The Transformation Effects Of The4^th Grade Pupil’s Learning Of Fractional Four Fundamental Operations Of Arithmetic And Proportion Operation By Worked-examples Learning

According to the theory about worked-examples learning of the mathematics operationrules, the pupils derived the new operational rules of mathematics by the mathematicaloperational worked example to be designed elaborately and them had possessed themathematical operational rules. Furthermore, the theory considered that designing the keystep in the mathematical operational worked examples were the key that the mathematicaloperational worked example learning. How to solve the key step in learning the mathematicaloperational worked examples? The theory deemed that the key step could be divided intoseveral simple steps. This method was termed as “the method of resolved”(Zhang Qi etal,2012).It ’s really sure? So we tested and verified the theory and the method by threeexperiments as below.In the experiment1,604th grade pupils after a pre-test screening were divided twogroups randomly and each group30subjects learned one kind of the worked-examples for8minutes. First kind of the worked-examples were8fractional addition and subtractionoperation worked-examples designed by “the method of resolved”. Second kind of theworked-examples were8ordinary fractional addition and subtraction operationworked-examples. After the worked-examples learning, all the subjects were tested bytransformation test that were made up of8fractional addition and subtraction operationproblems.In the experiment2,904th grade pupils after a pre-test screening were divided threegroups randomly and each group30subjects learned one kind of the worked-examples for8minutes. First kind of the worked-examples were8fractional multiplication and divisionoperation worked-examples designed by “the method of resolved and labeled”. Second kindof the worked-examples were8fractional multiplication and division operationworked-examples designed by “the method of resolved” and third kind of theworked-examples were8ordinary fractional multiplication and division operationworked-examples. After the worked-examples learning, all the subjects were tested bytransformation test that were made up of8fractional multiplication and division operationproblems. In the experiment3,30subjects of the first group came from other304th grade pupilsthat not joined both the experiment1and the experiment2,30subjects of the second groupcame from the experiment1and30subject of the third group came from the experiment2.They all learned the same4proportion operation worked-examples for16minis and then theywere tested by transformation test that were made up of4proportion operation problems.The results are the following:(1) Experiment1showed that all the subjects could putfractional addition and subtraction operation to use in differently degree, but the achievementsof the first group were better than the second group significantly by the results of thetransformation test.(2) Experiment2showed that all the subjects could put fractionalmultiplication and division operation to use in differently degree, but the achievements of thefirst group and the second group were all better than the third group significantly by theresults of the transformation test.(3) Experiment3showed that the achievements of the thirdgroup and the second group were all better than the first group significantly by the results ofthe transformation test.The conclusion derived from this study was that the effectiveness of worked-examplesdesigned by “the method of resolved” was verified, and the experimental results supported thetheory about worked-examples learning of the mathematics operation rules.