CN108888278B - Computational thinking evaluation system based on probability model - Google Patents

Computational thinking evaluation system based on probability model Download PDF

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CN108888278B
CN108888278B CN201810399637.0A CN201810399637A CN108888278B CN 108888278 B CN108888278 B CN 108888278B CN 201810399637 A CN201810399637 A CN 201810399637A CN 108888278 B CN108888278 B CN 108888278B
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冯筠
吴浩
杨帆
何凯强
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Northwestern University
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Abstract

The invention provides a probabilistic model-based computational thinking evaluation system, which comprises a test module and an evaluation module, wherein the test module comprises 7 test sub-modules, and the 7 test sub-modules comprise a computational complexity sub-module, an abstraction sub-module, a simplification sub-module, a design sub-module, a sequencing sub-module, a search sub-module and an evaluation sub-module. The invention tests the comprehensive abilities of abstraction, design and the like, reflects the level of the calculated thinking of the testee in the whole test group through the score, combines the game and the test, has various test forms and wide applicable groups, and accurately obtains the final score of the calculated thinking by utilizing a probability integral model.

Description

Computational thinking evaluation system based on probability model
Technical Field
The invention belongs to the field of computers, and particularly relates to a computational thinking evaluation system based on a probability model.
Background
The computing thinking is helpful for people to understand natural and social phenomena; the innovation and creativity are improved; expands the thinking and provides a new method for solving the problems. In summary, it is an important and potential thinking habit that needs to be cultivated from a small scale, and many developed countries have listed computational thinking as a cultivation that is as important as mathematics and physics. The existing teenager computational thinking evaluation technology and the limitations thereof are as follows:
the existing programming game platform such as Scratch has the defects that only the program design capability is considered, and the comprehensive capabilities such as abstraction, design and the like cannot be tested; the existing thinking computing evaluation test questions have the defects of single form and uneven difficulty, the level of the thinking computing of a tested person in the whole test group cannot be reflected through scores, and the capability of the tested person in each aspect cannot be obtained; the existing cognitive model-based computational thinking evaluation technology is mainly oriented to computer professionals, involves a lot of computer professional knowledge, is complex in test and high in difficulty, and is not suitable for teenagers. The existing computational thinking evaluation technology based on the algorithm flow chart has the defects that programming capacity is still mainly considered, no specific measurement scheme is provided, and no reasonable quantitative evaluation is provided for an evaluation result.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a computational thinking evaluation system based on a probability model, and solve the problem that the evaluation result cannot be reasonably and quantitatively evaluated in the prior art.
In order to solve the technical problems, the invention adopts the following technical scheme:
a probabilistic model-based computational thought evaluation system comprising:
the test module comprises 7 test sub-modules, wherein the 7 test sub-modules are a calculation complexity sub-module, an abstraction sub-module, a simplification sub-module, a design sub-module, a sequencing sub-module, a search sub-module and an evaluation sub-module;
the computation complexity submodule constructs a decision matrix of a first-level computing power by utilizing a computation problem preset by a tester test:
Figure GDA0002459369370000021
wherein, w11Is the weight value occupied by the initial time, w12For the weight occupied by the initial problem solving number, Time1 is the Time for solving the calculation problem, and Num is the number for solving the calculation problem;
the abstract submodule tests the abstract ability of a tester through an abstract picture to construct a decision matrix of a second-level computing ability:
Figure GDA0002459369370000022
where k is a weight constant, w21Is the weight value occupied by the initial time, w22For initial problem solvingAccounting for the weight; time2 is the test Time; correct is the accuracy of judgment of the tester;
the simplification submodule solves a preset complex problem by utilizing the simplification of a tester, and constructs a decision matrix of the third-level computing power:
Figure GDA0002459369370000023
wherein, w31To solve the weight of the Time spent on the preset complex problem, Time3 is the Time for completing the preset complex problem;
the design submodule utilizes a tester to answer basic concept selection questions of preset object-oriented design to construct a decision matrix of the fourth-level computing power:
Figure GDA0002459369370000031
wherein, w41To account for the weight of the completion time, w43Weight, w, of the initial design goodness Satisfix44In order to finish the weight occupied by the Correct degree Correct of the choice question, the Time4 is the Time for finishing the basic concept choice question of the preset object-oriented design;
the sequencing submodule utilizes a tester to sequence and construct a decision matrix of fifth-level computing power:
Figure GDA0002459369370000032
wherein, w51Is the weight value occupied by the initial time, w52Time5 is the Time to complete the sorting, which is the weight occupied by the correctness of the sorting process;
the search submodule utilizes a tester to light nodes of the binary tree in a depth-first or breadth-first sequence, judges whether the lighting sequence is correct, scores Score and required Time6, and constructs a decision matrix of the sixth-level computing capacity:
Figure GDA0002459369370000033
wherein, w61Is the weight value occupied by the initial time, w62The weight is occupied by the correctness of the sequence of the nodes which are lighted;
the evaluation submodule indicates a critical path according to a preset project activity diagram by using a tester to obtain the shortest activity completion Time7, and constructs a decision matrix of the seventh-level computing capacity:
Figure GDA0002459369370000041
wherein, w71Is the weight value occupied by the initial time, w72The weight value is occupied by the correctness of the sequence of the nodes being lighted up, Act is the time for all items of the activity diagram obtained by the testee to be completed, and minAct is the shortest completion time for all activities in the activity diagram to be completed.
