Conceptual Understanding Of Standard Deviation Among First-year University Students From Mathematics Department

With the rapid development of information society, statistics has penetrated into various aspects of social life. Recently, more emphasis has been paid to statistics education nation-wide. However, compared to more mature statistics education research in western countries, relevant domestic research has just started. More research is needed in this field in China. The main purpose of this study is to investigate conceptual understanding of standard deviation among first-year university students from mathematics department and to explore their difficulties in understanding standard deviation. The results of this study are of benefit for the teaching of standard deviation.This study used qualitative and quantitative research methods, by collecting data through a test and interviews on standard deviation and analyzing the collected quantitative data with t-test and one-way ANOVA. The research questions of this study are:(1) What are first-year university students’ understanding of the mathematical and statistical meaning of standard deviation?(2) Can students compare the size of standard deviations in different representation mode of data and what are their comparing strategies?(3) Can students use standard deviation to make decision in real life context?(4) Is there any significant difference in students’ understanding of standard deviation with regard to gender, major and region?The results of the study are listed below.(1) The students have a good mastery of the mathematical and statistical meaning of standard deviation, but they do not have a deep understanding of the formula of standard deviation. Only a few students can describe the formula correctly.(2) These students’ conceptual understanding of standard deviation is weak, and their ability to synthesize various factors that affect the size of standard deviation is not good. It seems that they do not have enough effective strategies to compare the size of standard deviations. These students are influenced by the different representation mode of data when comparing the size of standard deviation. They perform worst in comparing the size of standard deviations among more than two histograms.(3) Most of the students consider and use standard deviation correctly in a decision-making task in real situation.(4) There is no statistically significant gender difference in the students’ understanding of standard deviation, but there are significant major differences and region differences. Students majored in mathematics teaching perform significantly worse than those majored in applied mathematics. Students from central part and eastern part of China perform significantly better than those from western part of China.Based on the findings of this study, suggestions for instruction and further study are provided in the end.