Interactive digital learning system and method for multiple-representation assisted geometric proof

Abstract

The invention relates to interactive digital learning system and method of multiple-representation assisted geometric proof, used for a computer. The interactive digital learning system comprises a data base, a question representation display unit, a proof representation display unit and a visual representation display unit. The data base is respectively connected with a computer, the question representation display unit, the proof representation display unit and the visual representation display unit; the data base stores a known condition, a target to be proofed, and a geometric proof question and solutions of a static geometric figure; the geometric proof question is displayed by the question representation display unit, and the solutions are represented by a formal proof unit and a proof tree unit; the formal proof unit and the proof tree unit can adopt a completion question, a choice question and a sorting question as training applications; and the visual representation display unit can increase the understanding and familiarities of users to geometric proof questions by static and dynamic geometric figures inside.

Description

technical field [0001] The invention relates to improving students' understanding and familiarity with geometric proof questions, and in particular to an interactive digital learning system and method for assisting geometric proofs with multiple representation concepts. Background technique [0002] Geometry plays an important role in fundamental mathematics, and its application of proofs is intended to enhance the processes of ideation, inquiry and reasoning. [0003] General mathematical concepts have a formal and rigorous definition, called concept definition, which will be introduced in the school's geometry and mathematics courses, but when students decide whether a mathematical topic is an example of a certain concept, they do not necessarily Examining with a formal definition, it is often determined by an image of the concept definition in the mind, which is called a concept image. [0004] Since students' thinking, development and learning process of geometric figur...

AI Technical Summary

Problems solved by technology

[0005] In general, students learn geometry and mathematics by imitation. First, the school teaches concepts and definitions, and then the teacher solves the proof steps for the geometry proof questions. The learning methods of students are mostly imitation and memorization. And more than understanding, this is quite easy to cause the following problems: 1. I don’t know how to start the geometric proof; 2. Rely on typical mental images; 3. Use intuitive vision to prove, and I don’t have enough knowledge of mathematical symbols; 4. I don’t know the questions 5. Insufficient ability to integrate useful information; 6. Overly generalized arguments; 7. Ignoring some steps when copying proof steps, etc.

[0010] Another geometry learning software is Geometry Expert (GEX for short), which can not only provide graphical display, visualization and interactive dynamic geometric graphics, but also apply geometric inference methods to prove geometric theorems mechanically. It is developed by the Chinese The system designed by Gao Xiaoshan, Zhang Jingzhong and Zhou Chengqing (1998) integrates the proof methods of the past 20 years and develops a mechanical proof system. These methods include the deductive database method (Synthetic Search Method), Wu Method (WuMethod ), area method (Area Method), Groebner method, vector method (VectorMethod) and full-angle method (Full-Angle Method), but the symbols used in the proof system are different from general mathematical symbols, which are difficult to understand and read, but It is a set of tools that mathematics experts can use as a reference

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