Further, still include the evaluation module, the evaluation module includes:
step 1, setting a fitting polynomial matrix T of the ith test submoduleiComprises the following steps:
Ti＝[Gri 3,Gri 2,Gri,1]
wherein i is 1,2,3, 7;
step 2, giving a weight matrix V ═ V1,V2,···V7]Wherein V isiRespectively by the following steps: calculating complexity, abstract ability, simplification ability, design ability, sequencing ability, searching ability, evaluation ability, and the ratio of the occurrence frequency of seven words and their similar meaning words in the related websites of the computer.
Step 3, solving a final score matrix R of the ith test submodulei：
Ri＝Ti×Vi；
Step 4, presetting 100 initial samples as an initial sample space for the ith test submodule, and obtaining a final scoring matrix RiAdding to the initial sample space to obtain a new sample space Si，SiThe score R of all different testees is contained in the ith test sub-moduleiA set of (a);
step 5, utilizing the new sample space SiFitting to obtain a score distribution function f of the ith test submodulei(x)；
Step 6, mixing fi(x) Standardisation, i.e. ordering
Figure GDA0002459369370000051
To obtain ti(0,1) obtaining a new score distribution function g of the ith test submodulei(x)；
Wherein x is an arbitrary positive number, σiFor the standard deviation, mu, of all sample values in the sample space of the ith test sub-moduleiThe average value of all sample values in the sample space of the ith test sub-module is obtained;
step 7, fitting function g of 7 testing sub-modules obtained by testingi(x) Multiplying to obtain the final scoring function
Figure GDA0002459369370000052
Figure GDA0002459369370000053
Wherein n is the number of the test sub-modules and takes a value of 7,
Figure GDA0002459369370000054
the value calculated by inputting n-7 into the gamma function;
final scoring function
Figure GDA0002459369370000055
The density function of (a) is:
Figure GDA0002459369370000056
step 8, calculating a final score Z:
Figure GDA0002459369370000057
wherein, EX2σ is the standard deviation of the argument x in the probability density function ω (x), which is the mathematical expectation of the square of the argument x in the probability density function ω (x).
Compared with the prior art, the invention has the following technical effects:
the invention tests the comprehensive abilities of abstraction, design and the like, reflects the level of the calculated thinking of the testee in the whole test group through the score, combines the game and the test, has various test forms and wide applicable groups, and accurately obtains the final score of the calculated thinking by utilizing a probability integral model.
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FIG. 1 is a diagram of an abstract face of the present invention;
FIG. 2 is a schematic diagram of the multiple disk Hanno problem;
FIG. 3 is a schematic diagram of a rectangular ordering;
FIG. 4 is an activity diagram of an item, under an embodiment;
FIG. 5 is a schematic diagram of the final scoring function of the present invention;
fig. 6 is a schematic diagram of the system architecture of the present invention.
The present invention will be explained in further detail with reference to the accompanying drawings.
Detailed Description
The following embodiments of the present invention are provided, and it should be noted that the present invention is not limited to the following embodiments, and all equivalent changes based on the technical solutions of the present invention are within the protection scope of the present invention.
