Study On The Progression Of Eighth Grade Students’ Learning Of Unary Quadratic Equations

Learning progression refers to the process in which students have a deep understanding of a core concept from shallow to deep over a period of time.In recent years,my country has also been continuously increasing the pace of reform.The curriculum standards have also continuously emphasized that students are the subject of learning and focus on the process of student-side cognitive development.In the evaluation,it is also emphasized that not only the results should be paid attention to,but also the evaluation should be turned to the process.The appearance of learning progression coincides with the reform concept in our country.As an important branch of the algebraic system,equations play an important role in linking the past and the next,and their importance is self-evident.Based on the cognition of learning progression and analysis of the content of the equation,the researcher chose the core concept of the quadratic equation of one variable in the equation as the research object.In order to understand the learning law of the quadratic equation of one variable on the student side,two problems were solved in this study:(1)What is the learning progression of eighth grade students’ quadratic equation with one variable?(2)What advice can the research results provide for curriculum,teaching,and evaluation?In order to solve the above two problems,this research has carried out the following tasks.The first step is to use the literature research method to analyze the textual analysis of the learning progression,the curriculum standard of the quadratic equation of one variable,and the textbooks of different versions to construct the hypothesis of the quadratic equation of one variable learning progression;Step 2:Develop measurement tools based on preliminary hypotheses learning progression,and using expert consultation methods to modify learning progression and preliminary measurement tools;Step 3: Selecting a number of students from Shanghai School X for pre-testing,And combined with the pre-test results to select some students for interview method,based on the interview results to modify the measurement tool;the fourth step: use the survey method to formally test 90 students of Shanghai X school,and use the Winsteps software to use the Rasch model to measure the data Analyze and revise hypothetical learning progression;Step 5: Provide suggestions on teaching,curriculum,and evaluation based on the results of empirical research.The study concluded that the quadratic equation of one variable is divided into 5levels,namely level 1: preliminary perception form,mechanical memory to find the root formula;level 2: preliminary grasp of concepts,three solutions;level 3: deep grasp of concepts,flexibility Use three kinds of solution methods,will use algebraic expressions to express specific situations;level 4 use equations to solve practical problems;level 5: form a knowledge system,experience thinking methods,and master the essence.It can be seen that the development of the three core themes does not proceed from concept to solution to application,but spirals upward.Based on the research results,suggestions are made for teaching materials,teaching,and evaluation:For the textbooks,researchers combined three versions of the textbooks to give suggestions.For example,the concept modules of the textbooks of the People’s Education Edition and Beijing Normal University version lack a comparison of the concepts of one-variable linear equations and one-variable quadratic equations;Beijing Normal University and China Normal University Edition textbooks should increase the involvement of the idea of descending order;Beijing Normal University textbooks should strengthen the establishment of the connection between the matching method and the perfect square formula;the textbooks of the People’s Education Edition and China Normal University should add the essence of the application of equations in the application modules The content of inquiry,pay attention to the intake of modeling ideas.For teaching,the researchers suggest that teachers should pay attention to the organization of review in teaching,and at the same time keep one’s eyes open the system and connection of knowledge,and to guide students to understand the formation process of knowledge,grasp the essence of knowledge,and permeate the thinking methods.For evaluation,evaluation methods can be added to promote the diversification of evaluation methods,and formative evaluation should also be emphasized in the process of focusing on evaluation results.