CN107818597A - Intelligent tutoring system for solid geometry - Google Patents
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Abstract
The present invention relates to IT application in education sector technical field and mechanization of mathematics field, intelligent tutoring system for solid geometry is provided, the system is combined the solid geometry teaching system globe area relatively independent by one among electronic double board classroom instruction using IT application in education sector technology and the correlative study achievement of mechanization of mathematics with Mathematics Discipline, for current China's middle school geometry Education Situation, the problems such as efficiently solving difficult, numerous, slow-witted in middle school's solid geometry teaching, while mitigating teacher's mechanization work, students developing space imagination is helped.
Description
Technical field
The present invention relates to IT application in education sector technical field and mechanization of mathematics field, specifically one kind is applied to electronics
Middle school's solid geometry intelligent tutoring system of double plates.
Background technology
Electronic double board includes the electronic whiteboard and projecting apparatus of content in display teacher's computers, wherein electronic whiteboard and throwing
Shadow instrument uses in pairs, and to realize that the content of courses is presented in double pictures, the size of two electronic whiteboards is identical, and left and right is placed side by side；With
Going deep into for IT application in education sector, electronic double board with its interactivity it is good, be easy to carry out the advantages such as interactive teaching, gradually substitute " PPT+
The multimedia teaching facility of projecting apparatus ", will more and more it be applied in classroom.
Solid geometry is always the emphasis and difficult point of middle school geometry teaching.However, in the vertical of traditional " blackboard is single-handedly mapped "
During body several teaching, the most of the time of teacher is forced to be engaged in substantial amounts of low-level, the Hand drawing of repeatability, writing on the blackboard work
Make, efficiency of teaching is relatively low；On the other hand, for the most of students for being in middle and primary schools, their space imagining ability
Cultivation stage is still in, can't intactly be envisioned as the space geometry relation of complexity comprehensively；Further, since blackboard framework ring
The restriction in border, the space diagram of freehand be not often easy to maintain, it is difficult to positions and lacks the ability of dynamic change, its is distinctive
Space multistory sense usually can not be fully presented, and these all understand that solid geometry knowledge brings very big difficulty to student.
With the propulsion of Process of Educational Informationization, the country increasingly increases for the dynamic geometry educational system of Mathematics Discipline exploitation
More, they functionally cover the partially or mostly content in middle school mathematics knowledge, can mitigate teacher's to a certain extent
Mechanicalness, repeated labor, understand student abstract mathematical concept, find that the colourful mathematics world also plays guiding
And booster action.But because development difficulty is larger, it is domestic at present not imparted knowledge to students specifically for the dynamic geometry of solid geometry also
System, the educational system that only several moneys are related to solid geometry are also all analogous to CAD mapping software, lack intelligent interaction
The dynamic geometry such as mapping, animation, track, tracking, measurement function and automated reasoning correlation function, thus can not be by obscure solid
Geometric theory and the relation dynamic presentation for being hidden in figure behind, have impact on the teaching efficiency of teacher and proposing for students ' interest of study
It is high.
The content of the invention
The purpose of the present invention is exactly to overcome above mentioned problem, there is provided one kind utilizes IT application in education sector technology and Mathematics Mechanical
The intelligent tutoring system for solid geometry that the correlative study achievement of change is combined and designed and developed with Mathematics Discipline.This hair
It is bright a relatively independent tutoring system can be fused to electronic double board classroom instruction among, it is several for current middle school of China
What Education Situation, the problems such as being directed to solving difficult, numerous, slow-witted in middle school's solid geometry teaching, it is intended to mitigate teacher's mechanization
While work, students developing space imagination is helped, deepens the understanding and utilization to three-dimensional geometric knowledge.
For the intelligent tutoring system of solid geometry, following three-decker is included：
Bottom, by discipline knowledge repository, geological information data represent, three modules of material database form, there is provided used to intermediate layer；
Intermediate layer, it is made up of geometric information database and three dynamic geometry, courseware development tool, automated reasoning modules, to contact
Bottom and application layer；The encapsulation to bottom module is completed for specific application, the base needed for each system is provided for application layer
This function；
Application layer, it is made up of, uses with solving three unit, Interactive Drawing unit, courseware development and demonstration units problem generation
Exported in the input of processing user and terminal to realize man-machine interaction.
