| Mathematical ability is individual psychological character that the individualperform mathematical activities and his efficiency will be affected. The study onmathematical ability is an important project in the fields of mathematical educationand mathematical educational psychology. An impersonal scale to evaluate the pupil'smathematical abilities, to distinguish and screen the children with mathematicallearning disabilities, to remark the effect of mathematical education, or to judge therationality of the teaching content and course planning on mathematics is a necessary,and but there is not a recognized scale and its norms. Therefore, in order to provide animpersonal and feasible scale for the people who pursue mathematical education andmathematical educational psychology, the author introduced and edited the GermanyRating Scale of Pupil's Mathematics Abilities established by Heidelberg universitycollaborating with Heidelberg University and established the Chinese Rating Scale ofPupil's Mathematic Abilities (C-RSPMA) and its norms. To study the presentconditions of Chinese elementary education and to find out the differences of thepupil's mathematical abilities through the cross cultural study between China andGermany to offer scientific evidence for decision-making and enhancing Chinesemathematical elementary education, and to expose the influencing factors on thepupil's mathematical development so as to improve the condition for the developmentof children's mathematical abilities.According to the fifth national population census in China, 7377 and 7316students were selected randomly in urban and rural schools respectively from the 14provinces and areas adopting the multi-phase-stratified-cluster sampling method. Thereliability and validity of the rating scale were verified, the current status of pupil'smathematical development was studied by comparing the mathematical abilities ofprimary scholar from various sampling areas between China and Germany, and therelated factors affected the pupil's mathematical abilities were analyzed. The statisticsmethods employed included: The statistical description such as mean, standarddeviation, frequency and proportion, and the methods of statistical inferencesincluding t-test, analysis of variance, chi-square test, analysis of correlation and factoranalysis were adopted. A multi-ordinal-categories Logistic regression model wasemployed to analyze the influence-factors on the pupil's mathematical abilities.Results (1) The reliability indexes of the Chinese Rating Scale of Pupil's MathematicAbilities such as Chronbach's αcoefficients (α>0.7), split-half reliability coefficient(r=0.83) and the reliability coefficient of total revision (R=0.90), test-retest reliabilitycoefficients of the subtests were above 0.7, and the satisfactory validity indexes wereobtained including construct validity, content validity, criteria validity anddiscriminated validity. (2) The developmental level of children's mathematics was imbalance because ofthe differences of economical and cultural background. The mathematical abilities ofthe students from southwest area were lower than other areas. The differences weresignificant between male and female students, and the mathematical abilities of theboys were more excellent than that of the girls in the fields of math operation,spatial-visual functions and total score. (3) The differences between Chinese and Germanic children were that the mathoperation ability of Chinese students was more excellent, but there was preponderancein the field of spatial-visual functions. On the contrary, the scores of Chinese childrenin part subtests were lower than Germanic children. (4) The factors affected pupils'development on mathematic competences includethe self factors such as sex, activity, communication, language comprehension andpresentation, the family factors such as social status, family income, parent'seducational conception and family atmosphere et al, and the school factors such asteacher-student relationship, relation of schoolmates and learning burden et al. Basedon Logistic regression analysis, 6 related factors promoting the development ofmathematical abilities were identified as follows (ranked by contribution): democraticor strict family atmosphere, more satisfaction of parents on child's schoolwork,parents pay more attention to cultivating well learning custom, motivation andthinking, finer class environment and better achievement in schoolwork. 6 factorshampering the development were also distinguished as follows (ranked bycontribution): over-weighed learning burden, more activities, female student,watching TV overmuch and paying more attention to achievement.Discussion and Suggestion According to the current status reflecting Chinese pupils'mathematiccompetences and the results of cross-culture study between China and Germany, thesecommon problems have been found in Chinese elementary mathematic education. First, the teaching idea is out-dated. The students did not play a principal part,always received passively knowledge and were lack of active explorative inspirit. Second, the teaching contents were unilateral. Calculating abilities were overemphasized and the training was ignored on mathematic inferential capability,observation and abstract abilities and spatial-imagination. Third, the teaching thinking was parochial. The classifying of exercise type andtraining on special skill were laid the first place while the culture on teaching thoughtwas ignored. The difference between mathematic competency and skill was confused. Fourth, the teaching method is simple. The force-feed teaching was adopted andthe concepts were common that mathematic education was that pupils receivedpassively a lot of mathematic knowledge and owned some skills solving problem, andsuch students were taken for good pupils. Last but not the least, the students'learning burden was overweighed. The scoredominated the basic education, which leaded to that the textbooks were becomingdifficult and Chinese children were exigent, and that these have gone beyond majorstudents'current level in fact.
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