Example 1:
the embodiment provides a system for evaluating computational thinking based on a probabilistic model, as shown in fig. 6, including:
the test module comprises 7 test sub-modules, wherein the 7 test sub-modules are a calculation complexity sub-module, an abstraction sub-module, a simplification sub-module, a design sub-module, a sequencing sub-module, a search sub-module and an evaluation sub-module;
the calculation complexity submodule constructs a decision matrix of the first-level calculation capacity by using a calculation problem preset by a tester test:
Figure GDA0002459369370000061
wherein, w11Is the weight value occupied by the initial time, w12For the weight occupied by the initial problem solving number, Time1 is the Time for solving the calculation problem, and Num is the number for solving the calculation problem;
the present embodiment employs a calculation problem that is not addition, subtraction, multiplication, and division in the general sense, but a process of executing an algorithm. For example, two test problems adopted in the computation complexity submodule in the embodiment are respectively:
firstly, a pond with infinite water is assumed. The volume of the existing 2 empty kettles is respectively 5 liters and 6 liters. How to get 3 litres of water from the pond using only these 2 kettles?
② five RMB coins with same size. Two by two contact requirements, what should be put?
In the embodiment, the conjugate gradient method is used for solving the unconstrained optimal equation to solve the w11＝0.67，w12＝0.33；
The abstract submodule tests the abstract ability of a tester through an abstract picture to construct a decision matrix of a second-level computing ability:
Figure GDA0002459369370000071
wherein k is a weight constant with a value of 0.65 and w21Is the weight value occupied by the initial time, w22The number of the problems is initially solved and accounts for the weight; time2 is the test Time; correct is the accuracy of judgment of the tester;
the abstract picture of this embodiment is shown in fig. 1, and the tester needs to find out the abstract eyes, nose and mouth of fig. 1. Solving unconstrained optimal equation by conjugate gradient method to obtain w21＝0.53，w22＝0.47；
The simplification sub-module solves a preset complex problem by utilizing the simplification of a tester, such as a simplification iteration process, and constructs a decision matrix of the third-level computing power:
Figure GDA0002459369370000072
wherein, w31In order to solve the preset complex problem, the Time is the weight value, specifically 1, and the Time3 is the Time for completing the preset complex problem;
in this embodiment, the time for solving a hannauta problem as shown in fig. 2 is used to judge the simplification capability of the tester, and three discs are specifically adopted for testing:
three discs are stacked on one column from bottom to top in the order of size. The disks are placed on another column again in order of size from below. Also, it is specified that the discs cannot be enlarged on a small disc, and that only one disc can be moved at a time between three columns. If a one-stage test can be completed in 100s, the subject enters a multi-disk test.
The design submodule utilizes a tester to answer basic concept selection questions of preset object-oriented design to construct a decision matrix of the fourth-level computing power:
Figure GDA0002459369370000081
wherein, w41To account for the weight of the completion time, w43Weight, w, of the initial design goodness Satisfix44In order to finish the weight occupied by the Correct degree Correct of the choice question, the Time4 is the Time for finishing the basic concept choice question of the preset object-oriented design;
the basic concept of the object-oriented design of the present embodiment, for example: class, package, relationship between classes (is a, hasa), inheritance, polymorphism, etc. The user may create various types of classes. Thereafter, the properties and methods are dragged into the corresponding class. Users can also create classes such as is a, has a, inheritance between classesThe relationship (2) of (c). The user has great autonomy. In the description of the problem, it may be explicitly pointed out that those concepts are used, such as: the A class and the B class have an is a relation, the A class and the B class have inheritance, and certain attribute belongs to the class A, and the like, so that the concept is tested. And obtaining a decision matrix of the fourth-layer hierarchical computing capability of the tested person according to the correctness Correct of the selected question, the quality Satisconfiguration of the design and the completion Time 4. Wherein, w41＝0.32，w43＝0.48，w44＝0.20。
The sequencing submodule utilizes a tester to sequence and construct a decision matrix of fifth-level computing power:
Figure GDA0002459369370000091
wherein, w51Is the weight value occupied by the initial time, w52Time5 is the Time to complete the sorting, which is the weight occupied by the correctness of the sorting process;
the sorting problem adopted in this embodiment is as shown in fig. 3, a group of strips with different heights and disorder is randomly generated at first, and a tester changes the positions by dragging according to a required sorting algorithm, so that the strips are finally ordered. The decision matrix of the fifth-level computing power of the tested person is obtained through the correctness Correct and the completion Time5 of the sorting process.