In present system inter-layer information is carried out between each layer by the way of bottom-up, bottom provides service to top layer
Transmission, it is then associated with each other according to intermodule relation between each module inside layer.Wherein, geological information data structure represents
Based on the geometric knowledge that module is provided by subject knowledge place, the expression side of the geological information of geometric objects is constructed
Method, the data for constituting system represent basis.The data expression side of module offer is provided according to bottom geological information data structure
On the one hand method, geometric information database record all geometric object geological informations with dynamic geometry module and form data warehouse, be upper strata
Using and automated reasoning module provide data basis；In addition, provided using technologies such as computer graphics, space computational geometries
Interface is realized for Interactive Drawing, courseware development and demonstration unit.Automated reasoning module is according to pushing away in discipline knowledge repository
The geological information that reason rule and geometric information database provide completes automated reasoning, and problem generation is with solving system in the module basis
On, generation and the automatic calculation of geometrical issues are realized, constitutes the important content of system.
In the above-mentioned technical solutions, the subject knowledge library module is in the middle school's solid geometry represented using predicate logic
Basic period structure, including concept, the fact, theorem and axiom, they form inference rules, as reasoning basis for intermediate layer from
Dynamic reasoning module uses.
In the above-mentioned technical solutions, the geological information data representation module uses the data structure pair of multistage authority chained list
The geological informations such as the relation between the classification of geometric graphic element, position, size and pel carry out data expression；Its specific expression side
Method is
(1) a parameter chained list is designed to preserve all parameters in a page, designs another geometric element authority chained list
To preserve all geometric elements, sequentially synchronized update parameter list and element list when the page updates every time；
(2) geometry element of volume authority credentials is assigned successively by dimension size, its midpoint element authority credentials is 1；Line style element authority credentials
For 2；Face type element authority credentials is 3；Type elements authority credentials is 4；Then a chain is constructed for the geometric element of every kind of authority
Table, and it is the authority chained list that an authority presses low to high arrangement to combine four chained lists according to authority height；
(3) when thering is new geometric element to need to add or thering is geometric element to need to delete, it is only necessary to know that this is several
Type belonging to what element, the position then navigated to rapidly in authority chained list, then inserted or deletion action；
(4) when authority chained list searches for geometric element, chained list uses following search mechanisms, searches for since gauge outfit, if low
Searched in the geometric element of authority in child list, just do not continue search for the geometric element of high authority, if searched for less than if
By the higher leveled geometric element of sequential search authority of chained list, if searching multiple elements in the child list of same authority,
Then it is ranked up according to distance of the element from eye position, chooses one nearest from eyes.
In the above-mentioned technical solutions, the material library module is used to store the multimedias such as picture, text, animation and video and audio
File, basic material is provided with demo system to writting tool and courseware development.
In the above-mentioned technical solutions, the geometric information database is divided into geometric information database and dynamic geometry with dynamic geometry module
Two parts；Geometric information database is similar to information warehouse, using drawing all figures for finishing in the current engineering of chained list linear memory
Corresponding geological information, constitute the data basis of system；Three-Dimensional Dynamic geometry teaching of the dynamic geometry part according to parametrization
Model and " programmable point " method, realize that geometry is believed in geological information library module using computer graphical, space computational geometry technology
Breath renders the operation interaction presented and between user and geological information, and provides interactive operation for Interactive Drawing system and connect
Mouthful, realize the operation either statically or dynamically such as mobile tracking track of object corresponding to geological information.Wherein mainly use computer
OpenGL Renderings in figure, space computational geometry realize rendering and presenting for three-dimension space image, using " programmable
Point " method assigns solid dynamic geometry characteristic, and it concretely comprises the following steps a. and selectes parameter T constructing variable equations, represents three-dimensional respectively
The X, Y, Z axis respective coordinates of spatial point；B. constructed variable V relevant parameters T, is corresponded to therewith；C. user's foundation needs to change variable V
The dynamic change of point is realized, is such as tracked, track etc..
