Dynamic geometric figure drawing method suitable for teaching scene

Abstract

This invention discloses a dynamic geometric drawing method suitable for teaching scenarios, belonging to the field of teaching aid technology. Specifically, it includes the following steps: S1. Construction of teaching objectives and task scripts: Clearly define the invariants to be verified in class and the exploration path, outputting an objective list and activity script; S2. Construction of free points and dependencies: Control the degrees of freedom to ensure dragging stability, outputting a list of free points and a dependency graph; S3. Construction of basic objects: Build a stable geometric skeleton, outputting a set of basic objects; S4. Construction of constraint relationships: Explicitly construct the required geometric relationships, outputting a stable constraint structure. Adapting to the teaching process and strengthening goal orientation: Through the steps of "construction of teaching objectives and task scripts" and "classroom process design," it accurately matches the classroom logic of "phenomenon → questioning → induction → proof," decomposing geometric conclusions into testable relationships, designing an exploration activity chain, and ensuring that dynamic graphic drawing fully serves the teaching objectives, helping students intuitively understand geometric invariants.

Description

Technical Field

[0001] This invention relates to the field of teaching aids technology, and in particular to a method for drawing dynamic geometric figures suitable for teaching scenarios. Background Technology

[0002] In traditional geometry teaching, teachers often use static blackboard writing, wall charts, or PowerPoint presentations to display geometric figures. This makes it difficult to visually represent the dynamic changes in geometric figures and prevents students from exploring geometric invariants through interactive methods such as dragging and measuring. Existing dynamic geometry drawing tools mostly focus on general drawing functions and lack customized design for teaching scenarios: First, they lack clear teaching objectives and cannot match the classroom's "observation-questioning-induction-proof" teaching process; second, dragging figures is prone to degradation (such as collinearity or overlap), leading to demonstration failure and insufficient stability; third, they lack reusable teaching scripts and construction templates, resulting in low teacher preparation efficiency; and fourth, the visual presentation lacks hierarchy, making it difficult to highlight key geometric relationships and invariants, which is detrimental to student understanding. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a dynamic geometric drawing method suitable for teaching scenarios; it can solve the problems of lack of teaching adaptability, poor stability and low reusability of dynamic drawing in existing geometry teaching.

[0004] Technical Solution: To solve the above-mentioned technical problems, according to one aspect of the present invention, more specifically, a method for drawing dynamic geometric figures suitable for teaching scenarios, the method includes the following steps: S1. Construction of teaching objectives and task scripts: Clarify the invariants and inquiry paths to be verified in class, and output the list of objectives and activity scripts; S2. Free Point and Dependency Construction: Control the degree of freedom, ensure drag-and-drop stability, and output a list of free points and a dependency graph; S3. Basic Object Construction: Construct a stable geometric skeleton and output a collection of basic objects; S4. Constraint Relation Construction: Explicitly constructs the required geometric relations and outputs a stable constraint structure; S5. Construction of Parameters and Interaction Mechanisms: Provide controllable changes to support the investigation and output parameter control mechanisms; S6. Measurement and Invariant Validation: Enable students to "see invariants and output real-time measurement and validation expressions"; S7. Visual hierarchy and annotation optimization: Highlight teaching points, reduce visual noise, and output clear, teachable views; S8. Stability and Degradation Handling: Ensures stable rendering even under extreme dragging conditions, outputting robust dynamic graphics; S9. Classroom Process and Reusable Template Construction: Create reusable classroom activity templates and output reusable teaching scripts and construction templates.

[0005] Furthermore, step S1 specifically includes the following steps: S11. Write down the "observable conclusions" of this lesson; S12. Break down the conclusion into 2-3 testable geometric relationships; S13. Design an activity chain of "construction → dragging → measurement → induction" and prepare questions.

[0006] Furthermore, step S2 specifically includes the following steps: S21. Select 2-4 draggable free points; S22. Establish dependencies derived from the free point for the remaining objects; S23. Draw a dependency graph to ensure there are no circular dependencies.

[0007] Furthermore, step S3 specifically includes the following steps: S31. Construct basic objects including line segments, lines, and circles using free points; S32. Prefer using the "geometric construction method" instead of manual assignment to avoid drift; S33. Verify at each step whether the object is uniquely determined by the previous step.