Wherein, w51＝0.45，w52＝0.55；
The search submodule utilizes a tester to light nodes of the binary tree in a depth-first or breadth-first sequence, judges whether the lighting sequence is correct, scores Score and required Time6, and constructs a decision matrix of the sixth-level computing capacity:
Figure GDA0002459369370000092
wherein, w61Is the weight value occupied by the initial time, w62The weight is occupied by the correctness of the sequence of the nodes which are lighted; in this example w61＝0.27，w62＝0.73；
The evaluation submodule indicates a critical path according to a preset project activity diagram by using a tester to obtain the shortest activity completion Time7, and constructs a decision matrix of the seventh-level computing capacity:
Figure GDA0002459369370000093
wherein, w71Is the weight value occupied by the initial time, w72The weight value is the weight value occupied by the correctness of the sequence of the nodes being lighted, the time for completing all the items of the activity diagram obtained by the testee, and minAct is the shortest completion time for completing all the activities in the activity diagram.
The project activity diagram used in this embodiment is shown in fig. 4, and the tester needs to point out the critical path according to the given activity diagram (see fig. four, a project activity diagram) and propose which activities should be added with resources if the time consumption is to be reduced. According to the Time spent by the tested person and the obtained new activity resource map, comparing the shortest activity completion Time Time7 to obtain a decision matrix of the sixth layer level computing capability of the tested person; wherein, w71＝0.58，w72＝0.42。
This embodiment still includes the evaluation module, the evaluation module includes:
step 1, setting a fitting polynomial matrix T of the ith test submoduleiComprises the following steps:
Ti＝[Gri 3,Gri 2,Gri,1]
wherein i is 1,2,3, 7;
step 2, giving a weight matrix V ═ V1,V2,···V7]Wherein V isiBy crawling computer-related website content, according to: calculating complexity, abstract capability, simplification capability, design capability, sequencing capability, search capability and evaluation capability; the ratio of the occurrence frequencies of the seven words and the similar meaning words. It has a specific value of
V＝[0.1360,0.0446,0.3111,0.1214,0.0566,0.0951,0.2352]；
Step (ii) of3, solving a final score matrix R of the ith test submodulei：
Ri＝Ti×Vi；
Step 4, presetting 100 initial samples as an initial sample space for the ith test submodule, and obtaining a final scoring matrix RiAdding to the initial sample space to obtain a new sample space Si，SiThe score R of all different testees is contained in the ith test sub-moduleiA set of (a);
step 5, utilizing the new sample space SiFitting to obtain a score distribution function f of the ith test submodulei(x)；
Step 6, mixing fi(x) Standardisation, i.e. ordering
Figure GDA0002459369370000111
To obtain ti(0,1) obtaining a new score distribution function g of the ith test submodulei(x)
Wherein x is an arbitrary positive number, σiFor the standard deviation, mu, of all sample values in the sample space of the ith test sub-moduleiThe average value of all sample values in the sample space of the ith test sub-module is obtained; step 7, fitting function g of 7 testing sub-modules obtained by testingi(x) Multiplying to obtain the final scoring function
Figure GDA0002459369370000112
Figure GDA0002459369370000113
Wherein n is the number of the test sub-modules and takes a value of 7,
Figure GDA0002459369370000114
the value calculated by inputting n-7 into the gamma function;
final scoring function
Figure GDA0002459369370000115
Is close toThe degree function is:
Figure GDA0002459369370000116
step 8, calculating a final score Z:
Figure GDA0002459369370000117
wherein, EX2σ is the standard deviation of the argument x in the probability density function ω (x), which is the mathematical expectation of the square of the argument x in the probability density function ω (x).
