CN107203582A - A kind of smart group topic method based on item response theory analysis result - Google Patents
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Abstract
Method is inscribed the invention discloses a kind of smart group based on item response theory analysis result, grasping probability according to student knowledge point carries out smart group topic, and smart group topic comprises the following steps:Step one, it is determined that the knowledge point of required exercise;Step 2, determines that student's is topic total quantity N;Step 3, it is determined that topic quantity is done in each knowledge point;Step 4, it is determined which topic each knowledge point chooses.The present invention evaluates the probability that user grasps for knowledge point according to Item Response Pattern principle, and probability progress targetedly smart group topic is grasped according to student knowledge point, take into full account that student's personal knowledge point grasps the indexs such as situation, learning ability, study wish, answer speed, for different individual students, the control item difficulty of science, topic quantity, to setting a question for student individuality, the resistance mood in students'learning is reduced, and lift the results of learning of student.
Description
Technical field
Method is inscribed the present invention relates to on-line study group.
Background technology
With the development of network, study and the network of user are closely linked.Many schools and educational institution all design
Online teaching and Test System, but traditional group topic method, fully rely on and are randomly selected in exam pool, it is impossible to for difference
User, accomplish objective targetedly group topic.
The content of the invention
The technical problems to be solved by the invention are just to provide a kind of smart group based on item response theory analysis result
The on-line study data of user are analyzed by topic method according to item response theory, and grasp probability according to student knowledge point
Targetedly smart group is carried out to inscribe.
In order to solve the above technical problems, the present invention is adopted the following technical scheme that:One kind analyzes knot based on item response theory
The smart group topic method of fruit, grasps probability according to student knowledge point and carries out smart group topic, student knowledge point is grasped probability or adopted
Diagnostic result is provided automatically with being manually entered, or by system;
System automatic evaluation user is P (θ)=1/ (1+e^ (b- θ)), θ for the probability calculation formula that the knowledge point is grasped
The ability parameter of evaluation user is represented, b represents the degree-of-difficulty factor of each topic, θ and b value preset or calculated
Go out, e=2.71828;
Smart group topic comprises the following steps:
Step one, it is determined that the knowledge point of required exercise, method has two kinds, one kind is to manually select, and one kind is that system is automatic
Selection, system selects knowledge point according to the priority of knowledge point, and once at most selects 5 knowledge points, the knowledge of required exercise
Point priority orders are as follows:A1>A2>B>C1>C2,
A1 is that probability is grasped in knowledge point<75% and the knowledge point under topic do topic number be 0-30,
A2 is that probability is grasped in knowledge point<75% and the knowledge point under topic do topic number be>30,
B is that inscience point grasps probability data and practises data without the knowledge point,
It is 0-30 that C1, which is that knowledge point grasps topic under probability >=75% and the knowledge point to do topic number,
C2 is that knowledge point grasps topic under probability >=75% and the knowledge point and does topic number and is>30;
Step 2, determines that student's is topic total quantity N, either manually selects or calculated automatically by system;
Step 3, it is determined that topic quantity is done in each knowledge point;
When probability >=75% is grasped in certain knowledge point, the knowledge point topic radix is N/n+1;
When probability 50%-75% is grasped in certain knowledge point, the knowledge point topic radix is inscribed for N/n;
When probability is grasped in certain knowledge point<When 50%, the knowledge point at least 1 is inscribed;
N represents this knowledge points for needing to practise, and n is either manually selected or system is calculated automatically, when N/n can not
Rounded up when dividing exactly, when the knowledge point of required exercise adds up to group topic number<During N, by knowledge point priority from high to low according to
Secondary addition 1 is inscribed, until the minimum topic number of operation is met, when the knowledge point of required exercise adds up to group topic number>N, by knowledge point by
It is low to high to delete 1 topic successively, until meeting operation topic number requirement;
Step 4, it is determined which topic each knowledge point chooses, wherein, the derivative topic accounting of personal fallibility topic is
70%, the new topic under the knowledge point accounts for 30%.
