High school mathematics interactive teaching device and method based on dynamic geometric visualization

Abstract

The application discloses a high school mathematics interactive teaching device and method based on dynamic geometry visualization, and relates to the field of education technology and teaching aids. The device comprises a table body, which is provided with a parameterized coordinate construction board, a telescopic connecting arm, a parameter anchor point, an angle parameter generator, a physical parameter knob, a slider, a data processing host and a display screen. The parameter anchor point is magnetically fixed to the coordinate board, the connecting arm is provided with a length sensor, the angle parameter generator is provided with an angle sensor, and the coordinate board is provided with an optical positioning grid. The method comprises the following steps: placing the anchor point to form a basic geometric figure, measuring geometric parameters through the connecting arm, inputting algebraic parameters through the knob or the slider, and driving the three-dimensional model on the display screen to change synchronously in real time according to the sensor data, so as to realize dynamic mapping of the geometric figure and the algebraic relationship. The application improves the interactivity and intuitiveness of mathematics teaching and helps students to explore abstract concepts.

Description

Technical Field

[0001] This invention relates to the field of educational technology and teaching aids, specifically to an interactive teaching device and method for high school mathematics based on dynamic geometric visualization. Background Technology

[0002] In high school mathematics teaching, geometry, especially solid geometry and analytic geometry, is a core module for cultivating students' spatial imagination, logical reasoning, and the ability to combine numbers and shapes. However, traditional geometry teaching has long faced many difficulties. In solid geometry teaching, teachers usually rely on blackboard drawings, static solid models, or simple multimedia animations to present the relationships between points, lines, and planes in three-dimensional space. These methods have significant limitations: blackboard drawings are essentially two-dimensional, making them unintuitive in representing spatial relationships and prone to misleading; while solid models are intuitive, their fixed structure makes it difficult to dynamically demonstrate the process of geometric changes, and it is also impossible to accurately quantify their geometric parameters (such as side lengths, angles, and coordinates); and pre-made multimedia animations have weak interactivity, with the changes being predetermined and linear, preventing students from actively exploring and intervening in the parameters, essentially remaining a passive viewing experience that makes it difficult to achieve a deep understanding.

[0003] With the deepening of educational informatization, Dynamic Geometry (DGS) software, represented by Geometer's Sketchpad and GeoGebra, has been widely used. This type of software allows users to dynamically change geometric figures on the screen by defining variables and dragging points, providing a powerful tool for revealing invariant relationships and laws of motion within figures. However, pure software-based teaching also has inherent drawbacks. First, its interaction relies entirely on the mouse, keyboard, and screen, resulting in an indirect and "flat" interaction. Students manipulate virtual figures by dragging pixels on the screen, lacking direct tactile perception and physical manipulation experience of geometric entities (such as real line segments, angles, and spatial structures). This interaction, detached from physical perception, makes it difficult for high school students, whose spatial reasoning is in a critical developmental stage, to establish a solid and transferable spatial representation. Second, software operation has a certain threshold; its parameter settings and function input processes emphasize abstract symbols, which may divert some students' attention from the geometric essence to the software operation itself, making it less friendly to students with weaker mathematical foundations. Finally, graphics in a software environment are ultimately visual illusions on a screen, creating a psychological barrier between them and the real, tangible three-dimensional world, which is not conducive to establishing a profound connection between mathematics and the real world.

[0004] In recent years, intelligent teaching aids aiming to integrate virtual and real experiences have begun to emerge, such as mathematical puzzles or measurement kits with integrated sensors. However, existing products often have relatively limited functions, focusing only on plane geometry measurement or only achieving simple data acquisition. They lack a complete teaching solution that can systematically and comprehensively support the entire process from constructing plane coordinates to generating 3D spatial graphics and dynamically linking algebraic parameters. How to seamlessly combine the intuitiveness and operability of physical entities with the dynamism, precision, and generative nature of digital technology to create an immersive learning environment that allows users to "build" real spatial structures, "observe" their digital image changes in real time, and directly drive complex geometric transformations by adjusting physical parameters (such as knobs and sliders) has become a key direction for breaking through the current bottlenecks in geometry teaching. Therefore, it is necessary to design a new type of interactive teaching device and method to fill the aforementioned gaps. Summary of the Invention