In this embodiment, there are a total of 7 test sub-modules, each contributing a variable component, so EX2The final score Z was obtained as 7. (in this example take
Figure GDA0002459369370000121
)。

Claims (2)

1. A system for computational thought evaluation based on a probabilistic model, comprising:
the test module comprises 7 test sub-modules, wherein the 7 test sub-modules are a calculation complexity sub-module, an abstraction sub-module, a simplification sub-module, a design sub-module, a sequencing sub-module, a search sub-module and an evaluation sub-module;
the computation complexity submodule constructs a decision matrix of a first-level computing power by utilizing a computation problem preset by a tester test:
Figure FDA0002459369360000011
wherein, w11Is the weight value occupied by the initial time, w12For the weight occupied by the initial problem solving number, Time1 is the Time for solving the calculation problem, and Num is the number for solving the calculation problem;
the abstract submodule tests the abstract ability of a tester through an abstract picture to construct a decision matrix of a second-level computing ability:
Figure FDA0002459369360000012
where k is a weight constant, w21Is the weight value occupied by the initial time, w22The number of the problems is initially solved and accounts for the weight; time2 is the test Time; correct is the accuracy of judgment of the tester;
the simplification submodule solves a preset complex problem by utilizing the simplification of a tester, and constructs a decision matrix of the third-level computing power:
Figure FDA0002459369360000013
wherein, w31To solve the weight of the Time spent on the preset complex problem, Time3 is the Time for completing the preset complex problem;
the design submodule utilizes a tester to answer basic concept selection questions of preset object-oriented design to construct a decision matrix of the fourth-level computing power:
Figure FDA0002459369360000021
wherein, w41To account for the weight of the completion time, w43Weight, w, of the initial design goodness Satisfix44In order to finish the weight occupied by the Correct degree Correct of the choice question, the Time4 is the Time for finishing the basic concept choice question of the preset object-oriented design;
the sequencing submodule utilizes a tester to sequence and construct a decision matrix of fifth-level computing power:
Figure FDA0002459369360000022
wherein, w51Is the weight value occupied by the initial time, w52In order to take the weight of the correctness of the sorting process,time5 is the Time to complete the sort;
the search submodule utilizes a tester to light nodes of the binary tree in a depth-first or breadth-first sequence, judges whether the lighting sequence is correct, scores Score and required Time6, and constructs a decision matrix of the sixth-level computing capacity:
Figure FDA0002459369360000023
wherein, w61Is the weight value occupied by the initial time, w62The weight is occupied by the correctness of the sequence of the nodes which are lighted;
the evaluation submodule indicates a critical path according to a preset project activity diagram by using a tester to obtain the shortest activity completion Time7, and constructs a decision matrix of the seventh-level computing capacity:
Figure FDA0002459369360000024
wherein, w71Is the weight value occupied by the initial time, w72The weight value is occupied by the correctness of the sequence of the nodes being lighted up, Act is the time for all items of the activity diagram obtained by the testee to be completed, and minAct is the shortest completion time for all activities in the activity diagram to be completed.
2. The probabilistic model-based computational thought evaluation system of claim 1 further comprising an evaluation module, the evaluation module comprising:
step 1, setting a fitting polynomial matrix T of the ith test submoduleiComprises the following steps:
Ti＝[Gri 3,Gri 2,Gri,1]
wherein i is 1,2,3, 7;
step 2, giving a weight matrix V ═ V1,V2,…V7]Wherein V isiRespectively by the following steps: computational complexity, abstraction capability, simplification capability, design capability, sequencing capability, searchThe retrieval ability and the evaluation ability are obtained by the ratio of the occurrence frequency of seven words and similar meaning words thereof in the related websites of the computer;
step 3, solving a final score matrix R of the ith test submodulei：
Ri＝Ti×Vi；
Step 4, presetting 100 initial samples as an initial sample space for the ith test submodule, and obtaining a final scoring matrix RiAdding to the initial sample space to obtain a new sample space Si，SiThe score R of all different testees is contained in the ith test sub-moduleiA set of (a);
step 5, utilizing the new sample space SiFitting to obtain a score distribution function f of the ith test submodulei(x)；
Step 6, mixing fi(x) Standardisation, i.e. ordering
Figure FDA0002459369360000031
To obtain ti(0,1) obtaining a new score distribution function g of the ith test submodulei(x)；
Wherein x is an arbitrary positive number, σiFor the standard deviation, mu, of all sample values in the sample space of the ith test sub-moduleiThe average value of all sample values in the sample space of the ith test sub-module is obtained;
step 7, fitting function g of 7 testing sub-modules obtained by testingi(x) Multiplying to obtain the final scoring function
Figure FDA0002459369360000041
Figure FDA0002459369360000042
Wherein n is the number of the test sub-modules and takes a value of 7,
Figure FDA0002459369360000043
to change n to 7 input gamma functionThe value obtained by the calculation in (1);
final scoring function
Figure FDA0002459369360000044
The density function of (a) is:
Figure FDA0002459369360000045
step 8, calculating a final score Z:
Figure FDA0002459369360000046
wherein, EX2σ is the standard deviation of the argument x in the probability density function ω (x), which is the mathematical expectation of the square of the argument x in the probability density function ω (x).
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