Preferably, in step one, when the knowledge points of same priority are no more than 5, choosing next preferential
The knowledge point of level, when the knowledge point quantity of same priority is more than 5:The priority of A1, C1 same type is true by probability is grasped
Recognize priority, grasp probability more low priority higher;The priority of A2, C2 same type confirms priority by topic quantity is done, and inscribes
Quantity is lower, and priority is higher, as topic quantity it is identical when priority by grasp probability arrange from low to high.
Preferably, in step 2 system calculate student automatically be topic total quantity N, N=Nmin+ X, X span is
(0, Nmax- Nmin), Nmax、NminPreset or give tacit consent to Nmax=8, Nmin=0, X are according to student's subject knowledge ability, study
Wish, do topic speed to student carry out classification determination,
Subject knowledge ability is determined that θ values are bigger to represent that subject knowledge ability is stronger by θ values;
Study wish choose student do topic quantity be measurement index, student do topic quantity it is more, study wish it is stronger;Do
Topic speed is determined that the smaller topic speed of doing of ratio is got over by the ratio for doing topic total duration and doing topic quantity of all topics under knowledge point
It hurry up;
Respectively by the learning knowledge ability of student by weak, learning wish by weak, doing topic speed by force and existing from fast to slow by force
The whole nation is ranked up, when ranking be in the whole nation preceding 33.33%, learning ability, study wish, do inscribe speed be defined as in, in,
In;When ranking be in the whole nation in the middle of 33.33%, learning ability, study wish, do topic speed be defined as it is low, low, slow;Work as ranking
33.33% behind the whole nation, learning ability, study wish, do topic speed be defined as it is low, low, slow.
Preferably, for each topic of the knowledge point, unified degree-of-difficulty factor mark is preset to full platform user
Standard, the degree-of-difficulty factor of each topic is preset, or is determined according to sampling results, and sampling determination method comprises the following steps:
Step one, student's sample is chosen;
Step 2, the student's sample extracted according to every problem, calculates the average accuracy of every problem, to accuracy most
Low PminItem difficulty coefficient be entered as 1, accuracy highest PmaxItem difficulty coefficient be entered as 0.01, and for accuracy
The method determined for m item difficulty coefficient is K=1- (1-0.01) (m-Pmin)/(Pmax-Pmin)。
Preferably, θ computational methods are:Nearest 30 topic in the knowledge point is chosen, calculating ln, (the positive exact figures of answer/answer is wrong
Miss number), when the positive exact figures of answer are 0 or answer error number is 0, the positive exact figures of answer or answer error number use correction value 0.5.
The technical solution adopted by the present invention, the probability that user grasps for knowledge point is evaluated according to Item Response Pattern principle, and
According to student knowledge point grasp probability carry out targetedly smart group inscribe, taken into full account student's personal knowledge point grasp situation,
The indexs such as learning ability, study wish, answer speed, for different individual students, control item difficulty, the topic number of science
Amount, to setting a question for student individuality, reduces the resistance mood in students'learning, and lift the results of learning of student.
Embodiment
The invention provides a kind of smart group topic method analyzed based on big data, entered according to student knowledge point diagnostic result
Row smart group is inscribed, and student knowledge point diagnostic result, which either uses to be manually entered or calculated automatically by system, provides diagnostic result.
Student knowledge point diagnostic result is manually entered assignment, generally teacher by the keeper with corresponding authority, the religion
The study situation of teacher's students ', involved below to be manually entered assignment also identical.
Certainly, the teacher can also determine that student knowledge point is diagnosed according to the study big data analysis result of student in the past
As a result.
System provides diagnostic result automatically, carries out big data analysis according to item response theory, or Item Response Pattern is managed
Analysis calculating is carried out by being combined with the R values of forgetting curve.
Item response theory (Item Response Theory, IRT) is a series of general name of Psychological Statistics models, is
What the limitation for classical testing (Classical Test Theory, abbreviation CTT) put forward.IRT is for analyzing
The mathematical modeling of total marks of the examination or survey data, the targets of these models is come the potential psychological characteristics that determines
Whether (latent trait) can be reflected by test question, and the interactive pass between test question and testee
System.
