Research On Thinking Structure Of High School Students' Statistical Reasoning

Statistical reasoning is one of the statistical learning objectives which received internationally recognition. It has also been attention in the country's new curricula, but the research of statistics reasoning in China is still very small. I translate and card the study of statistical reasoning abroad first, including the definition, the correct and incorrect types and evaluation assessment of statistical reasoning, particularly the most extensive instrument SRA. In the process of carding the literature, I found that the current assessment for large-group evaluation didn't reveal the structure of different levels, so I worked out the"Questionnaire of statistical reasoning"with SOLO taxonomy and the SRA. Through the testing of 246 students of 5 high school in Beijing, and data analysis from the SOLO descriptive level and the Quantitative level of Rasch model, I draw the following conclusions:There are some incorrect types statistical reasoning of high school students. In the statistic, most high school students tend to not consider outliers when calculating mean, and mistaken the mean, median and mode. In the charts, they easily choose the wrong figures, and comprehend the charts from the visually intuitive. In the sampling method, they believe that good samples have to represent a high percentage of the population, groups can only be compared if they are the same size. In the reasoning of possibility, an intuitive model of probability that leads students to make yes or no decisions about single events rather than looking at the series of events. They believe that samples should resemble the populations from which they are sampled, which led them to use small samples for making inferences and generalizations about populations. Some students also have the equiprobability bias, and different outcomes of an experiment tend to be viewed as equally likely.In this study, high school students at different levels of statistical reasoning are described. High school students at the uni-stuctural level can not judge data types, they believe that correlation implies causation, and they vulnerable to the figures intuitive visual misleading. Students at the multi-structural level can calculate mean, consider outliners in easy situations, but in the use of the mode and the median circumstances, easily misuse the mean. In the description of the specific data, they may make inappropriate choice in several statistical figure. They don't only reason from the intuition, but seriously figures on the relations of number, arrive at a correct conclusion. They understand that probability is the possibility of the incident, but tend to believe that the incident with big probability should occur. They can estimate the possibility in simple cases, but in the experimental sequence, they estimate the possibility only depends on the similarity with the population. They can infer the possibility according to the sample frequency. They understand the importance of big sample, knowing to be skeptical of inferences made using small or biased samples. They understand the difference between correlation and causation. They don't understand the random sampling clearly, worrying that the result will be uneven because two groups are occasionally divided. Students at the Relational level can judge the possibility and impossibility of events of repeat sequence, and they have the initial awareness and concept of sample space. They understand the variability of sampling, sampling process, as well as the effect of big samples and small samples. They can infer that the small samples are more likely to breach the population characteristics.According to the findings above, the study discussed the recommendations of the statistics teaching: teachers should rectify the students'misconceptions while teaching; teaching should be concentrated on enhancing statistical reasoning level of thinking; teachers should give students as many opportunities as possible to experience statistical process; students are exposed to actual cases as far as possible.