[0005] The purpose of this invention is to provide an interactive teaching device and method for high school mathematics based on dynamic geometric visualization. The purpose is to enable students to intuitively operate the device by using a physical interface composed of magnetic anchor points, a telescopic arm and sensors, combined with the real-time dynamic feedback of knobs, sliders and graphic displays. Through the instant linkage between the physical configuration and the three-dimensional model on the screen, students can personally explore and deeply understand the dynamic correspondence between geometric shapes, parameter changes and algebraic relationships, thereby effectively improving their spatial imagination and ability to combine numbers and shapes.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution: an interactive teaching device and method for high school mathematics based on dynamic geometric visualization, comprising a table, a parametric construction panel for establishing a coordinate system on the upper surface of the table, a retractable connecting arm device on the upper surface of the table, an anchor point for positioning between the parametric construction panel and the retractable connecting arm device, and a measuring mechanism for generating angle parameters installed at the end of the retractable connecting arm device.

[0007] Furthermore, the upper surface of the table is provided with a physical rotary knob that can be physically rotated and adjusted, and the upper surface of the table is also provided with an adjustment slider that can slide linearly. The upper surface of the table is provided with a core computing host for processing data, and the surface of the core computing host is provided with an image display screen.

[0008] Furthermore, the anchor point used for positioning has a magnetic adsorption function, which can be firmly adsorbed and fixed on the surface of the parametric structure panel.

[0009] Furthermore, both ends of the telescopic connecting arm device are equipped with magnetic hinge joints that can attract and connect with the magnetic anchor point.

[0010] Furthermore, the telescopic connecting arm device is equipped with a linear displacement measurement sensor that can detect and provide feedback on its telescopic length in real time.

[0011] Furthermore, the measuring mechanism used to generate angle parameters is internally equipped with a rotary angle encoder capable of accurately measuring the angle between the two arms.

[0012] Furthermore, the parametrically constructed panel integrates a precision positioning grid system capable of optically positioning the anchor points adsorbed on its surface.

[0013] Furthermore, the current rotation parameter value of the physical knob device and the current position parameter value of the adjustment slider can be read in real time and displayed on the image display screen.

[0014] Furthermore, the core computing host is used to receive measurement data from all sensors, perform calculations, and render synchronously changing three-dimensional spatial geometry on the image display screen in real time.

[0015] Furthermore, the implementation steps include: Step 1: Attach at least three magnetic anchor points and place them in different positions on the parametric construction panel; Step 2: Use the telescopic connecting arm device to connect each magnetic anchor point in sequence to form a basic geometric frame; Step 3: Install the angle parameter measuring mechanism onto the two connecting arms of the target angle to measure the angle in real time or preset the angle in advance; Step 4: Input independent algebraic control parameters into the core computing host by manually rotating the physical knob or moving the adjustment slider; Step 5: The core computing host performs calculations based on the received algebraic parameters and the geometric data collected from the sensors, and drives the three-dimensional geometric model on the image display screen to make synchronous and continuous changes. Step Six: By manually changing the position of the magnetic anchor point on the panel, adjusting the length of the telescopic connecting arm device, or changing the input parameters of the physical knob and slider, dynamically observe and explore the real-time mapping law between the shape changes of the geometric figure and the algebraic relationship behind it.

[0016] This invention provides an interactive teaching device and method for high school mathematics based on dynamic geometric visualization, which has the following beneficial effects: 1. This device integrates abstract geometric concepts with algebraic relationships in a tangible way, significantly enhancing the intuitiveness of teaching and the depth of student understanding. Through innovative components such as magnetic parameter anchors, retractable connecting arms, and angle parameter generators, students can personally construct and manipulate basic geometric figures such as triangles and polygons. During the physical operation, components such as linear displacement sensors and rotary encoders convert geometric quantities such as length and angle into data in real time, while physical parameter knobs and sliders are used to directly input algebraic parameters. This closed-loop interaction of "hands-on construction of geometric figures - real-time synchronous parameter changes - observation of dynamic models on the screen" makes the generation and transformation process of complex knowledge such as function curves, solid figures, and parametric equations clear at a glance, effectively breaking through the cognitive barrier of "from abstract to abstract" in traditional teaching and achieving a smooth transition from embodied experience to mathematical abstraction.