The links of teaching are implemented in modern distance education based on computer network, have the level of IT application high
Feature.This special teaching environment is very beneficial for Item Response Pattern principle (also known as IRT, Item Response Theory) hair
Advantage is waved, is improved the quality of teaching.
Forgetting curve finds that this curve tells people by German psychologist Chinese mugwort guest great this (H.Ebbinghaus) research
Forgetting in study be it is regular, the process of forgetting quickly, and first quick and back slow.
The R values of P (θ) and forgetting curve below in conjunction with the 1PL models of Item Response Pattern principle (IRT) are calculated, right
Grasp situation and diagnosed in the knowledge point of platform user.
A kind of embodiment 1, on-line study knowledge point diagnostic method, comprises the following steps:
Step one, the probability that evaluation user grasps for the knowledge point, calculation formula is P (θ)=1/ (1+e^ (b- θ)),
Wherein, θ represents to evaluate the ability parameter of user, and b represents the degree-of-difficulty factor of each topic, and e is constant 2.71828;
Wherein, for the knowledge point, b uses standard degree-of-difficulty factor, refers to for full platform user, by quantitative with determining
Property research method, analyze determine unified degree-of-difficulty factor standard.
According to the exercise cumulative data of full platform mass users, with reference to per pass topic accuracy (per pass topic it is correct
Rate is using the average accuracy of (counties and districts) in all parts of the country, the influence to reduce teaching level difference in area's in all parts of the country, Jin Erbao
Card standard degree-of-difficulty factor is for versatility and reasonability in all parts of the country), according to the statistical analysis technique of science, to item difficulty
Coefficient carry out assignment (to all parts of the country using proportioning sampling, composition item difficulty evaluation sample, according to accuracy it is minimum with it is correct
Rate highest carries out difficulty assignment to defining difficulty highest coefficient and the minimum coefficient of difficulty, and to per pass topic).Specifically include as follows
Step:
The methods of sampling is carefully stated:The problem of studying first is the average accuracy of topic a area students in all parts of the country, regional level
Not Wei counties and districts, estimation error is gone out no more than 0.5%, and with 95% confidence level.
UtilizeConfirmatory sample size, wherein d are the estimation error 0.5% allowed, α=1-
95%=0.05, Za/2By looking into standard, just too distribution table is being obtained, upside area α/2=0.05/2=0.025, then corresponding Z values
Z0.025=1.96, π are the accuracy of the national topic determined according to history answer data.The problem student is answered according to various regions
Ratio-dependent sample in sample number of students (the sample number * of the sample number=determination in each area that need to randomly select of this area
(all number of student of the number of student that this area is answered a question/the answer problem)), final composition research sample.
The above-mentioned methods of sampling is a kind of citing, naturally it is also possible to use other existing methods of samplings, herein no longer
Repeat one by one.For purposes of the invention, it is prior to also reside according to sampling results, the method for carrying out degree-of-difficulty factor assignment.
Degree-of-difficulty factor assignment method:The student's sample extracted according to every problem, can calculate the average correct of every problem
Rate.(P minimum to accuracymin) item difficulty coefficient be entered as 1, accuracy highest (Pmax) item difficulty coefficient be entered as
0.01, it is K=1- (1-0.01) (m-P for the method that the item difficulty coefficient that accuracy is m is determinedmin)/(Pmax-Pmin)。
In addition, the degree-of-difficulty factor of topic is monthly updated.
θ computational methods are:Influence for reduction history capabilities to newest ability, while Evaluation in Support Ability is accurate
Property, choose 30 topics that the knowledge point practises recently, calculate ln (the positive exact figures of answer/answer error number), when the positive exact figures of answer be 0 or
When person's answer error number is 0, the positive exact figures of answer or answer error number use correction value 0.5.Of course for the accuracy for ensureing θ,
It can also select to choose more than the nearest topic of exercise 30 in the knowledge point even more many topics.
Step 2, evaluation user is for the memory degree of the knowledge point, and calculation formula is R=e^ (- t/s), wherein, t is
Using day as the time interval of base unit, s is memory intensity, and e is constant 2.71828;
S computational methods are, each initial s=1 in knowledge point, and s minimum 1, and Exercise Answer Key is correct, then the topic is direct
With the s=s+1 of mediate knowledge point, Exercise Answer Key mistake, immediate knowledge point s=s-1, mediate knowledge point s=s- (1-0.2n), n
To be separated by level, n between the mediate knowledge point and immediate knowledge point>N is considered as 5 when 5.
