Teaching Research On Geometric Progression From The Perspective Of HPM

As an important part of the teaching of high school series,the newly revised curriculum standards require students to explore and be able to master the definition,nature,understanding and application of the formula of the series,so as to help students understand the knowledge structure of the series more perfectly,provide an important guarantee for solving the corresponding mathematical problems and applying them in life practice,and widely involve practical applications in real life such as calculating savings interest and biological occurrence laws.Moreover,the mathematical ideas and methods such as analogy,reduction,classification discussion,special to general and equation permeated in the derivation process of the summation formula of the isometric sequence are widely used by students in their future learning and life,and are also mathematical education for students’ emotional values.The teaching integration of the history of mathematics itself is to guide students to open the inquiry of mathematical knowledge from a new perspective,in fact,in our textbooks and many application topics,it has appeared many times in the background of mathematical culture,but we often give it to students as reading materials.It is worth noting that when we integrate the history of mathematics into classroom teaching,students through personal exploration and practice of applying the research ideas of mathematicians in history,truly carry out teaching and research from the perspective of students,more follow the cognitive laws of students’ knowledge development,integrate into the life of the mathematics classroom,students’ enthusiasm for learning mathematics is more excited,and the ability to solve problems is naturally integrated in practice,so that creativity can also be improved.From the perspective of HPM,this paper analyzes the development history of equal ratio series and their summation formulas,and considers the relevant requirements of equal ratio series in the curriculum standards,and conducts action research on the teaching of summation formulas of equal ratio series and equal ratio series respectively.During the implementation of the research,the literature was consulted,the interactive inquiry between teachers and students in the classroom practice,the design of student and teacher questionnaires,and the corresponding teaching reflection,mainly focused on the following issues:(1)What do students think about the integration of the history of mathematics into the classroom? Is classroom inquiry similar to the development of historical equiproportional sequences?(2)What is the impact of teaching of equal ratio series from the perspective of HPM on students’ understanding of knowledge structure and emotional attitudes?(3)What is the impact of teaching of equal ratio series on teachers’ professional growth and development from the perspective of HPM?After classroom practice research,through the corresponding data collation and analysis of questionnaires and interview records,the following conclusions were drawn: the classroom atmosphere after the teaching of the history of mathematics is strong,which can stimulate the source of students’ learning,and the integration of the history of mathematics into the classroom teaching students are very much looking forward to it,students feel very vivid about the integration of the history of mathematics into the classroom teaching,which can help them effectively overcome the fear of learning mathematics,and the students feel that the integration of the history of mathematics into the new course is very innovative and practical.At the same time,the confusion encountered in the process of inquiry coincides with the problems of predecessors thinking about development many times in history,which further reflects the similarity between the students’ inquiry process and the development of the historical superior ratio series.In the teaching of equal ratio series effectively integrate the history of mathematics,students have personally experienced the evolution of the history of equal ratio series,and a variety of derivation methods are a step-by-step process with the development of history,which is carried out on the recent development area of students’ cognition.So that students can truly understand the "source" and "flow" in the teaching of equal ratio series,make full use of the knowledge of equal ratio series in the process of derivation and research,and deepen their learning and understanding of knowledge,and greatly improve their creativity.From the perspective of HPM,the classroom teaching of equal ratio series is carried out,following the law of students’ cognitive development,experiencing the development process of mathematical knowledge,using vivid and interesting practical life problems in history,exploring the general terms and summation formulas of equal ratio series from special to general,helping students construct the context of knowledge,establish confidence in learning,stimulate enthusiasm for mathematical inquiry,help students overcome the fear of difficulties in the original modeling process,constantly break through themselves in thinking about problems,and cultivate their spirit of courage to explore and face difficulties.In terms of teachers’ professional growth,the integration of the history of mathematics into teaching can deepen teachers’ understanding of the nature of mathematics,expand their mathematical horizons,and continuously improve their practical ability to apply teaching,and develop the effectiveness of teaching.In personally experiencing the process of mathematicians exploring problems in history,stimulating our enthusiasm and confidence in research,mathematics comes from life,teachers can also find problems in the process of practice,find the connection between related quantities behind the practice,build the corresponding mathematical model,firmly believe that we can continue to innovate in teaching practice,achieve self-leap,and can also add their own wonderful chapters in the history of mathematics.