In the above-mentioned technical solutions, the automated reasoning module uses the Interconnection Inference based on prospective method, reasoning module bag
Containing input system, inferencing information initialization, automated reasoning engine, four parts of inference conclusion, in initial phase, current field
The parameter of geological information and user's addition in scape, conditional information are put into geometric information database and are converted into internal reasoning information,
Then inference rule is iteratively operating on Given information storehouse, the information generated every time is all put into geometric information database, until not regenerating
Into fresh information or it is concluded that untill, its main flow is as follows,
(1) geological information is obtained from the additional parameter condition that user mutual formula is mapped and is added；
(2) geological information is converted into internal reasoning information；
(3) internal inferencing information is made inferences using inference rule n in discipline knowledge repository, n initial value is 0；
(4) if inference rule produces new geological information, step (7) is gone to；
(5) if n ＜=maximum fuzzy rules, number of regulation n add 1, step (3) is gone to；
(6) if reaching fixed point, step (10) is gone to；If not reaching fixed point, it is 0 to reset number of regulation n, goes to step
(3)；
(7) if new geological information is not present in information bank, it is deposited into information bank；Conversely, go to step (5)；
(8) if including conclusion in fresh information, generation answer information chained list；Otherwise go to step (5)；
(9) internal reasoning information is converted into external information, exports readable proofs；
(10) terminate.
In the above-mentioned technical solutions, the courseware development tool module uses multi-page management, and single courseware is by many fortune
The independent page rearranges in order.
In the above-mentioned technical solutions, the Interactive Drawing unit, for realizing that the interactivity of user and geometric graphic element are grasped
Make.
In the above-mentioned technical solutions, described problem generation is with solving unit, for supporting user according to Interactive Drawing system
System, or addition additional parameter, condition, conclusion guess or target call are proposed to form Solve problems, and the problem is used
Automated reasoning is solved.
In the above-mentioned technical solutions, the courseware development and demonstration unit, Interactive Drawing side is utilized for assisted teacher
Method and writting tool making or demonstration courseware.
The present invention is combined using the correlative study achievement of IT application in education sector technology and mechanization of mathematics in Mathematics Discipline
Mode, specifically using technologies such as dynamic geometry, automated reasoning, computer graphics, space computational geometries, the middle school that combines closely is stood
Body several teaching relevant knowledge, construct the intellectual education system towards middle school geometry especially solid geometry.
By this technological means, teacher can be used during being imparted knowledge to students using the system according to teaching demand
Interactive Drawing system draws three-dimensional geometrical figure from simple to complexity, having dynamic geometry characteristic, can be easily
Observation and manipulation solid figure, implement dynamic geometry, conversion and measurement to figure, can combine writting tool and make or demonstrate use
In the courseware of several teaching, geometrical issues are built with solving system by problem generation and automatic deduction solves, assisted teacher's religion
Learn；By the interaction between teacher, system, student, student can profoundly know from experience the study enjoyment thought in dynamic middle school, change, improve
Side is provided to the learning interest and exploring ability of solid geometry, and then for their deep layer understanding three dimensions solid geometry knowledge
Help.
Present invention contrast prior art and conventional education system have advantages below：
1. can be integrated on electronic double board class teaching platform, using the advantage of electronic double board class teaching platform, carry out dynamic
The education activities such as the demonstration of state case, interactive drawing, interactive teaching；
2. Mathematics Discipline concrete knowledge is combined, the three dimensions solid geometry intellectual education using IT application in education sector technique construction
The concept of system, solve the problems such as middle school's solid geometry teaching is difficult, numerous, slow-witted, filled up China's IT application in education sector three-dimensional several
The blank of what teaching field；
3. utilizing dynamic geometry technology, make geometric object that not only there is very strong space multistory sense, and possess excellent dynamic
Geometrical property, realizes the computings such as the Interactive Drawing of three dimensions, conversion, measurement, dynamic geometry, and solid geometry teaching becomes
Obtain more vivid, directly perceived；
4. proposing the concept and method of " programmable point ", will successfully parameterize and dynamic geometry close-coupled, Mathematics Discipline
The thought of " figure-shape combination " is fully reflected；
5. using the demand of three dimensions dynamic geometry as starting point, substituted and passed using brand-new authority multistage linked list data structure
The set membership tree construction for plane dynamic geometry system complex of uniting, data model is simple, practical, greatly reduces space geometry
The computation complexity of body computing；
Generation and solving system 6. synthesis dynamic geometry and automated reasoning technique construction go wrong, have further expanded system
It is intelligent, it is truly realized the target for carrying out the mechanical mathematics work of repeatability for people using computer generation.