Immediate knowledge point refers to the knowledge point with the topic direct correlation, and mediate knowledge point refers to related to the knowledge point of the topic
The knowledge point of connection.Because knowledge point and knowledge point are not separate, there are priority or father and son's level relation, student is learned
All knowledge points be to be associated with one another between network relation, knowledge point.For example multiplication and division hybrid operation belongs to sub- level and known
Point is known, four fundamental rules hybrid operation belongs to parent knowledge point, when a student has practiced the topic of a multiplication and division hybrid operation, but simultaneously
Four fundamental rules hybrid operation is also indirectly practised, because including multiplication and division hybrid operation inside four fundamental rules hybrid operation, at this moment
Multiplication hybrid operation is immediate knowledge point, and four fundamental rules hybrid operation is mediate knowledge point.The phase of mediate knowledge point and immediate knowledge point
Interlayer level refer in the graph of a relation of knowledge point, between be separated by several knowledge points, the association depth of lower two knowledge points of level is bigger,
Level is bigger, and the association depth of two knowledge points is smaller.
T computational methods are, t=current dates-memory time, when a problem does correct, the immediate knowledge point of the topic
With the date of memory time of mediate knowledge point=topic exercise, that is, exact date when answering questions the topic.
Initial R=0 of each knowledge point, daily (morning) recalculates R, when a problem does correct, the topic it is direct
Knowledge point and the R=1 of mediate knowledge point.
Step 3, calculates P (θ) * R in real time, and when result is more than or equal to 0.75, the user knowledge point is up to standard, otherwise does not reach
Mark.
Why 75% is determined, one is the analysis for combining specific answer data and representative student, while also using
Expert interviewing, i.e., the opinion of experienced teacher.
It is of course also possible to not consider the R values of forgetting curve, directly according to calculation formula P (θ)=1/ (1+e^ (b- θ)), really
Determine student knowledge point and grasp probability, this probability is student knowledge point diagnostic result.
Embodiment 2, is with the difference of embodiment 1, further, to each difficulty section topic, randomly drawing sample,
Degree-of-difficulty factor is on the basis of statistic analysis result, by expert evaluation, final to determine, it is ensured that the objective standard of item difficulty coefficient
Really.That is the degree-of-difficulty factor of expert's rule of thumb difficulty highest topic clear and definite first, then according to abundant experience with students, to indivedual
Topic is tested.
Embodiment 3, is with the difference of Examples 1 and 2, expert evaluation result and statistical analysis assigned result is carried out comprehensive
Close, it is determined that final degree-of-difficulty factor b=0.5* accumulations data results+0.5* expert's difficulty assignment per each and every one topic.
Determine after student knowledge point diagnostic result that system can be carried out smart group and inscribe according to the above method.
The method inscribed below in conjunction with embodiment to smart group is described as follows:
Step one, it is determined that the knowledge point of required exercise, method has two kinds, one kind is to manually select, and one kind is that system is automatic
Selection, teacher can determine the knowledge point for needing to practise according to the grasp number of each knowledge point class, and system is according to knowledge point
Priority selects knowledge point, and once 5 knowledge points of most selections,
The knowledge point priority orders of required exercise are as follows:A1>A2>B>C1>C2,
A1 is that probability is grasped in knowledge point<75% and the knowledge point under topic do topic number be 0-30,
A2 is that probability is grasped in knowledge point<75% and the knowledge point under topic do topic number be>30,
B is that inscience point grasps probability data and practises data without the knowledge point,
It is 0-30 that C1, which is that knowledge point grasps topic under probability >=75% and the knowledge point to do topic number,
C2 is that knowledge point grasps topic under probability >=75% and the knowledge point and does topic number and is>30;
When the knowledge points of same priority are no more than 5, the knowledge point of next priority is chosen, when same preferential
When the knowledge point quantity of level is more than 5:The priority of A1, C1 same type confirms priority by probability is grasped, and grasps probability lower
Priority is higher;The priority of A2, C2 same type by do topic quantity confirm priority, do topic quantity it is lower, priority is higher, when
Do topic quantity it is identical when priority by grasp probability arrange from low to high.
