High School Stuends' Understanding Of Measure Of Central Tendercy

According to the three tier theory of statistical literacy by Watson(1997)and the idea of statistical literacy of Lajoie, Jacobs, Lavigne (1995) and Gal (2002), this study proposed a three-level framework of high school students' understanding of measures of central tendency.Based on Watson's three-level theory on statistical literacy and also on the statistical literacy cognition of, this thesis divided senior students' comprehension about central tendency into three levels:The first level: students can compute using the formulas about measures of central tendency.The second level: under the real situation, students can use suitable measures of central tendency to deal with practical problems.The third level: under the real situation, students can reasonably explain or interpret their use of the measure of Central Tendency to deal with practical problems.In light of this framework, the thesis has four research questions: first, what is students' level in computation about average, mode and median? Second, in the real situation,, what is students' level to use average or mode or median to describe "average level" of a group of data? Third, in the actual background problems, what is students' level in interpret or explain their use of the measure of central tendency? Fourth, Is there any difference in students' understanding of measures of central Tendency in terms of grade, school and gender?The study selected 155 students from a key high school and 176 students from an ordinary high school in Shanghai. These students took a test on their understanding measure of Central Tendency and 11 of them were interviewed. The main findings of study are listed in the following.1. Almost all the students can give correct answer to the computation question.2. The majority of students can use suitable measures of central tendency to solve real world problem.3. Students can judge which measure of central tendency to use to, but they have difficult to explain why they choose this measure.4. Average was still students' "first choice" to describe average level of the data.5. As the difficult level of questions increase more and more students did not attempt the question.6. There are statistically differences in understanding of measures of central tendency between the key school and ordinary school. But there are no statistically differences in terms of gender and grade.At last, this thesis offered some teaching suggestions on the basis of research results:1. Teachers should change their attitudes, fully focus on the value of statistics education in real life, and lay stress on effective applications of statistical knowledge in Classroom Training.2. Teachers should highlight the relationships among the three measures of Central Tendency in classroom teaching.3. Because it was found that students had difficulty in explaining their uses of measures of Central Tendency, teachers should pay more attention to cultivate students' communication abilities (including writing communication and oral communication) in math.4. Teachers should pay attention to students' errors and misconceptions, and provide pertinent teaching activities to deal with these errors and misconceptions.