Research On Mathematical Problem-Posing Ability

Mathematical problem-posing ability is increasingly regarded as a significant mathematical ability,which is nowadays considered as part of Mathematical subject core ability or Mathematical literacy.The proportion it accounts for in Mathematics Curriculum Standards,a programmatic document on national education,is getting larger and larger,from occasional reference at first(1932?1936?1941),to "Four CANs"(2011),till the standard division of Six Mathematical Core Literacy in Subject Standard for Senior Mathematics(2017),here and there.Apart from this,Mathematical problem-posing ability is paid highly attention to outside China.To take US as an example,as early as 2000 the importance of Mathematical problemposing ability was stressed several times in Principles and Standards of School Mathematics.In a back ground where Mathematical core literacy is increasingly stressed,there is high necessity that more study should be done on Mathematical problem-posing ability.This paper focuses itself on the following three projects: One is the intention,formation as well as development of mathematical problem-posing ability,under the background of mathematical core literacy;Another is the analysis of the status quo of Shanghai Grade Eight and Grade Nine students' mathematical problem-posing,including the status quo of ability and attitude;The third is the analysis of the relationship between mathematical problem-posing ability and grade,mathematical problem-posing attitude as well as mathematical academic achievements.With regard to Project One,the content analysis is mainly applied while questionnaire and interviewing method are used regarding Project Two and the quantitative analysis method is used regarding Project Three.Test subjects are altogether 432 Grade Eight and Grade Ten students from six districts of Shanghai.The results of the study are as follows:(1)Mathematical problem-posing ability refers to that students can base themselves on mathematical experience so as to comprehend certain specific situation provided,positively and initiatively make careful observations and analysis of the messages under that situation from mathematical perspective and then pursue diligently and pose problems bravely so that meaningful and well-structured mathematical problems can be raised from the given situations before,during and after problems solving;(2)The students master a low level of mathematical problem-posing ability,mainly at Level One and Level Two and that students' mathematical problem-posing ability varies greatly in various situations,saying the better in free situation and semi-structured situation than in strctured situation;The whole mathematical problem-posing attitude of the students is ordinary.The students were positive towards problem posing cognition but not very positive towards the emotional experience and behavior disposition of mathematical problem-posing;(3)Students' mathematical problem-posing ability has nothing to do with mathematical problem-posing attitude,however,students' mathematical problem-posing ability is highly related to grades,Grade Ten students show better Mathematical problem-posing ability than Grade Eight students;the relationship between mathematical problem-posing ability and mathematics academic achievement of different grade students is not consistent,Grade Eight students' Mathematical problem-posing ability is highly associated with Mathematical academic achievements,while Grade Ten students' Mathematical problem-posing ability isn't relevant to Mathematical academic achievements.Based on the paper's study,the author suggests: 1)The evaluation and cultivation of Mathematical problem-posing ability can start from different situations,which can be more targeted and comprehensive and reasonable;2)The methods and strategies of Mathematical problem-posing should be imparted,leading the students to comprehend the value and interest of Mathematical problem-posing and bringing a positive emotional experience of Mathematical problem-posing to the students.