[0017] 2. This teaching system creates a deeply immersive, inquiry-based learning environment that effectively stimulates students' interest in actively exploring and discovering mathematical patterns. The device allows users to change system variables in real time through various physical interaction methods (moving anchor points, extending arms, rotating angles, and adjusting knobs), and immediately observe the corresponding responses of the 3D geometric model on the display screen. For example, when exploring the relationship between the sides and angles of a triangle, dragging the vertex to change the side length causes the screen model to deform synchronously and update angle and area data in real time; rotating the parameter knob to change the quadratic coefficient causes the parabola on the screen to change dynamically. This immediate and visual causal feedback transforms mathematics from static formulas and graphs into manipulable and experimental dynamic objects, greatly enhancing the playfulness and exploratory nature of the learning process and helping to cultivate students' scientific inquiry abilities to propose and verify conjectures.

[0018] 3. This device constructs a multimodal, multi-channel collaborative sensory learning framework, effectively promoting the coordinated development of students' spatial imagination and logical thinking abilities. The device integrates multiple sensory channels, including tactile (manipulating physical components), visual (observing the physical graphics on the coordinate board and the dynamic model on the screen), and even auditory (the sounds of components clicking together, the sounds of knob adjustments). Students manually construct geometric figures on the coordinate board, exercising their spatial layout and hands-on skills; simultaneously, the screen renders the two-dimensional construction into a three-dimensional model in real time and provides a dynamic demonstration, achieving a leap from two-dimensional manipulation to three-dimensional imagination. This learning method, which combines hands, eyes, and brain, and integrates physical and virtual elements, not only deepens students' spatial understanding of the relationships between points, lines, planes, and volumes, but also strengthens the core mathematical idea of ​​combining numbers and shapes through precise control of geometric figures using algebraic parameters, achieving comprehensive training in both visual and abstract logical thinking.

[0019] 4. This invention provides a highly flexible and scalable mathematical experiment platform, capable of broadly covering core high school mathematics teaching content, from plane geometry to solid geometry, analytic geometry, and even basic function graphs. The combination of a parameterized coordinate construction board and a retractable connecting arm allows the device to adapt to various teaching scenarios, from simple two-point distances and triangle congruence criteria to complex conic section definitions and vector operations. By changing different parameter anchor points (such as marking special points) or pre-setting different software modules, teachers can quickly design a series of interactive experiments, such as exploring the properties of parabolic foci, demonstrating solid geometric cross-sections, and simulating function graph transformations. This "one device, multiple scenarios" design greatly enriches classroom teaching methods, enabling teachers to flexibly design interactive elements according to the teaching progress, improving the efficiency of teaching resource utilization and the adaptability of curriculum implementation.

[0020] 5. This technical solution combines the intuitive reliability of physical teaching aids with the dynamic and intelligent advantages of digital technology, providing an efficient and precise interactive tool for classroom teaching. Built-in high-precision sensors (linear displacement, rotational encoding, optical positioning) ensure the accuracy and real-time nature of the conversion from physical operations to digital information, avoiding errors that may occur with traditional drawing and measurement. The data processing host can quickly process multi-channel sensor data and perform complex graphic calculations and 3D rendering, ensuring smooth dynamic visualization. Teachers can use this device for accurate and efficient classroom demonstrations, while students can confidently observe and summarize based on precise data. This retains the "realism" and "controllability" of hands-on practice while leveraging the advantages of computers in "computing power" and "demonstration flexibility," providing a practical and effective hardware support solution for the digital transformation of traditional mathematics classrooms. Attached Figure Description

[0021] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the overall structure of the present invention; Figure 2 This is a flowchart illustrating the hardware composition of the device of the present invention; Figure 3 This is a flowchart illustrating the data acquisition and visualization process of this invention. Figure 4 This is a flowchart illustrating the operation of the teaching method of the present invention.

[0023] Part Name: Table 1; Parametric coordinate construction board 2; Telescopic connecting arm 3; Parametric anchor point 4; Angle parameter generator 5; Solid parameter knob 6; Slider 7; Data processing host 8; Display screen 9. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses consistent with some aspects of this disclosure as detailed in the appended claims.

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. How to use: 1. Equipment preparation and startup First, confirm that the table 1 is placed stably. Turn on the power to the data processing host 8 located at the top of the table 1. The display screen 9 on its end face will light up normally, displaying the initial operation interface. Check whether the parametric coordinate construction plate 2, the retractable connecting arm 3, the parameter anchor point 4, the angle parameter generator 5, the solid parameter knob 6, and the slider 7 are complete.

