A Quantitative Measurement Of The Difficulty Of Mathematical Examination Questions And Its Application

At present,there is no perfect theoretical basis for the study on the difficulty of mathematical examination questions,but its research has a strong practical value.There are roughly two kinds of methods for the study on the difficulty of mathematical examination questions: post-definition and pre-definition.The former uses the measurement of pass rate,which focuses on checking the learning ability of students,while ignoring the difficulty of examination questions themselves,and the later is not mature.The quantitative measurement proposed in this paper belongs to the type of pre-definitions.The purpose of this paper is threefold: The first is to improve the effectiveness of the mathematical examination questions.By studying the factors influencing on the difficulty of mathematical examination questions and its corresponding quantitative measurement,the question settler can grasp key points of examination and make the difficulty of the examination questions to be proper.The second is to guide teachers' teaching behavior correctly.A better analysis of difficulty of mathematical examination questions will standardize teachers' teaching of concepts,methods and their relationships to arrive at enhancing the quality of teaching.The third is to motivate students to improve their learning methods and enhancing their learning efficiency.If the students grasp the factors that affect the difficulty of the mathematical examination questions,they will be urged to pay attention to the concepts,methods,and relationship among them,i.e.,the mind map of mathematical knowledge being learned.The drawing of the corresponding mind map of the learned knowledge will impel students to understand much more precisely the concepts,methods and their relationship,help them to grasp knowledge and cope with various types of examinations and raise test scores.We read some literatures on the “difficulty of examination questions” to prepare for our research.Finally,a correlation analysis by SPSS 21.0 between the method of traditional pass rate and that of the quantitative measurement of the difficulty of mathematical examination questions proposed in this paper was given.The results show that the method proposed in this paper has some positive advantages.The structure of this paper is as follows: The first chapter mainly introduces the background,purpose,methods,domestic and abroad statuses of this research,and the innovation of this paper.The second chapter introduces the mind map of high school mathematical knowledge.The third chapter introduces the concept of the difficulty of the existing examination questions and its measurements,analyzes their merits and faults,and proposes the concept of difficulty of a single examination question and a set of examination questions based on mind map,respectively.The fourth chapter introduces a quantitative measurement of the difficulty of the examination questions,which taking the factor of human intelligence into account.Chapter 5 shows the application of the quantitative measurement to the specific examples.The results show the effectiveness of the measurement proposed finally.