[0008] Furthermore, step S4 specifically includes the following steps: S41. Use construction constraints including perpendicular lines, parallel lines, and circular intersections. S42. Transform key conclusions into "relationships between objects". S43. Provide alternative construction paths for potentially degenerate relationships; the potentially degenerate relationships include: parallel and collinear.

[0009] Furthermore, step S5 specifically includes the following steps: S51. Select 1-2 core parameters, including: side length, radius, and angle; S52. Bind the parameter to a draggable point or slider; S53. Record the range of impact of each parameter change on the graph.

[0010] Furthermore, step S6 specifically includes the following steps: S61. Add measurements including length, angle, and area. S62. Display the conclusion in the form of "difference close to 0" or "ratio constant". S63. Drag and drop multiple times to verify the stability of the conclusion.

[0011] Furthermore, step S7 specifically includes the following steps: S71. Bold or use color to highlight key objects; fade auxiliary objects; S72. Name and label important points to avoid ambiguity; S73. Add text descriptions to the conclusion objects, including: "equal length" and "perpendicular".

[0012] Furthermore, step S8 specifically includes the following steps: S81. The test includes extreme cases such as collinearity, coincidence, and near-parallelism. S82. To address degradation issues, restrict dragging or add auxiliary structures; S83. Provide a warning for inevitable degradation, including: the current form is unavailable.

[0013] Furthermore, step S9 specifically includes the following steps: S91. Organize the classroom process according to "phenomenon → questioning → induction → proof". S92. Prepare teacher's questions and student observation points. S93. Summarize the conclusions and record the transferable construction methods.

[0014] Beneficial effects: Adapting to the teaching process and strengthening goal orientation: Through the steps of "constructing teaching objectives and task scripts" and "designing classroom processes", the classroom logic of "phenomenon → questioning → induction → proof" is accurately matched, geometric conclusions are broken down into testable relationships, and inquiry activity chains are designed so that the dynamic drawing of graphics fully serves the teaching objectives and helps students intuitively understand geometric invariants.

[0015] To improve dynamic stability and prevent demonstration failures: By controlling the number of free points, building non-cyclic dependencies, designing alternative construction paths, and handling extreme degradation cases, we ensure that no failures such as collinearity or overlap occur when dragging graphics, thus guaranteeing the continuity and reliability of classroom demonstrations.

[0016] Improve the reusability of lesson preparation and reduce the burden on teachers: Generate reusable teaching scripts and construction templates, and extract transferable construction methods (such as "midpoint construction → measurement verification"). Teachers can directly reuse or fine-tune these methods when teaching similar geometric theorems in the future, which greatly improves the efficiency of lesson preparation.

[0017] Optimize visual and interactive experiences to facilitate student inquiry: By designing visual hierarchy (highlighting key objects and downplaying auxiliary objects), clear labeling, and parameter binding interactions, visual distractions are reduced, allowing students to quickly focus on core geometric relationships and independently verify conclusions through dragging, measuring, and other methods, thereby enhancing classroom participation. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the method. Detailed Implementation

[0019] To make the technical solution of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Example Implementation Theme Junior High School Mathematics: "Midpoint Theorem of a Triangle" (Theorem states that the midpoint of a triangle is parallel to the third side and equal to half the length of the third side) - Dynamic Geometric Drawing and Classroom Application.

[0021] Implementation steps S1. Construction of Teaching Objectives and Task Scripts Observable conclusion from S11: The midline of the triangle is parallel to the third side, and the length of the midline is half the length of the third side.

[0022] S12 splitting can test geometric relationships: ① The angle between the median and the third side is 0° (parallel relationship); ② The ratio of the length of the median to the length of the third side is constant at 0.5.

[0023] S13 Activity Chain Design: Constructing a triangle and midline → Dragging vertices to change the triangle shape → Real-time measurement of key data → Summarizing theorems; Core questions: "Will the positional relationship between the midline and the third side change after dragging the vertex?" "What is the pattern in the ratio of the lengths measured twice?" S2. Free Points and Dependency Construction S21 Select 3 draggable free points: A (triangle vertex 1), B (triangle vertex 2), C (triangle vertex 3).

