Research On Project-based Learning Design Of High School Mathematics To Promote Deep Understanding

With the accelerated aging of knowledge in the information society,cultivating core competencies has become an important issue in the field of education.The "General High School Mathematics Curriculum Standard(2017 Edition)" strengthens the key value of mathematical thinking,key abilities and mathematical character,and the new college entrance examination mathematics proposition gradually reflects the characteristics of comprehensiveness,openness and application.As an efficient learning method,project-based learning is in line with the new curriculum reform and the new college entrance examination mathematics reform and proposition trend.However,the current project-based learning practice has bottlenecks such as formalization and shallow-levelization,and lacks attention to the coherence and consistency of objectives,content,process,and evaluation.It is undoubtedly the main factor that hinders project-based learning to realize the cultivation of core literacy.Deep understanding is a kind of deep learning that takes understanding as goal orientation,adopts methods and strategies to promote understanding,and takes understanding as representation.Therefore,taking deep understanding as the conceptual goal of project-based learning can provide feasible ideas for breaking the bottleneck of project-based learning practice.This research aims to solve the core question of "how to design project-based learning that promotes deep understanding to achieve deep learning in high school mathematics".It is subdivided into four sub-questions:(1)What is the connotation of project-based learning for deep understanding?(2)What is the high school mathematics project-based learning design framework that promotes deep understanding?(3)How to design high school mathematics project-based learning activities based on the above framework?(4)How effective is the application of high school mathematics project-based learning activities that promote deep understanding?Based on the review of literature and theoretical research,it is believed that project-based learning is the learning of core subject knowledge and ability in the process of completing real projects.Deep understanding gives project-based learning a new connotation,which can provide clear target orientation for project-based learning,provide a strong grasp for the project development process,and provide measurement standards for project evaluation.Conversely,project-based learning can provide ways and methods for deep understanding.Therefore,the study proposes that the project-based learning of deep understanding is proposed to promote learners to deeply understand the key concepts of disciplines and form core competencies in the process of doing projects by creating real social situations and being problem-led and taskdriven,and finally produce learning results that can show the depth of understanding.This answers the first research question.Comprehensive consideration of the high school mathematics subject knowledge content of abstractness,the rigor of logical reasoning,mathematics application of the universality of the domain characteristics,based on the six key links of comprehension learning,with the four general elements of project-based learning content,activities,situations and results as the benchmarks,combined with the practical dilemma of the two roles of teachers and learners in the current high school mathematics project-based learning teaching practice,and from the perspective of innovative combination of theory and practice,a project-based learning design framework for high school mathematics that promotes deep understanding is constructed.Specifically including six design strategies:(1)focus on the core concepts of the mathematics unit and determine the level of understanding goals;(2)correlate real social topics and create mathematical problem situations;(3)build an understanding learning environment and provide a mathematical learning scaffold;(4)derivative Problems are tasked,and project-based learning activities are organized;(5)produce multiple project results,externalize the depth of understanding;(6)collect evidence of understanding process,support continuous evaluation,and clarify around the design strategy specific design content.Taking 48 students from an experimental middle school in Northeast China as the research object,the application advantages of the information-based learning environment are fully utilized,and the interactive electronic whiteboard and learning tablet are used to construct the effective link between the physical environment and the network environment and integrate a variety of digital learning tools.Using design-based research ideas and methods,three rounds of project-based learning design and practice were carried out,and the specific design content corresponding to the design strategy was improved and optimized.Finally,a high school mathematics project-based learning design framework that can effectively promote deep understanding was formed,and the design framework responds to the second research question.In order to effectively guide classroom teaching practice and implement the above design strategies,the practice path formed after three rounds of iterative revisions responds to the third research question.In order to explore the application effect of the design and practice of the three rounds of project-based learning activities,the application effect analysis framework is constructed from three dimensions of cognition,interpersonal dimension and self-dimension,and the three dimensions are in line with the core literacy.Based on in-depth analysis of empirical data,high school mathematics project-based learning from the perspective of deep understanding can significantly improve the effectiveness of deep learning,and it will gradually deepen with the advancement of activities.It is embodied in:(1)The level of knowledge understanding is significantly improved,and the depth level of knowledge understanding increases more significantly;(2)The level of mathematical thinking is developed and gradually shows the characteristics of rigorous and complex cognitive structure;(3)Group inquiry gradually breaks the pattern of single and independent,and presents a trend of balanced and networked interaction;(4)Learners present a more positive and in-depth learning state,which plays a positive role in improving learners’ drive and learning initiative.This answers the fourth research question.Due to the limitation of time and practical environment,this research still has certain limitations.The three rounds of iterative activities lasted for a short period of nine weeks,and the learners faced greater academic pressure,which led to limited investment,etc.Subsequent research can extend the length of the project-based learning,design a more comprehensive and more challenging high school mathematics project learning,further improve the design framework through more rounds of project-based learning design and practice,continue to track the process and results of high school mathematics project-based learning that represents deep understanding,and dig and analyze in depth.In general,this study provides a new perspective of deep understanding for the effective development of high school mathematics project-based learning,so as to maximize the advantages of project-based learning.It emphasizes the theoretical guidance of deep understanding from three aspects of goal,process and evaluation to high school mathematics project-based learning design.The project-based learning design framework of senior high school mathematics that promotes deep understanding has been constructed and achieved significant application effect.The learners can maintain the emotional state of deep learning,promote mathematics learners to achieve deep understanding of knowledge,enhance mathematical thinking ability,improve mathematical expression ability.The above results have achieved the research purpose of this study.At the same time,it shows the improvement of testtaking ability,which provides a strong guarantee for high school mathematics learners who are responding to the new curriculum reform and the new college entrance examination.