The Ability Of Fraction Concept Understanding And Its Prediction To Fraction Arithmetic For The Students In Grade Six, Seven And Eight

On the basis of the fraction concept and fraction arithmetic review of previous studies, the dissertationadopted the methods of literature, questionnaire, laboratory method and interview to investigate the abilityof fraction concept understanding and the differences of distribution number in different type fractions inthree levels with180students in Grade Six, Seven and Eight being used as subjects. What’s more, weexplore the forecast effect of fraction concept understanding ability to the different type and complexityfraction arithmetic result.The positivistic portion of the dissertation includes two studies: in study Ⅰ, we used a mixed designof three factors, i.e.3(grade: six, seven, eight)×2(school type: city, village)×3(fraction constitute form:proper fraction, improper fraction, mixed fraction) studied the fraction concept understanding ability of thestudents in Grade Six, Seven and Eight. In study Ⅱ, the fraction concept understanding ability’s predictingfunction to fraction arithmetic result was proved up.Findings were obtained as follows:(1) Fraction concept understanding ability of the students in Grade Six, Seven and Eight developedsignificantly with the grades rising, and the ability developed more quickly in Grade Seven. The fractionconcept understanding ability was very significant difference between the students of Grade Six to Seven,and was very significant difference between the students of Grade Six to Eight.(2) The fraction concept understanding ability was very significant difference between the students ofcity to village. The city students’ fraction concept understanding ability was higher than village students’fraction concept understanding ability.(3) The population of fraction concept understanding ability in the different forms in three levels isvery significant. The population in level3is the largest, and the population in level2is larger than thepopulation in level1. The students have the best fraction concept understanding ability in proper fraction,that of mixed fraction not better than it, and the improper fraction the weakest.(4) There was a remarkable correlation between fraction concept understanding ability and fractionarithmetic result. The students’ fraction concept understanding ability was very significant predictor for thefraction arithmetic result. The predictor rate of the students in city was higher than the students in village. (5) Students’ fraction concept understanding ability was very significant predictor for the differenttypes and complexity fraction arithmetic score. The explain rate of addition and subtraction fractionarithmetic was higher than multiplication and division; the explain rate of high complexity fractionarithmetic was higher.(6) Students’ fraction concept understanding ability was very significant predictor for the time of thedifferent types and complexity fraction arithmetic. The explain rate of addition and subtraction fractionarithmetic was higher than multiplication and division; the explain rate of low complexity fractionarithmetic was higher.