[0024] S22 Dependency relationships are established: Midpoint D of AB (dependent on A and B), Midpoint E of AC (dependent on A and C), Midline DE (dependent on D and E), Third side BC (dependent on B and C).

[0025] S23 Dependency Graph Verification: A→D, E; B→D, BC; C→E, BC; D→DE; E→DE, no circular dependencies, ensuring smooth drag-and-drop logic.

[0026] S3. Basic Object Construction S31 Constructing the basic object: Construct line segment AB using free points A and B, construct line segment AC using points A and C, and construct line segment BC using points B and C (forming △ABC); automatically generate D (midpoint of AB) and E (midpoint of AC) using the "geometric construction method" (midpoint tool), and then construct line segment DE (midline).

[0027] S32 Priority Selection: The entire process uses the geometric construction method, without manually inputting coordinates or lengths, to avoid "drifting" when dragging graphics.

[0028] S33 Uniqueness Verification: If AB is determined, then D is unique; if AC is determined, then E is unique; DE is uniquely determined by D and E; BC is uniquely determined by B and C; the basic framework is stable.

[0029] S4. Constructing Constraint Relations S41 Construction Constraints: The parallel constraints of DE and BC are naturally bound by the "midpoint construction", and the "circle intersection auxiliary construction" is added as a backup scheme.

[0030] S42 Conclusion Transformation: Transform "parallel" into "the angle between DE and BC = 0°", and transform "length ratio 1:2" into "DE length ÷ BC length = 0.5".

[0031] S43 Alternate Path: If A, B, and C are approximately collinear during dragging, it automatically switches to the auxiliary construction of "extending AB to F so that BF=AB" to ensure that the parallel relationship between DE and BC can be verified.

[0032] S5. Parameter and Interaction Mechanism Construction S51 core parameters: BC side length (range 5-15), ∠ABC (range 30°-120°).

[0033] S52 parameter binding: Bind the side length of BC to the horizontal drag of point B (drag to the right to increase the side length), and bind ∠ABC to the slider (drag the slider to change the angle).

[0034] S53 Effect Record: Changes in the length of side BC only affect the length of DE (increases and decreases synchronously), and do not affect the parallel relationship; changes in ∠ABC only change the shape of the triangle, and do not affect the length ratio and parallel relationship.

[0035] S6. Measurement and Invariant Verification S61 adds the following measurement items: DE length (labeled L1), BC length (labeled L2), and the angle between DE and BC (labeled θ).

[0036] S62 display format: Real-time display of "L1 / L2≈0.5" and "θ≈0°", with constant results highlighted in green font.

[0037] S63 drag verification: Drag points A, B, and C multiple times, switching between acute, right, and obtuse triangles. It was observed that L1 / L2 was always between 0.49 and 0.51, and θ was always between -1° and 1°. The conclusion is that it is stable.

[0038] S7. Visual Hierarchy and Annotation Optimization S71 visual distinction: the median line DE is thickened (red, line width 2pt), the third side BC is thickened (blue, line width 2pt); AB, AC and vertices A, B, C are faded (gray, line width 1pt).

[0039] S72 Clear Labeling: Label D (midpoint of AB) and E (midpoint of AC) to avoid vertex confusion.

[0040] S73 Text Description: Mark "Midline" next to DE, "Third Side" next to BC, "Constant Ratio 1:2" next to L1 / L2, and "Parallel (θ≈0°)" next to θ.

[0041] S8. Stability and Degradation Treatment S81 Extreme Test: Tests extreme cases such as A, B, and C being collinear, B coinciding with C, and ∠ABC = 180°.

[0042] S82 Degradation Handling: When three points are collinear, the drag range of point A is limited (a prompt "Please adjust point A away from BC" will pop up); when B and C coincide, point C is locked (a prompt "Cannot coincide, point C is locked" will appear).

[0043] S83 Failure Warning: When ∠ABC≤20° or≥160°, a pop-up window will display the message "The current angle is too small / too large. It is recommended to adjust it to 30°-120°".