[0026] 2. Constructing basic physical geometry Step S1: Take at least three parameter anchor points 4. Utilize their built-in magnetic attraction to attach and fix them at any position on the parameterized coordinate construction plate 2. The positioning grid built into the parameterized coordinate construction plate 2 can optically identify the precise coordinates of each parameter anchor point 4.

[0027] Step S2: Take the telescopic connecting arm 3. Its magnetic hinge plugs at both ends can be matched with the parameter anchor points 4 for quick magnetic connection. Using magnetic attraction, connect both ends of the telescopic connecting arm 3 to different parameter anchor points 4 to form basic geometric shapes such as triangles. The linear displacement sensor built into the telescopic connecting arm 3 can measure its telescopic length in real time.

[0028] 3. Define and measure angle parameters Step S3: If a specific angle is desired, the angle parameter generator 5 can be clipped onto the junction of the two retractable connecting arms 3 that form the target angle. The rotary encoder built into the angle parameter generator 5 can measure the angle value in real time, or fix it at a specific angle.

[0029] 4. Input and adjust algebraic parameters Step S4: By rotating the solid parameter knob 6 at the top of the table 1 or sliding the slider 7 at the top of the table 1, algebraic parameters such as slope, radius, and equation coefficients can be input into the system. The current values ​​of these parameters will be displayed on the display screen 9 in real time.

[0030] 5. Observe dynamic geometric mapping Step S5: The data processing host 8 continuously receives all data from the linear displacement sensor, rotary encoder, positioning grid, solid parameter knob 6, and slider 7. It integrates the geometric information of these physical structures with the input algebraic parameters, and generates and drives the corresponding synchronously changing three-dimensional geometric figures on the display screen 9 in real time.

[0031] Step S6: Conduct interactive exploration. At this point, you can perform any or all of the following operations to observe the dynamic changes: Change the position of parameter anchor point 4 on parameterized coordinate construction board 2.

[0032] Manually stretch or compress the telescopic connecting arm 3 to change its length.

[0033] Adjust the solid parameter knob 6 or slide the slider 7 to change the algebraic parameters.

[0034] While operating, observe how the 3D model on display screen 9 responds to these changes in real time, thereby intuitively exploring the dynamic mapping and intrinsic connection between geometric shapes, positions and abstract algebraic relationships.

[0035] Example 1: This example demonstrates the teaching process of using the device to dynamically construct triangles and explore the relationship between angles and side lengths.

[0036] Step S1: The teacher guides the students to remove three parameter anchor points 4 from the component. Students can freely attach these three parameter anchor points 4 to different positions on the surface of the parameterized coordinate construction board 2 using their magnetic attraction function. At this time, the positioning grid built into the parameterized coordinate construction board 2 has silently captured the two-dimensional coordinates of these three points.

[0037] Step S2: Students select three retractable connecting arms 3. Using the magnetic hinge plugs at both ends of the retractable connecting arms 3 that match the parameter anchor points 4, the three connecting arms are connected end to end and attached to the three parameter anchor points 4 respectively, thus physically forming a solid triangle on the table. During this process, the linear displacement sensor built into each retractable connecting arm 3 starts working, continuously measuring and reporting the real-time length of the three sides.

[0038] Step S3: If the course focuses on the relationships between the interior angles of a triangle, students can attach the angle parameter generator 5 to the two retractable connecting arms 3 of any one angle. The rotary encoder built into the angle parameter generator 5 will immediately begin measuring and output the degree of that angle. The teacher can ask students to measure the three interior angles separately and observe their sum.

[0039] Step S4: Simultaneously, the teacher can guide students to focus on the display screen 9 at the top of the table 1. The data processing host 8 has received all sensor data and synchronously generates a three-dimensional geometric figure of the physical triangle, which is then displayed on the screen. Students can also adjust a physical parameter knob 6 at the top of the table 1. This knob can be preset to control the height of a side of the triangle or a parameter of a circumscribed circle, and its value changes are displayed on the display screen 9 in real time.

