Pupils Digital Representation And Quantity Estimation Research

Numerical estimation is a kind of important mathematical cognitive ability, which refers toa kind of rough estimate about the number of objects in the conditions that you do not haveenough time to count, or the objects are too many to count, or the objects are moving so that youcan’t count. And the core of this kind of estimates is alternative representation, which mainlyincludes the logarithmic representation and linear representation. The way that one how tocharacterize the digital system directly affects the accuracy of his numerical estimation. People’sattention to estimates has gradually increased since the1970s to1980s. While, the home andabroad studies usually focus on computational estimation rather than on numerical estimation.What’s more, the study of whether the material’s colors affect the numerical estimation is stillblank in China. The existing theories think that the alternative representation greatly affectspeople’s numerical estimation, and the number line task is the most main method to study thealternative representation. In order to study whether the alternative representation affects thenumerical estimation, this research makes a within-subject design between the numericalestimation and the number line task. This is beneficial for us to have a further study about therelationship between the alternative representation and the numerical estimation ability.This research contains4experiments, and the1st experiment is a pre-experiment. The goalof this experiment is to determine the appropriate time of presenting target stimulus in formalexperiment. Thus, we can make sure that the testers are not making wild guess nor able to countthe objects in experiments, instead they can have an appropriate estimates about the targetstimulus, and make sure that the research is of reliability and validity. The rest three experimentsare the numerical estimation experiment, the number line experiment and the mixed experiment,which respectively investigate the elementary school students’ numerical estimation ability,alternative representation, and their numerical estimation abilities when they use different kindsof alternative representations.The results of the research show that:(1) From the perspective of the estimated accuracy ofthe number line task, we can see that the accuracy of the number line estimates is obviouslydifferent in different grades, and the higher the students’ grades are, the more accurate theyestimate.(2)The analysis of elementary school students’ alternative representation shows that thefive tested grades are all use linear representation mode. By further analysis of every tester’srepresentation mode, we can see that a half of grade2students are using logarithmicrepresentation mode, and the other are using linear representation mode. At last, through a wholeanalysis, the research shows that the proportion of the students who are using logarithmicrepresentation mode is decreasing, while the proportion of the students who are using linear representation mode is increasing. All the grade6students are using linear representationmode.(3) From the perspective of the accuracy of the numerical estimation, we can see that theaccuracy of the numerical estimation is obviously different in different grades of primary school,and the higher the students’ grades are, the more accurate they estimate.(4) The analysis of theco-relationship between the stimulus’ properties and the accuracy of the numerical estimationshows that the testers are tend to make more accurate numerical estimation when the colors ofthe target stimulus is different from those of the Interference stimulus.(5) The analysis of theaccuracy of primary school students’ point numerical estimation reveals that the grade2studentsare tend to make more accurate numerical estimation when they use linear representation moderather than use logarithmic representation mode.From the above, we can come to several conclusions:(1) The accuracy of the numericalestimation is obviously different in different grades of primary school, and the higher thestudents’ grades are, the more accurate they estimate.(2) Primary school students use both linearrepresentation mode and logarithmic representation mode. With the rise of their grades, thenumbers of the students who use linear representation mode are increasing, while those of thestudents who use logarithmic representation mode are decreasing.(3) The properties of thestimulus have a prominent influence on testers’ estimates accuracy. Testers tend to make moreaccurate numerical estimation when the colors of the target stimulus are different from that of theInterference stimulus.(4)Students in the same grade, who use linear representation mode aretend to make more accurate numerical estimation than those who use logarithmic representationmode.