Difference Research Of Solving Math Problem By Constructing G.P. After Learning Single And Double Content Samples Material

Sample learning is an autonomous and efficient way of learning.It shows a state of learning that is more conductive to beginners by showing the entire solution process in the form of teaching.Single-content and double-content samples are new research fields that have emerged in recent years.Single-content samples are samples that contain only one learning content,and double-content samples include two domains(namely,learning domain and example domain).This study uses experiment,questionnaire,interview and textual analysis to solve the following problems: 1)From an objective perspective,using scores as a measurement index to survey the differences of learning geometric series and constructing geometric series to solve mathematical problems between students who using single content sample materials to study and the one who using double content sample materials to study.2)Using student-questionnaire constructed by three-dimensional(ability,psychology,behavior)to evaluate their mathematics self-study ability.Also using interview to further analyze the learning psychology of students,achieving the differences in the learning process between single and double content samples' learning;3)Interviewing high school mathematics teachers for understanding their experience of using single and double content samples to teach.The results show that: 1)There is no significant difference in the knowledge learning result between using the single-content and double-content sample materials,but the post-test scores of the student who use the double-content sample materials are higher than the one who use single-content sample materials to study.2)There is a significant difference in the mathematical thought learning result between student using the single-content and student using double-content sample materials.Measuring the ability of solving mathematical problems by constructing a geometric sequence,we found that the average score of single-content learners are higher than double-content learners.3)After learning through single and double content samples,boys' post-test scores of knowledge learning are higher than girls',but girls' post-test scores of mathematical thought learning are higher than boys'.4)High school students have good self-learning ability in mathematics;5)Double--content sample materials increase students' interest in learning and promote students' enthusiasm for learning mathematics.The following suggestions are made: 1)Auxiliary design of single and double content samples,combining dynamic and static,enriching the form of independent learning materials;2)Improve the effectivity of using samples to teach,giving full play to the subjective initiative of students;3)Teachers should be a good guide for students' learning from teaching,confusion,evaluation feedback and other aspects.