Magnitude Representation Of Fractions For Children Of Higher Grades In Primary School

Magnitude representation has been one of the focuses, which researches concentrate on, and making sense of magnitude representation of human beings can aid us a lot in numerical cognition and the process of studying maths. Researches have made use of all kinds of number line estimations to carry out researches on magnitude representation. Siegler and other researchers has conducted a series of researches on the 0-100 number line estimations and the 0-1000 number line estimation, which discovered children's magnitude representation on whole numbers. The findings before revealed individuals'magnitude representation on the 0-100 number line estimation and the 0-1000 number line estimation, and they shift from reliance on logarithmic representation to linear representation with age and numerical experience. The studies on magnitude representation before mainly included whole numbers, but magnitude representation includes not only the representation of whole numbers but also that of fractions. When the individuals are faced with a fraction, the magnitudes of the denominator and numerator-but not the magnitude of the fraction itself-are represented automatically, so fractions typically pose enormous difficulties for children and adults. In addition, there are few studies on magnitude representation of fractions; therefore, the present study has great significance.The article involves the following studies:Study 1 involves individual's magnitude representation for fractions on the 0-1 number line estimation, whose numerators are 1 or not 1.Study 2 inspects individual's magnitude representation for fractions on the 1/100-1/10 number line estimation, whose numerators are 1. To examine whether the scale has an effect on magnitude representation for fractions or not, we also use the data in study 1 (numerators are 1 on the 0-1 number lien estimation) in data processing.Study 3 is about feedback on 1/100-1/10 number line estimation of fractions, aiming to examine whether individual's representation of fractions will change after being given feedback.The findings indicated:(1) on 0-1 number line estimation, whether the numerator is 1 or not, the sixth graders followed a linear pattern. The freshman colleges mostly followed a linear pattern (except on position to number task, numerators are 1). Sixth graders made more error than the freshman colleges did. That is to say, sixth graders made more accurate estimation than the freshman colleges did. On PN task, individual's error for fractions whose numerators are not 1 is higher than that for fractions whose numerators are 1. That is to say, individual's made more accurate estimation for the fractions whose numerator is 1 than they made for the fractions whose numerator are not 1.(2) On 1/100-1/10 number line estimation, whether sixth graders or freshman colleges, they followed a logarithmic pattern on NP task and an exponential pattern on PN task. Whether NP task or PN task, individual made more error on 0-1 number line estimation than they did on 1/100-1/10 number line estimation. That is to say, individual made more accurate estimation on 0-1 number line estimation than they did on 1/100-1/10 number line estimation. College's error is smaller than sixth graders on 0-1 PN task, 1/100-1/10 NP task and PN task. That is to say, freshman collegers made more accurate estimation on 0-1 PN task, 1/100-1/10 NP task than sixth graders did.(3) After the individuals were given a feedback, their fractional representation and accuracy changed a little. For sixth graders, the logarithmic equation accounted for more than the linear one, and had significant differences before the feedback. But after the feedback, the two functions had no significant differences. For the freshman colleges, the representational function before and after had no significance. As for the accuracy of the estimation, the individual made more accurate estimation after the feedback. That is to say, the feedback helped a little.To sum up, the following conclusions were drawn:(1) On 0-1 number line estimation, regardless of the kind of the fraction, the sixth graders followed a linear pattern. The freshman colleges mostly followed a linear pattern (except on position to number task, numerators are 1). Sixth graders made more error than the freshman colleges. On position to number task, individual's error for fractions whose numerators are not 1 is higher than that for fractions whose numerators are 1.(2) On 1/100-1/10 number line estimation, whether sixth graders or freshman colleges, they followed a logarithmic pattern on number to position task and a exponential pattern on position to number task. Whether number to position task or position to number task, individual's error on 0-1 number line estimation is smaller than that on 1/100-1/10 number line estimation. Collier's error is smaller than sixth graders on 0-1 pn task, 1/100-1/10 np task and pn task.(3) After being given feedback, individual's fractional representation and accuracy changed a little. For sixth graders, the logarithmic equation accounted for more than the linear one, and had significant differences before feedback. But after feedback, the two functions had no differences. For collegers, the representational function before and after had no significance.