[0040] Steps S5 and S6: Entering the dynamic exploration stage. Students can manually drag any parameter anchor point 4 on the parametric coordinate construction board 2, and the shape of the physical triangle changes accordingly. Simultaneously, the 3D model, the length data of the three sides, and the degree of the three interior angles on the display screen 9 all undergo real-time and continuous dynamic changes. Students can intuitively see how the digital model responds and how the angles change when a side is physically stretched, thus gaining a deeper understanding of the constraint relationship between the side length and angle of a triangle. By adjusting the entity parameter knob 6, students can further observe the constraint changes in the shape of the triangle when specific algebraic conditions are met. The entire process achieves a closed-loop teaching from concrete operation to abstract understanding.

[0041] Example 2: This example demonstrates how to use the device to provide intuitive teaching of function graphs and parametric equations.

[0042] Step S1: The teacher sets the topic as exploring the graph of a linear function. Students fix two parameter anchor points 4 horizontally on the parametric coordinate construction board 2 as reference points for the domain. The x-coordinates of these two points are captured by the positioning grid.

[0043] Step S2: Connect the two parameter anchor points 4 using a retractable connecting arm 3. This connecting arm can be mapped onto a segment of the x-axis on the screen. The length measured by its built-in linear displacement sensor can be correlated with the range of change of the independent variable.

[0044] Step S3: This embodiment focuses on the algebraic control of the slope and intercept. The angle parameter generator 5 can be used as an auxiliary tool here, clipped between the straight line representing the function graph and the reference line, for intuitive measurement of the tilt angle.

[0045] Step S4: This step is crucial. The upper part of the table 1 has two physical parameter knobs 6 and a slider 7, defined to control the slope k and intercept b of a linear function, respectively. Students can change the magnitude and sign of the slope by rotating the physical parameter knob 6 (representing the value of k); and change the intercept by sliding the slider 7 (representing the value of b). The parameter values ​​of the knobs and slider are displayed in real-time on the display screen 9.

[0046] Step S5: The data processing host 8 receives control signals from the knob and slider, as well as coordinate signals from the parameter anchor point 4. Based on the linear function equation y=kx+b, it calculates and draws the corresponding straight line image in three-dimensional space, or its projection onto the coordinate plane, on the display screen 9 in real time.

[0047] Step S6: Students perform interactive operations. They can quickly rotate the solid parameter knob 6, which controls the slope, and observe how the straight line on display screen 9 rotates around a point, understanding the geometric meaning of k. Simultaneously, they can slide the slider 7, which controls the intercept, to observe how the straight line translates vertically. Furthermore, students can drag the parameter anchor point 4 on the parametric coordinate construction board 2 to move the reference interval; the image on the screen will change accordingly, showing the function's behavior in different domains. This process of solidifying algebraic parameters and interacting with dynamic graphics in real time greatly enhances students' understanding of the meaning of function parameters.

[0048] Example 3: This example demonstrates the teaching application of this device in the construction of pyramids and the exploration of volume formulas in solid geometry.

[0049] Step S1: Construct the base of the pyramid. Students select four parametric anchor points 4 and attach them to the parametric coordinate construction board 2 to form an arbitrary quadrilateral. The coordinates of the vertices of the base are determined by the positioning mesh of these four points.

[0050] Step S2: Using four retractable connecting arms 3, connect them sequentially to four parameter anchor points 4 via magnetic hinge plugs to form the four sides of a quadrilateral. The linear displacement sensor of each retractable connecting arm 3 measures its side length. Then, take two connecting arms as the diagonals of the quadrilateral and connect them to form the internal structure of the bottom surface.

[0051] Step S3: Next, construct the vertices. Outside the plane containing the base of the quadrilateral, take another parameter anchor point 4 and attach it to the extension rod of the telescopic connecting arm 3, or support it above the base with a lifting mechanism (considered as an extension of the function of the telescopic connecting arm 3), as the vertex of the pyramid.

[0052] Step S4: Use four retractable connecting arms 3 to connect the vertex parameter anchor points 4 to the four bottom parameter anchor points 4, thereby physically constructing a quadrangular pyramid skeleton model. At the same time, attach the angle parameter generator 5 between the side edges and the bottom edge to measure the angle between the side edges and the bottom surface.

[0053] Step S5: The data processing host 8 receives the coordinates of all parameter anchor points 4, the lengths of all retractable connecting arms 3, and the angle data from the angle parameter generator 5. It generates a corresponding, solid 3D pyramid wireframe model or rendered model on the display screen 9.

