on the learning opportunities for students. It needed to pay attention to promote teachers’ professional development.According to the conclusion, we put forward some suggestions on instruction of statistical concepts:(1) We should rich classroom instruction by means of mathematical history activities so that students could obtain a wide range of mathematical fundamental activity experience;(2) We should improve the students’cognitive level on statistical concepts through mathematical history activities;(3) We should design and practice mathematical history activities in order to improve teachers’professional development.