Performance Of Grade 11 Students' Problem Posing And Their Understanding Of Probability Knowledge In Probability Contexts

In recent years,probability literacy has received increasing attention,which is one of the key points and difficulties in teaching mathematics in primary and secondary schools throughout the basic education in China.With the deepening of the new curriculum reform,the content of "probability and statistics" in the high school mathematics curriculum has been changing.A lot of research and teaching practices show that students' knowledge of probability is not satisfactory compared with other mathematics contents.Therefore,it is important to assess students' understanding of probability to improve the quality of probability teaching in primary and secondary schools.Also,the role of problem posing in diagnosing and assessing mathematical understanding has received more attention.Therefore,this study investigates the performance of Grade 11 students in problem posing in probability contexts and analyzes their understanding of probability knowledge by using problem posing as a grip.A total of 175 Grade 11 students from J High School in Shanghai participated in this study,and three problem posing tasks in probability contexts were used.In general,this paper aims to address the following three research questions.(1)Given probability contexts,how specifically do the Grade 11 students perform in posing mathematical problems?(2)From the probability problems posed by students,how do the Grade 11 students understand probability knowledge?(3)What is the relationship between the performance of Grade 11 students' problem posing and their level of understanding of probability in the probability contexts?It is found that the Grade 11 students are able to pose a large number of reasonable mathematical problems.However,compared with other mathematical topics,students' problem-posing performance in probability contexts is more general.In terms of the content,students tend to pose problems about probability calculations.In addition,there are sample space problems,probability comparison problems,probability distribution problems,conditional probability problems and so on.The students also show potential for cognitive understanding of the deeper content of probability.In terms of understanding level,most students can put forward reasonable probability questions on at least one aspect and give U-level responses.In addition,some students are also able to give R-level and E-level responses,indicating that this group of students can actively make connections between knowledge within probability,and between knowledge of probability and knowledge of other mathematical domains.Based on the above findings,we put forward some suggestions for the teaching of probability.Firstly,problem-posing tasks can be used to assess students' mathematical understanding levels to provide a basis for classroom instruction.Secondly,teachers should pay attention to improving students' problem-posing skills in daily instruction.At the same time,the problems posed by students can be reasonably used for teaching to resolve teaching difficulties and enhance students' classroom engagement.Finally,teachers need to be good at identifying and making use of students' cognitive potential to improve their cognitive levels and probability literacy in a targeted manner.