[0054] Step S6: Dynamic Exploration Begins. Students can observe the changing patterns of the pyramid through the following operations: First, drag any of the four parameter anchor points 4 that form the base on the parametric coordinate construction board 2 to change the shape of the base (e.g., to a rectangle or trapezoid). The 3D pyramid model on the display screen 9 will deform synchronously, and data such as the base area and edge length will be updated in real time. Second, manually move the parameter anchor point 4 representing the vertex up or down to change the height of the pyramid. During this process, students can observe the changes in the model height on the screen and, in conjunction with adjusting the solid parameter knob 6 (which can be preset to control a scaling factor related to volume calculation), intuitively feel the dynamic relationship between the base shape, height, and solid volume, thereby gaining a deeper understanding of the geometric origin of the pyramid volume formula, rather than rote memorization of the formula.

[0055] Example 4: This example illustrates how to use a device to teach the dynamic conversion between circular and elliptical trajectories.

[0056] Step S1: Define the foci and the moving point. Students fix two parametric anchor points 4 on the parametric coordinate construction board 2 as the foci F1 and F2 of the ellipse. Then fix a third parametric anchor point 4 as the moving point P.

[0057] Step S2: Use two retractable connecting arms 3. The first connecting arm connects the moving point P to the focus F1, and the second connecting arm connects the moving point P to the focus F2. The linear displacement sensors built into the two retractable connecting arms 3 measure the distances to PF1 and PF2 in real time, respectively.

[0058] Step S3: The core of this embodiment is the definition of an ellipse as "the sum of the distances to two fixed points is a constant". This "constant" can be set and explored using a device. The angle parameter generator 5 can be used here to measure the angles in the focal triangle.

[0059] Step S4: By adjusting the solid parameter knob 6 or slider 7 on the upper end of the table 1, input a specific length value into the data processing host 8. This value represents the fixed length 2a in the definition of the ellipse. This value is displayed on the display screen 9 in real time.

[0060] Step S5: The data processing host 8 continuously calculates the sum of the lengths of PF1 and PF2 and compares it with the fixed length 2a input through the entity parameter knob 6. At the same time, it draws the elliptical trajectory with F1 and F2 as foci and the position of the current moving point P on the display screen 9.

[0061] Step S6: Students conduct exploratory operations. They can manually move the moving point parameter anchor point 4 on the parametric coordinate construction board 2. When point P is moved so that the sum of the lengths of PF1 and PF2 is exactly equal to the fixed length 2a displayed on the screen, point P falls on the elliptical trajectory drawn on the display screen 9. If moving point P results in the sum of the two distances being less than 2a, point P is displayed inside the ellipse; otherwise, it is outside. Through dynamic, experimental movement, students can personally "touch" the trajectory boundary of the ellipse. In particular, when the fixed length 2a is set to be exactly equal to the distance between the two foci F1 and F2 by adjusting the solid parameter knob 6, the ellipse degenerates into a line segment, which is the extreme case of a circle; while when the two focal parameter anchor points 4 coincide on the parametric coordinate construction board 2, the trajectory becomes a circle, at which point the equation of a circle can be introduced for teaching. This dynamic transformation from general to specific vividly demonstrates the intrinsic connection between conic sections.

[0062] Example 5: This example illustrates the teaching process of exploring trigonometric function graphs and their period and amplitude parameters using a device.

[0063] Step S1: On the parameterized coordinate construction plate 2, a series of parameter anchor points 4 are attached and fixed at equal intervals along the horizontal direction. These points represent discrete sampling points on the time axis or angle axis.

[0064] Step S2: The focus of this embodiment is on controlling the parameters of the trigonometric functions through the device components, rather than constructing geometric shapes. The retractable connecting arm 3 can be used here to construct auxiliary triangles (such as the radius of rotation on a unit circle), the length of which can be related to the sine value. One end of a retractable connecting arm 3 is fixed to a parameter anchor point 4 corresponding to the origin of the coordinate system, and the other end is connected to a parameter anchor point 4 representing a moving point.

[0065] Step S3: Connect the angle parameter generator 5 between the telescopic connecting arm 3 and a reference baseline (such as the positive x-axis). When the telescopic connecting arm 3 rotates around the origin, the rotary encoder built into the angle parameter generator 5 can measure the angle it rotates through in real time (e.g., in radians), and this angle is used as the independent variable of the trigonometric function.

