Research On Middle And Primary School Student's Cognition Level To Statistics

Since the seventies of twenty century, the research on the probability and statistics hasbecome the hotspots of western scholars. In studying of students' cognition to probability andstatistics, both psychologists and mathematical educators were focus on the mistake cognitionand reasoning of the probability and statistics. From the beginning of 1980's, in the globalextent, 'the elementary knowledge of statistics and probability' as a part of mathematicalliteracy was absorbed into the curriculum of primary school, middle school and senior highschool. The curriculum reformations of Australia, America and New Zealand advise thatstudents should begin to study the probability and statistics in the earlier school education.But statistics only has ten years history in the curriculum of middle and primary school;evenmany countries just start the statistics education. While in our country the statistics wasabsorbed into middle and primary schools' mathematical curriculum not longer than fiveyears so that there is no enough research on the middle and primary schools' statisticseducation. Which caused the passive situation that educational research was not keep up withthe curriculum reformation. Generally speaking, inside and outside scholars' research, on themiddle and primary school students' cognizing the statistics, their concept of statistics,whether there are some differences between the middle and primary school students whostudied and did not studied the statistics, is always relatively unsubstantial.Therefore, my thesis will make the systematic experimental study around the mainsubject of the middle and primary school students' cognition level. The specific aims of myexperiment are following:Firstly, to explore the statistics cognition development of the students from grade one tograde eight;Secondly, to discuss whether there are some differences in the statistics cognitionbetween the students who studied statistics and those did not;Thirdly, to analyze the origin ofdifferences. I will set the middle and primary school students as the subjects and make fourseries of studying: uncertainty, chance, sample and data analyzing.To sum, the characteristic and main conclusions of my thesis are following: Firstly, thestudent could understand some knowledge of uncertainty if some knowledge of uncertaintywas not taught;the student can't understand it if they are not taught. Research shows, thereare remarkable differences in the level of recognition of representing all probable outcomes ofsimple or complicated matter between the students from grade one to grade eight who studiedthe statistics and those did not. From grade one to grade five the students, who studied thestatistics or those did not, nearly could not recognize the uncertainty in the view of ratio. Thestudents of grade seven and grade eight, who studied the statistics or those did not, couldrecognize the certainty from the angle of ratio, but their understanding level differs evidently.But primary and middle school students can recognize which phenomena are certain, whichone is uncertain. Secondly, the students don't understand knowledge of chance until theknowledge of chance was taught. Research shows, the students from grade one to grade eight,who studied the statistics and did not study, have distinct differences in the level ofunderstanding the chance. From grade one to grade five the students, who studied thestatistics or those did not, nearly could not comparative chance in the view of ratio. Thestudents of grade seven and grade eight, who studied the statistics or those did not, couldcomparative chance from the angle of ratio, but their understanding level differs evidently.Thirdly, the students don't understand knowledge of sample until the knowledge of samplewas taught. The students of grade one and grade two, whether they studied knowledge ofstatistics or not, don't understand knowledge of sample. The students from grade three tograde eight, whether they studied knowledge of statistics or not, have the elementary thoughtof stratified sampling(not random). Research shows, from grade one to grade four the students,who studied the statistics or those did not, have no difference in the level of understanding thesamples. The students of grade one and grade two, who studied statistics or those did not, arelimited to the population in understanding the samples and they do not understand the relationbetween population and sample. About forty percent of students from grade three to gradefive and about fifty percent of students from grade six to grade eight, who did not studystatistics, have the elementary thought of sampling. Fourthly, primary school students couldnot analyze data, but middle school students who studied the statistics can use simple statisticto analyze data. Research shows, from grade one to grade six the students, who studied orthose did not, have no difference in the level of understanding the data analyzing. While thestudents from grade seven to grade eight, who both have studied and have not studiedstatistics, differ greatly in the level of understanding the data analyzing. Fifthly, the studentsfrom grade one to grade two, who have studied statistics, are nearly the same in the level ofunderstanding statistics. The students of grade three are superior to the students of grade oneand two in the level of understanding statistics. Research shows, the students from grade twoto grade three, who have studied statistics, have great differences in the level of understandingstatistics. The students of grade three are superior to the students of grade two in the level ofunderstanding the chance, sample and population, sampling as well as data analyzing.For the limit of experimental condition and time, the deepness and extent of middle andprimary school students' statistics cognition and the essential origin of different cognitionsshould be studied and discussed further in the future.