Step 2, determines that student's is topic total quantity N, either manually selects or calculated automatically by system;
System calculates doing for student and inscribes total quantity N, N=N automaticallymin+ X, X span are (0, Nmax- Nmin), Nmax、
NminPreset or give tacit consent to Nmax=8, Nmin=0,
X according to student's subject knowledge ability, study wish, do topic speed to student carry out classification determination,
Subject knowledge ability is determined that θ values are bigger to represent that subject knowledge ability is stronger by θ values;
Study wish choose student do topic quantity be measurement index, student do topic quantity it is more, study wish it is stronger;
Do topic speed and determine that ratio is smaller to be done by the ratio for doing topic total duration and doing topic quantity of all topics under knowledge point
Inscribe speed faster;
Respectively by the learning knowledge ability of student by weak, learning wish by weak, doing topic speed by force and existing from fast to slow by force
The whole nation is ranked up, when ranking be in the whole nation preceding 33.33%, learning ability, study wish, do inscribe speed be defined as in, in,
In;When ranking be in the whole nation in the middle of 33.33%, learning ability, study wish, do topic speed be defined as it is low, low, slow;Work as ranking
33.33% behind the whole nation, learning ability, study wish, do topic speed be defined as it is low, low, slow.
Step 3, it is determined that topic quantity is done in each knowledge point;
When probability >=75% is grasped in certain knowledge point, the knowledge point topic radix is N/n+1;
When probability 50%-75% is grasped in certain knowledge point, the knowledge point topic radix is inscribed for N/n;
When probability is grasped in certain knowledge point<When 50%, the knowledge point at least 1 is inscribed;
N represents this knowledge points for needing to practise, and n is either manually selected or system is calculated automatically, when N/n can not
Rounded up when dividing exactly, when the knowledge point of required exercise adds up to group topic number<During N, by knowledge point priority from high to low according to
Secondary addition 1 is inscribed, until the minimum topic number of operation is met, when the knowledge point of required exercise adds up to group topic number>N, by knowledge point by
It is low to high to delete 1 topic successively, until meeting operation topic number requirement;
Step 4, it is determined which topic each knowledge point chooses, wherein, the derivative topic accounting of personal fallibility topic is
70%, the new topic under the knowledge point accounts for 30%.
Before intelligence is set a question every time, the foundation that P (θ) * R are inscribed as smart group is recalculated.
In addition to above preferred embodiment, the present invention also has other embodiments, and those skilled in the art can be according to this
Invention is variously modified and deformed, and without departing from the spirit of the present invention, all should belong in claims of the present invention and determine
The scope of justice.
Claims (5)
1. a kind of smart group topic method based on item response theory analysis result, it is characterised in that slapped according to student knowledge point
Hold probability and carry out smart group topic, student knowledge point grasp probability, which is either used, to be manually entered or provide diagnosis automatically by system
As a result;
The probability calculation formula that system automatic evaluation user grasps for the knowledge point is P (θ)=1/ (1+e^ (b- θ)), and θ is represented
The ability parameter of user is evaluated, b represents the degree-of-difficulty factor of each topic, θ and b value preset or calculated, e=
2.71828;
Smart group topic comprises the following steps:
Step one, it is determined that the knowledge point of required exercise, method has two kinds, one kind is to manually select, and one kind is that system is automatically selected,
System selects knowledge point according to the priority of knowledge point, and once at most selects 5 knowledge points, and the knowledge point of required exercise is preferential
Level order is as follows:A1>A2>B>C1>C2,
A1 is that probability is grasped in knowledge point<75% and the knowledge point under topic do topic number be 0-30,
A2 is that probability is grasped in knowledge point<75% and the knowledge point under topic do topic number be>30,
B is that inscience point grasps probability data and practises data without the knowledge point,
It is 0-30 that C1, which is that knowledge point grasps topic under probability >=75% and the knowledge point to do topic number,
C2 is that knowledge point grasps topic under probability >=75% and the knowledge point and does topic number and is>30;