Brief description of the drawings
Fig. 1 is the block schematic illustration for the intelligent tutoring system that the embodiment of the present invention is used for solid geometry.
Fig. 2 is the authority multistage linked list data structure schematic diagram used in the embodiment of the present invention.
Fig. 3 is the automated reasoning modular program flow chart in the embodiment of the present invention.
Embodiment
The invention will be further described with reference to the accompanying drawings and examples.
As shown in figure 1, be the intelligent tutoring system that the present embodiment is used for solid geometry, including following three-tier architecture：
Bottom, including discipline knowledge repository, geological information data represent and three modules of material database, they are as underlying basis
Respectively intermediate layer modules use, and constitute the basis of system.
Intermediate layer, including the functional module such as geometric information database and dynamic geometry, courseware development tool and automated reasoning, they
The encapsulation to bottom module is completed for specific application, the basic function needed for each system is provided for application layer, is contact
The bridge of bottom and application layer.
Application layer, including problem generation and solving system, Interactive Drawing system and courseware development and demo system, it is main
The input for being used to handling user and terminal output to realize man-machine interaction, be intermediate layer basic function in a particular application be
Systemization is realized.
Modules in above-mentioned three layers are specifically described next coming in order.
Subject knowledge library module：This module uses the Basic period structure in middle school's solid geometry of predicate logic expression, bag
Concept, the fact, theorem and axiom are included, they form inference rule, are used as reasoning basis for intermediate layer automated reasoning module.
Geological information data structure represents module：The data structure expression of pel geological information is the base of present system
Plinth, it mainly includes the information such as relation between classification, position, size and the pel of geometric graphic element, using what kind of data
Structure carries out storing the function and efficiency for directly determining dynamic geometry and automated reasoning module.The present invention is using a kind of brand-new
Authority multistage linked list data structure, solve asking for geometric element relational dependence by the real-time update parameterized with list
Topic, and the pick-up operation by turning to solid to the authority of geometry element of volume is provided convenience.As shown in figure 3, it is specific real
Now method is
(1) a parameter chained list is designed to preserve all parameters in a page, designs another geometric element authority chained list
To preserve all geometric elements, sequentially synchronized update parameter list and element list when the page updates every time, from
And solves the problems, such as geometric element relational dependence；
(2) geometry element of volume authority credentials is assigned successively by dimension size, wherein：Point element (free point, intersection point, in geometric object
Point etc.) authority credentials be 1；Line style element (straight line, ray, conic section etc.) authority credentials is 2；Face type element (polygon, plane
Deng) authority credentials be 3；Type elements (polyhedron etc.) authority credentials is 4；Then a chain is constructed for the geometric element of every kind of authority
Table, and it is the authority chained list that an authority presses low to high arrangement to combine four chained lists according to authority height；
(3) when thering is new geometric element to need to add or thering is geometric element to need to delete, it is only necessary to know that this is several
Type belonging to what element, then by " sentry " the rapid position navigated in authority chained list, then inserted or deleted
Division operation；
(4) when authority chained list searches for geometric element, chained list uses following search mechanisms：Search is since gauge outfit, if low
Searched in the geometric element of authority in child list, just do not continue search for the geometric element of high authority, if searched for less than if
By the higher leveled geometric element of sequential search authority of chained list.If searching multiple elements in the child list of same authority,
Then it is ranked up according to distance of the element from eye position, chooses one nearest from eyes.
In dynamic geometry, the concept of " dynamic " and " relation is constant between solid " constitutes its core content, same page
There is the incidence relation of complexity, in the case of the relation of holding is constant, a mobile point tends to band between the solid in face
The dynamic change of multiple other geometric objects that contact therewith be present in dynamic scene.When dynamic change occurs for page object, make
Only need to update a chained list with the real-time update mechanism of authority chained list, compared to the complexity that legacy system uses set membership tree
Structure, time of the opening relationships tree to the related geometric element of lookup during renewal is eliminated, has maximumlly played effectiveness.
