The Investigation Research About The Proof Without Words In Classroom

"Proof Without Words",which is the origin of many concepts and theories,plays an important role in the development of mathematics.Due to the uniqueness and the interest laid in the proof process,it is often actively used as an intuitive or geometric interpretation in class.Under the new curriculum standards,visual literacy is included in one of the six major core qualities of mathematics.This indicates that teachers need to strengthen students' image and graphic cognitive ability,exercise their abilities of abstracting language or expressing intuition and improve their abilities to make plane and three-dimensional graphics in the brain's visual appearance.Domestic researches on "Proof Without Words" basically remain in the other understanding of the concept and theorem or simple examples of "proof without word".This study,on the contrary,focus on forming a special mathematical seminar in the "proof without words",selecting appropriate learning materials combined with the excellent experience of HPM lesson development to expand the school class in the lesson development.This is a new attempt to "proof without words" used in teaching,which is also based on the imagination of literacy training requirements.This study mainly carries out researches in two aspects of "integer summation series" and "triangle ratio",with three times of lesson development.With systematic description and analysis of lesson design,classroom presentation and course feedback results,the main conclusions are as follows:1.High school students value "Proof Without Words" seminar highly.The curriculum not only broaden students' knowledge in the visual and imaginary part of mathematics,but also compares their similarities and differences with traditional "combination of numbers and shapes",which deepens the understanding of geometric reasoning and logical argumentation.2."Proof Without Words" can help students deepen the understanding of their prior knowledge.From the perspective of content,more concrete graphics and pictures can help students understand and memorize formula in a more ideal way.From the perspective of emotion attitude and values,such seminar stimulates the students' interest in learning,and with the better understanding of the history of mathematics and mathematics can greatly enhance the students' mathematical literacy.3.“Proof Without Words" seminar can promote the students' perception of intuitive graphical and mathematical imagination structure ability,which can be used as one of the main methods to cultivate the imagination of core literacy.Thus,"Proof Without Words" seminar contains high educational value,which is worthwhile for teachers to discuss and develop together.