[0066] Step S4: Parameter control is key. The upper part of the table 1 has multiple physical parameter knobs 6 and sliders 7. For example, knob A is defined to control the amplitude A in the sine function y=A sin(ωx+φ); knob B is defined to control the angular frequency ω; and slider C is defined to control the initial phase φ. Students can intuitively change these algebraic parameters by rotating and sliding these controls, and their values ​​are displayed in real time on the display screen 9.

[0067] Step S5: The data processing host 8 receives continuous angle values ​​from the angle parameter generator 5, as well as the A, ω, φ parameter values ​​set by the solid parameter knob 6 and slider 7. It calculates the ordinate y in real time according to the trigonometric function formula and dynamically draws a continuous and smooth three-dimensional or two-dimensional trigonometric function waveform on the display screen 9.

[0068] Step S6: Students engage in interactive learning. They can slowly rotate the retractable connecting arm 3, observing the uniform change in angle of the angle parameter generator 5, while simultaneously watching how the waveform is generated point by point on the display screen 9, understanding the correspondence between angle and sine value. More importantly, they can operate different parameter controllers separately: rapidly rotating the knob controlling amplitude A, observing the waveform being stretched or compressed vertically; adjusting the knob controlling angular frequency ω, observing the waveform becoming denser or sparser horizontally (periodic change); adjusting the slider controlling initial phase φ, observing the waveform shifting left or right as a whole. Through this method of independently materializing each abstract parameter and allowing real-time manipulation, students can clearly and deeply separate and understand the specific influence of amplitude, period, and initial phase on the function graph shape, achieving an intuitive understanding from parameter manipulation to graphical transformation.

[0069] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A high school mathematics interactive teaching device and method based on dynamic geometric visualization, comprising a table (1), characterized in that: The upper end of the table (1) is provided with a parameterized coordinate construction plate (2), the upper end of the table (1) is provided with a retractable connecting arm (3), a parameter anchor point (4) is provided between the parameterized coordinate construction plate (2) and the retractable connecting arm (3), and an angle parameter generator (5) is provided on the end face of the retractable connecting arm (3).

2. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 1, characterized in that: The upper end of the table (1) is provided with a physical parameter knob (6), the upper end of the table (1) is provided with a slider (7), the upper end of the table (1) is provided with a data processing host (8), and the end face of the data processing host (8) is provided with a display screen (9).

3. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 1, characterized in that: The parameter anchor point (4) has a magnetic attraction function and is used to be attracted and fixed to the surface of the parameterized coordinate construction plate (2).

4. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 1, characterized in that: The telescopic connecting arm (3) has magnetic hinge plugs at both ends that match the parameter anchor point (4).

5. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 1, characterized in that: The retractable connecting arm (3) has a built-in linear displacement sensor for real-time measurement of its own length.

6. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 1, characterized in that: The angle parameter generator (5) has a built-in rotary encoder for measuring the included angle.

7. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 1, characterized in that: The parameterized coordinate construction plate (2) has a built-in positioning grid for optically positioning the coordinates of the parameter anchor point (4).

8. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 2, characterized in that: The parameter values ​​of the physical parameter knob (6) and the slider (7) can be displayed on the display screen (9) in real time.

9. The interactive teaching device and method for high school mathematics based on dynamic geometric visualization according to claim 2, characterized in that: The data processing host (8) is used to receive data from all sensors and generate synchronously changing three-dimensional geometric figures on the display screen (9).

10. A teaching method based on the apparatus of any one of claims 1 to 10, comprising the following steps: S1: Place at least three parameter anchor points (4) onto the parameterized coordinate construction plate (2); S2: Use the telescopic connecting arm (3) to connect the anchor points (4) of each parameter to form the basic geometry; S3: Attach the angle parameter generator (5) to the two retractable connecting arms (3) of the target angle to measure or fix the angle; S4: Input algebraic parameters into the data processing host (8) by adjusting the solid parameter knob (6) or slider (7); S5: The data processing host (8) drives the three-dimensional model on the display screen (9) to change synchronously according to the input parameters and the geometric data collected by the sensor; S6: By changing the position of the parameter anchor point (4), the length of the retractable connecting arm (3), or the input algebraic parameters, observe and explore the dynamic mapping between geometric figures and algebraic relationships.

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