Using the data model of authority multistage linked list data structure, geometric element relation in dynamic process can not only be kept
Consistency, and in the pick-up operation of solid, also provided the user great convenience.For example, a spheroid is created, one
On bar line segment and line segment a bit, sheltering from line segment with spheroid makes invocation point in spheroid, it is now desired to which the point is picked up.Using
Ray Tracing Algorithm is picked up operation, and in general thinking will make ray intersection algorithm three times, and it is respectively light and spheroid phase
Hand over, light and line segment intersection, light and point are intersecting；And the authority search attribute of authority chained list is utilized, actually it is only used as once
Ray intersection algorithm can is picked up to the point on line segment, significantly simplify the amount of calculation in pick process.
Material library module：For storing the multimedia files such as picture, text, animation and video and audio, to writting tool and class
Part makes provides basic material with demo system.
Geometric information database and dynamic geometry module：The geometric information database and dynamic geometry module be divided into geometric information database and
Dynamic geometry part, wherein geometric information database are corresponding using all figures that drafting finishes in the current engineering of chained list linear memory
Geological information, constitute the data basis of system；Dynamic geometry part according to parametrization Three-Dimensional Dynamic geometry teaching model and
" programmable point " method, realize that rendering for geological information is in geometric information database using computer graphical, space computational geometry technology
Existing and between user and geological information operation is interactive, and provides interactive operation interface for Interactive Drawing system, realizes several
The operation either statically or dynamically of what object corresponding to information；Wherein mainly using in computer graphical, space computational geometry
OpenGL Renderings realize rendering and presenting for three-dimension space image, and solid dynamic geometry is assigned using " programmable point " method
Characteristic, it concretely comprises the following steps a. and selectes parameter T constructing variable equations, represents the X, Y, Z axis respective coordinates of three dimensions point respectively；
B. constructed variable V relevant parameters T, is corresponded to therewith；C. user is according to the dynamic change for needing change variable V to realize point.
For example, if user is programmed to free point T coordinate, if T X-axis coordinate is：4*sin(3*V)*
Cos (V), the coordinate of Y-axis are：0, the coordinate of Z axis is：4*sin (3*V) * sin (V), wherein V are variable.So now tracking T
Allow variable V to be moved in scope (- 10 10), a pattern for being similar to petal can be obtained.Based on " programmable point " side
Method, using this dynamic geometry technology, geometric figure can be converted, measured, track, tracking and the measurement of algebraic expression
Deng sequence of operations.
Automated reasoning module：Automated reasoning module is the critical function of system, and it can be in the base of current geometric information database
On plinth, a large amount of fresh informations are inferred.The system uses the Interconnection Inference based on prospective method, and reasoning module includes input system, pushed away
Manage information initializing, automated reasoning engine, four parts of inference conclusion.In initial phase, the geometry in current scene is believed
Breath and the parameter of user's addition, conditional information are put into geometric information database and are converted into internal reasoning information, then advise reasoning
Then be iteratively operating on Given information storehouse, the information generated every time is all put into geometric information database, until do not regenerate fresh information or
Untill it is concluded that.Its working mechanism is as shown in figure 3, main flow is as follows：
Step S1, geological information is obtained from the additional parameter condition that user mutual formula is mapped and is added；
Step S2, geological information is converted into internal reasoning information；
Step S3, internal inferencing information is made inferences using inference rule n, n initial value is 0；
Step S4, if inference rule produces new geological information, go to step S7；
Step S5, if n ＜=maximum fuzzy rules, number of regulation n add 1, go to step S3；
Step S6, if reaching fixed point, go to step S10；If not reaching fixed point, it is 0 to reset number of regulation, goes to step
Rapid S3；
Step S7, if new geological information is not present in information bank, it is deposited into information bank；Conversely, go to step S5；
Step S8, if including conclusion in fresh information, generation answer information chained list；Otherwise go to step S5；
Step S9, internal reasoning information is converted into external information, exports readable proofs；
Step S10, terminate.
By this Intelligent treatment mechanism, automated reasoning module composition basis and core of the problem generation with solving unit
The heart, added for system novel, practicality intelligent.