Step 2, determines that student's is topic total quantity N, either manually selects or calculated automatically by system;
Step 3, it is determined that topic quantity is done in each knowledge point;
When probability >=75% is grasped in certain knowledge point, the knowledge point topic radix is N/n+1;
When probability 50%-75% is grasped in certain knowledge point, the knowledge point topic radix is inscribed for N/n;
When probability is grasped in certain knowledge point<When 50%, the knowledge point at least 1 is inscribed;
N represents this knowledge points for needing to practise, and n is either manually selected or system is calculated automatically, when N/n can not divide exactly
When round up, when required exercise knowledge point add up to group topic a number<During N, add successively from high to low by the priority of knowledge point
Plus 1 and inscribe, until the minimum topic number of operation is met, when the knowledge point of required exercise adds up to a group topic number>N, by knowledge point by it is low to
It is high to delete 1 topic successively, until meeting operation topic number requirement;Step 4, it is determined which topic each knowledge point chooses, wherein, it is individual
The derivative topic accounting of people's fallibility topic is that the new topic under 70%, the knowledge point accounts for 30%.
2. a kind of smart group topic method based on item response theory analysis result according to claim 1, its feature exists
In:In step one, when the knowledge points of same priority are no more than 5, the knowledge point of next priority is chosen, when same
When the knowledge point quantity of one priority is more than 5:The priority of A1, C1 same type confirms priority by probability is grasped, and grasps general
Rate more low priority is higher;The priority of A2, C2 same type by do topic quantity confirm priority, do topic quantity it is lower, priority
It is higher, as topic quantity it is identical when priority by grasp probability arrange from low to high.
3. a kind of smart group topic method based on item response theory analysis result according to claim 1, its feature exists
In:System calculates doing for student and inscribes total quantity N, N=N automatically in step 2min+ X, X span are (0, Nmax- Nmin),
Nmax、NminPreset or give tacit consent to Nmax=8, Nmin=0, X according to student's subject knowledge ability, learn wish, do topic speed
Classification determination is carried out to student,
Subject knowledge ability is determined that θ values are bigger to represent that subject knowledge ability is stronger by θ values;
Study wish choose student do topic quantity be measurement index, student do topic quantity it is more, study wish it is stronger;Do topic speed
Spend and determined by the ratio for doing topic total duration and doing topic quantity of all topics under knowledge point, ratio is smaller, and to do topic speed faster;
Respectively by the learning knowledge ability of student by weak, learning wish by weak, doing topic speed from fast to slow in the whole nation by force by force
Be ranked up, when ranking be in the whole nation preceding 33.33%, learning ability, study wish, do inscribe speed be defined as in, in, in;When
Ranking be in the whole nation in the middle of 33.33%, learning ability, study wish, do topic speed be defined as it is low, low, slow;When ranking is in entirely
33.33% after state, learning ability, study wish, do topic speed be defined as it is low, low, slow.
4. a kind of smart group topic side based on item response theory analysis result according to claims 1 to 3 any one
Method, it is characterised in that:For each topic of the knowledge point, unified degree-of-difficulty factor standard is preset to full platform user,
The degree-of-difficulty factor of each topic is preset, or is determined according to sampling results, and sampling determination method comprises the following steps:
Step one, student's sample is chosen;
Step 2, the student's sample extracted according to every problem calculates the average accuracy of every problem, minimum to accuracy
PminItem difficulty coefficient be entered as 1, accuracy highest PmaxItem difficulty coefficient be entered as 0.01, and be for accuracy
The method that m item difficulty coefficient is determined is K=1- (1-0.01) (m-Pmin)/(Pmax-Pmin)。
5. a kind of smart group topic method based on item response theory analysis result according to claim 1, its feature exists
In:θ computational methods are:Choose the knowledge point it is nearest 30 topic, calculate ln (the positive exact figures of answer/answer error number), when answer just
When exact figures are 0 or answer error number is 0, the positive exact figures of answer or answer error number use correction value 0.5.
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