[0044] S9. Classroom Flow and Reusable Template Construction S91 Classroom Flow: ① Phenomenon Demonstration (Teacher drags point A, students observe the unchanged parallel relationship and length ratio of DE); ② Questioning Guidance (Combined with the core questions in S13); ③ Summarization (Students state the theorem based on measurement data); ④ Proof Extension (Teacher guides students to prove using the properties of parallelograms).

[0045] S92 Teaching Preparation: Supplement the question "In a right triangle, what is the relationship between the midline and the hypotenuse?", and have students observe "In an isosceles triangle, does the midline bisect the side opposite the vertex angle?".

[0046] S93 Template Summary: A reusable template for "midpoint-type line segment relationships" is formed, which includes the general steps of "constructing the midpoint → connecting the line segments → measuring the ratio → verifying parallelism" and can be directly transferred to the teaching of "trapezoidal midline theorem".

[0047] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for drawing dynamic geometric figures suitable for teaching scenarios, characterized in that, Specifically, the following steps are included: S1. Construction of teaching objectives and task scripts: Clarify the invariants and inquiry paths to be verified in class, and output the list of objectives and activity scripts; S2. Free Point and Dependency Construction: Control the degree of freedom, ensure drag-and-drop stability, and output a list of free points and a dependency graph; S3. Basic Object Construction: Construct a stable geometric skeleton and output a collection of basic objects; S4. Constraint Relation Construction: Explicitly constructs the required geometric relations and outputs a stable constraint structure; S5. Construction of Parameters and Interaction Mechanisms: Provide controllable changes to support the investigation and output parameter control mechanisms; S6. Measurement and Invariant Validation: Enable students to "see invariants and output real-time measurement and validation expressions"; S7. Visual hierarchy and annotation optimization: Highlight teaching points, reduce visual noise, and output clear, teachable views; S8. Stability and Degradation Handling: Ensures stable rendering even under extreme dragging conditions, outputting robust dynamic graphics; S9. Classroom Process and Reusable Template Construction: Create reusable classroom activity templates and output reusable teaching scripts and construction templates.

2. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Write down the "observable conclusions" from this lesson. S12. Break down the conclusion into 2-3 testable geometric relationships; S13. Design an activity chain of "construction → dragging → measurement → induction" and prepare questions.

3. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S2 specifically includes the following steps: S21. Select 2-4 draggable free points; S22. Establish dependencies derived from the free point for the remaining objects; S23. Draw a dependency graph to ensure there are no circular dependencies.

4. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31. Construct basic objects including line segments, lines, and circles using free points; S32. Prefer using the "geometric construction method" instead of manual assignment to avoid drift; S33. Verify at each step whether the object is uniquely determined by the previous step.

5. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S4 specifically includes the following steps: S41. Use construction constraints including perpendicular lines, parallel lines, and circular intersections. S42. Transform key conclusions into "relationships between objects". S43. Provide alternative construction paths for potentially degenerate relationships; the potentially degenerate relationships include: parallel and collinear.

6. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S5 specifically includes the following steps: S51. Select 1-2 core parameters, including: side length, radius, and angle; S52. Bind the parameter to a draggable point or slider; S53. Record the range of impact of each parameter change on the graph.

7. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S6 specifically includes the following steps: S61. Add measurements including length, angle, and area. S62. Display the conclusion in the form of "difference close to 0" or "ratio constant". S63. Drag and drop multiple times to verify the stability of the conclusion.

8. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S7 specifically includes the following steps: S71. Bold or use color to highlight key objects; fade auxiliary objects; S72. Name and label important points to avoid ambiguity; S73. Add text descriptions to the conclusion objects, including: "equal length" and "perpendicular".

9. The dynamic geometric figure drawing method suitable for teaching scenarios according to claim 1, characterized in that: Step S8 specifically includes the following steps: S81. Tests include extreme cases such as collinearity, coincidence, and near-parallelism. S82. To address degradation issues, restrict dragging or add auxiliary structures; S83. Provide a warning for inevitable degradation, including: the current form is unavailable.

10. The method for drawing dynamic geometric figures suitable for teaching scenarios according to claim 1, characterized in that: Step S9 specifically includes the following steps: S91. Organize the classroom process according to "phenomenon → questioning → summarizing → proof". S92. Prepare teacher's questions and student observation points. S93. Summarize the conclusions and record the transferable construction methods.

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