Courseware development tool module：Made for the ease of teacher, demonstration courseware, improve efficiency of teaching, system, which provides, to be used for
Make the courseware development tool towards solid geometry teaching.In order to reduce because of scenario objects Numerous and caused by internal memory disappear
Consumption, propose multi-page management concept：Single courseware is rearranged in order by the page of many computing independences, therefore, can be incited somebody to action
Geometric object in scene is assigned in each page, them is distributed in independent memory block, can so as to realize courseware
With property, and the consumption of internal memory is reduced to greatest extent.By designing button, for managing the broadcast state of courseware sequence,
By designing page manager, the page resource of management composition courseware, such as picture, text, video and audio etc..
Interactive Drawing unit：For realizing the interactive operation of user and geometric graphic element, by menu item, tool bar,
Operation, the users such as mouse is clicked on, mobile and input through keyboard can easily draw out three with dynamic geometry characteristic very much
Dimension space geometric figure, complete the interactive operations such as graphic attribute is set and solid is converted, measured.The Interactive Drawing list
Member supports a variety of mapping modes such as geometric construction and relation mapping, can draw point-line-surface, conic section (face), polygon, more
The geometric graphic elements such as face body, relation can be used to draw the relational graphs such as vertical line, parallel lines, midpoint, intersection point, parallel surface.
The Interactive Drawing unit supports the dynamic geometry of geometric object to include animation, variable, track, tracking, measurement
Including angle, distance, length, area, volume, variate-value, equation value, and conversion include translation, rotation, scaling, symmetrically.
Interactive Drawing unit has not only provided the user the multinomial energy such as Dynamic Drawing, graph transformation, track, tracking fully
The Critical policies of solid geometry spatial impression are showed, are also equipped with dynamic measurement, the drawing of intelligent paintbrush, relation mapping, algebraic operation, text
The important means such as this input, further improve the convenience of man-machine interaction.
Problem is generated with solving unit：For supporting user according to Interactive Drawing system, or addition additional parameter, bar
Part, conclusion guess or target call are proposed to form Solve problems, and the problem is solved using automated reasoning module, ask
Solution preocess is output to user terminal with text readable form.
It is that the intelligent solution built based on a solid geometry automated reasoning engine is demonstrate,proved that problem, which generates and solves unit,
Bright application system.When user is by Interactive Drawing, after addition additional conditions, parameter input reasoning primary condition, can propose
Conclusion is guessed or target call is to form Solve problems.Solving system can be solved to problem using automated reasoning, or
During user takes interactive secondary proof mode to carry out proposition one-step inference, system prompt and help are provided, to make
The mathematical operation that computer substitutes people's progress repeatability provides a great convenience.
During generating and solving unit using problem and carry out mechanical theorem proving, when user clicks on " reasoning " button, from
Dynamic reasoning module derives new knowledge using prospective method according to existing rule base, when reaching reasoning fixed-point, pushes away automatically
Manage module to stop continuing reasoning, then by the geological information classification storage derived into geometric information database.User can be with
According to the geological information for needing to derive in selection geometric information database of oneself, at this moment one can be ejected by then clicking on right mouse button
This information is to be listed the step of how proving out by individual window.In addition, user can also first click on, " inferencing information is set
Put " button, " conclusion " button is then clicked on, by the conclusion for manually entering the method for summit sequence number to set to be proved, finally
Click on the proof that " proof " carries out geometric proposition.Such as：Make space tetrahedron A, B, C, a D, then make the midpoint on side respectively
E, F, G, H, point E, F, G, H are sequentially connected with into a quadrangle, is now to prove E, F, G, H is parallelogram.Can first point
" reasoning " to be hit, then finds parallel information inside geometry character breath storehouse, it can be seen that there are one group of parallelogram G, F, E in the inside,
H, click right can generate proof step；It is of course also possible to " inferencing information setting " button is first clicked on, by clicking on " conclusion "
Button, parallelogram options therein is selected, then sequentially input E, F, G, the sequence number on tetra- summits of H, then click on " card
It is bright " button, E, F, G can be also generated, H is the proof step of parallelogram.
Courseware development and demonstration unit：Make or demonstrate using Interactive Drawing method and writting tool for assisted teacher
Courseware, complete preparing lessons and giving lessons for several teaching.One courseware is combined by a series of relatively independent pages, each
The page recites multiple buttons, and they distinguish the special object in corresponding page.User can control the page by clicking on button
The motion of middle object, show or hide.In order to make a complete courseware, can under same opertions engineering in create some pages
Face, every page has a main button, and it controls a string of states, and each state is made up of several actions again., can in demonstration courseware
Its automatic demonstrating again and again is allowed, wherein the time shared by each state is arbitrarily to set in advance.Page turning can also be used
The manual demonstration of key, or direct control button.In presentation process, it can at any time stop demonstrating, impromptu behaviour is carried out on picture
Make or change the content of courseware, or made according to the reaction of audience and timely illustrate or illustrate.User is using system carry out class
When part is demonstrated, the Courseware Resource of the high quality of system offer can be used to carry out aided education, oneself can also design and produce symbol
The courseware of teaching demand is closed, supports and helps to prepare lessons, giving lessons to provide.
Claims (10)
1. the intelligent tutoring system for solid geometry, it is characterised in that the system includes following three-decker：
Bottom, by discipline knowledge repository, geological information data represent, three modules of material database form, there is provided used to intermediate layer；
Intermediate layer, it is made up of geometric information database and three dynamic geometry, courseware development tool and automated reasoning modules, to contact
Bottom and application layer；The encapsulation to bottom module is completed for specific application, the base needed for each system is provided for application layer
This function；
Application layer, it is made up of, uses with solving three unit, Interactive Drawing system, courseware development and demonstration units problem generation
Exported in the input of processing user and terminal to realize man-machine interaction.
2. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：The subject knowledge
Library module is the Basic period structure in the middle school's solid geometry represented using predicate logic, including concept, the fact, theorem and public affairs
Reason, they form inference rule, are used as reasoning basis for intermediate layer automated reasoning module.
3. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：The geological information
Data representation module is using the data structure of multistage authority chained list between the classification of geometric graphic element, position, size and pel
The geological information such as relation carry out data expression；Its specific method for expressing is
(1) a parameter chained list is designed to preserve all parameters in a page, designs another geometric element authority chained list
To preserve all geometric elements, sequentially synchronized update parameter list and element list when the page updates every time；
(2) geometry element of volume authority credentials is assigned successively by dimension size, its midpoint element authority credentials is 1；Line style element authority credentials
For 2；Face type element authority credentials is 3；Type elements authority credentials is 4；Then a chained list is constructed for the geometric element of every kind of authority,
And it is the authority chained list that an authority presses low to high arrangement to combine four chained lists according to authority height；
(3) when thering is new geometric element to need to add or thering is geometric element to need to delete, it is only necessary to know that this is several
Type belonging to what element, the position then navigated to rapidly in authority chained list, then inserted or deletion action；
(4) when authority chained list searches for geometric element, chained list uses following search mechanisms, searches for since gauge outfit, if low
Searched in the geometric element of authority in child list, just do not continue search for the geometric element of high authority, if searched for less than if
By the higher leveled geometric element of sequential search authority of chained list, if searching multiple elements in the child list of same authority,
Then it is ranked up according to distance of the element from eye position, chooses one nearest from eyes.
4. a kind of middle school's solid geometry intelligent tutoring system based on electronic double board according to claim 1, its feature exist
In：The material library module is used to store the multimedia files such as picture, text, animation and video and audio, to writting tool and courseware
Make and provide basic material with demo system.
5. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：The geological information
Storehouse is divided into geometric information database and dynamic geometry part with dynamic geometry module, and wherein geometric information database uses chained list linear memory
The corresponding geological information of all figures finished is drawn in current engineering, constitutes the data basis of system；Dynamic geometry part
According to the Three-Dimensional Dynamic geometry teaching model and " programmable point " method of parametrization, computer graphical, space computational geometry skill are utilized
Art realizes that rendering for geological information in geometric information database is presented and the operation between user and geological information is interactive, and to hand over
Mutual formula Graphics System provides interactive operation interface, realizes the operation either statically or dynamically of object corresponding to geological information；It is wherein main
The OpenGL Renderings in computer graphical, space computational geometry are used to realize rendering and presenting for three-dimension space image,
Solid dynamic geometry characteristic is assigned using " programmable point " method, it concretely comprises the following steps a. and selectes parameter T constructing variable equations,
The X, Y, Z axis respective coordinates of three dimensions point are represented respectively；B. constructed variable V relevant parameters T, is corresponded to therewith；C. user's foundation
Need to change the dynamic change that variable V realizes point.
6. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：The automated reasoning
Module uses the Interconnection Inference based on prospective method, and reasoning module includes input system, inferencing information initializes, automated reasoning draws
Hold up, four parts of inference conclusion, in initial phase, the parameter that the geological information in current scene and user are added, bar
Part information is put into geometric information database and is converted into internal reasoning information, and inference rule then is iteratively operating on into Given information storehouse,
The information generated every time is all put into geometric information database, until do not regenerate fresh information or it is concluded that untill, its flow is as follows,
(1) geological information is obtained from the additional parameter condition that user mutual formula is mapped and is added；
(2) geological information is converted into internal reasoning information；
(3) internal inferencing information is made inferences using inference rule n in discipline knowledge repository, n initial value is 0；
(4) if inference rule produces new geological information, step (7) is gone to；
(5) if n ＜=maximum fuzzy rules, number of regulation n add 1, step (3) is gone to；
(6) if reaching fixed point, step (10) is gone to；If not reaching fixed point, it is 0 to reset number of regulation n, goes to step
(3)；
(7) if new geological information is not present in information bank, it is deposited into information bank；Conversely, go to step (5)；
(8) if including conclusion in fresh information, generation answer information chained list；Otherwise go to step (5)；
(9) internal reasoning information is converted into external information, exports readable proofs；
(10) terminate.
7. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：The courseware development work
Tool module uses multi-page management, and single courseware is rearranged in order by the page of many computing independences.
8. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：The Interactive Drawing
Unit, for realizing the interactive operation of user and geometric graphic element.
9. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：Described problem generate with
Solve unit, for supporting user according to Interactive Drawing system, or addition additional parameter, condition, propose conclusion guess or
Target call is solved with forming Solve problems to the problem using automated reasoning.
10. the intelligent tutoring system according to claim 1 for solid geometry, it is characterised in that：The courseware development
With demonstration unit, Interactive Drawing method and writting tool making or demonstration courseware are utilized for assisted teacher.
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| CN201710907962.9A CN107818597A (en) | 2017-09-29 | 2017-09-29 | Intelligent tutoring system for solid geometry |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111507076A (en) * | 2019-01-29 | 2020-08-07 | 北京新唐思创教育科技有限公司 | Common case courseware making method and device for teaching system and terminal |
| CN111564072A (en) * | 2020-06-09 | 2020-08-21 | 暗物智能科技(广州)有限公司 | Automatic question setting method and system for plane geometry |
| CN112215933A (en) * | 2020-10-19 | 2021-01-12 | 南京大学 | Three-dimensional solid geometry drawing system based on pen type interaction and voice interaction |
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2017
- 2017-09-29 CN CN201710907962.9A patent/CN107818597A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111507076A (en) * | 2019-01-29 | 2020-08-07 | 北京新唐思创教育科技有限公司 | Common case courseware making method and device for teaching system and terminal |
| CN111507076B (en) * | 2019-01-29 | 2022-07-05 | 北京新唐思创教育科技有限公司 | Common case courseware making method and device for teaching system and terminal |
| CN111564072A (en) * | 2020-06-09 | 2020-08-21 | 暗物智能科技(广州)有限公司 | Automatic question setting method and system for plane geometry |
| CN111564072B (en) * | 2020-06-09 | 2022-02-01 | 暗物智能科技(广州)有限公司 | Automatic question setting method and system for plane geometry |
| CN112215933A (en) * | 2020-10-19 | 2021-01-12 | 南京大学 | Three-dimensional solid geometry drawing system based on pen type interaction and voice interaction |
| CN112215933B (en) * | 2020-10-19 | 2024-04-30 | 南京大学 | Three-dimensional solid geometry drawing system based on pen type interaction and voice interaction |
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