JP2007041179A - Method for evaluating answer to math examination - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce the burden of a creator in creating description type examinations by making a correct solution to be automatically generated from a examination, by making it possible to make correct/incorrect judgement even when the arrangement of character strings in the correct solution is different from that in the answer, and by making it sufficient to prepare only one correct solution even when there exist several ways to describe the correct solution. <P>SOLUTION: A method for evaluating an answer to a math examination comprises: an examination generation means for generating a description type math examination on a computer; a correct solution generation means for generating just one solution to the examination; an examination display means for displaying the examination; an answer input means for a user to input an answer; a correct/incorrect judgement means which recognizes the correct solution and the answer, and calculates and compare the results of assigning a numeric value to the correct solution and to the answer; and a judgement result display means for displaying the result in the correct/incorrect judgement means. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for evaluating a correct answer of a mathematical description formula calculation problem using a computer and a user's answer, and particularly in the case of an integer coefficient polynomial, a rational coefficient polynomial, a rational function, and a standard mathematical function other than a polynomial. It is related to a method of performing correct / incorrect determination of answer and answer by substituting a certain numerical value.

  In recent years, IT technology such as the Internet in the education field has been developed, and the introduction of classes using computers has been increasing.

  In a descriptive exercise with correct / incorrect judgment using a conventional computer, the creator of the exercise creates not only a problem but also a correct answer and a solution. Further, when there are a plurality of different solutions and correct solutions, it is necessary to register all the different solutions and solutions as correct data in advance. For example, in a learning support apparatus having a correct / incorrect judgment function between correct answer data and answer data, if the answer of the answerer is determined to be correct by correct / incorrect judgment, and the answer content is different from the other answer data, Register the contents as a model answer to the server. Thus, Patent Document 1 discloses a technique that can provide information on a solution without preparing the solution data in advance by the creator.

In addition, a program or program that divides numerical values and character strings handled in questions such as exercises into units that can be changed and places them on spreadsheet software cells, and changes the numerical values and character strings in question according to pattern values. In a learning device that has a program that gives an answer to a question and a program that evaluates the answer value by matching the answer value with the answer, if the mathematical problem is assigned to the left side and the answer field is assigned to the right side, the answer value is between cells on the left side. It is calculated by the following equation. Further, Patent Document 2 discloses a technique that allows a single exercise problem to be changed into several patterns and repeatedly learned by setting up a formula change program corresponding to a cell.
JP 2004-093915 A Japanese Patent Laid-Open No. 2005-084405

  However, as described above, in a descriptive exercise with correct / incorrect judgment using a conventional computer as described above, in order to make correct / incorrect correct / incorrect answers, the creator must create not only the problem but also the correct answer / solution. It was. When there are a plurality of correct answers and solutions, it is necessary to register all correct answers and solutions in the server in advance, which increases the burden on the creator.

  In addition, since the correct / incorrect determination of the correct answer and the answer is determined by matching the character string sequence, there is a problem that the correct determination cannot be made when the answer sequence is different from the correct answer sequence. In addition, in order to make a correct / incorrect determination by matching the character strings, it is necessary to prepare notation rules and identities in the library in the computer, and there is a problem that it takes time to call the library and it takes a long time for correct / incorrect determination. .

  Furthermore, there is a problem that correctness / incorrectness determination cannot be made if the correct answer or answer includes a functional expression or polynomial.

  Furthermore, in order to prove the agreement between the correct answer and the answer, it is necessary to confirm that the two match at all points, which is troublesome.

  Finally, there has been a demand for an improvement in the level of problems that can be handled in a descriptive exercise problem with correct / incorrect determination, and an improvement in the accuracy of correct / incorrect determination.

  The present invention has been made in view of the above-described problems. Problem generating means for generating a mathematical descriptive exercise problem on a computer and correct answer generating means for generating only one correct answer of the exercise problem The problem display means for displaying the exercise problem on the computer, the answer input means for the user to input the answer, the correct answer and the answer are recognized, and the result obtained by substituting the numerical values in both is calculated. The problem is solved by having a correct / incorrect determination means for calculating and comparing the results, and a determination result display means for displaying a correct answer or an incorrect answer depending on whether the results in the correct / incorrect determination means match.

  In addition, the correct answer and the answer are displayed as functional expressions.

  Furthermore, the correct answer generating means is automatically generated by inputting a question.

  Furthermore, the certain numerical value is a rational number, and the lowest value is 10 and a relatively prime number.

  Further, the correctness / incorrectness determination means is characterized in that the determination can be made in the case of a standard mathematical function other than an integer coefficient polynomial, a rational number coefficient polynomial, a rational function, and a polynomial.

  As described above, the mathematical problem answer evaluation method according to the present invention includes a problem generating means for generating a mathematical description formula exercise problem, a correct answer generating means for inputting only one correct answer, and a problem display means for displaying a problem on a computer. And an answer input means for the user to input, a correct / incorrect determination means for comparing the result of recognizing the correct answer and the answer and substituting numerical values in both, and a determination result display means for displaying the result of the correct / incorrect determination means Thus, a correct answer is automatically generated from the problem. And even if the correct answer and the answer string are different, correct / incorrect determination can be made, so even if there are multiple correct answer descriptions, only one is prepared, and the creator concentrates on creating the question be able to. As a result, the burden on the creator's descriptive exercise problem can be reduced.

  For example, by comparing the result of substituting numerical values in the correct answer and the answer to make a correct / incorrect determination, the correct answer or the answer can include a functional expression or a polynomial. That is, the function expression means an integer coefficient polynomial, a rational coefficient polynomial, a rational function, or a standard mathematical function other than a polynomial. As a result, the range of exercise questions can be expanded and higher level exercises can be asked.

  Further, for example, when a certain numerical value is a rational number and the lowest value is a relatively prime number with 10, the correct answer and the answer can be compared with only one value. As a result, it is not necessary to perform mathematical formula processing for correct / incorrect determination, and all numerical calculations can be performed. Therefore, the processing can be speeded up and quantified, and the accuracy of correct / incorrect determination is improved.

  Furthermore, the correctness / incorrectness determination can be determined by a standard mathematical function provided in most programming languages as a standard, so that the processing speed is faster than the case of calling an identity from a library.

  Furthermore, since the user solves the exercise problem by himself and derives an answer, the user can understand the proficiency level of learning through the exercise problem.

  Hereinafter, embodiments of the present invention will be described in detail with reference to FIGS.

  A mathematical problem answer evaluation method according to the present invention includes a user terminal such as a computer including an input unit, an output unit, a display unit, a storage unit, and the like, a network, and a server that is accessed via the user terminal and the network. Consists of systems that include.

In addition, for example, a T _EX format is used as a format for expressing mathematical expressions. The T _E X format is a format for expressing mathematical expressions, and it is not necessary to add anything new to the mathematical expression, and is used by most people.

  Furthermore, the problem to be handled is a polynomial descriptive exercise problem, and the coefficient of the polynomial is, for example, an integer from −900 to 900. In the case of a multiplier, it is possible to calculate up to the 10th power. If the processing speed and processing capability of the computer are increased, it is possible to increase the digit of the coefficient and increase the maximum value of the multiplier.

  FIG. 1 is a configuration diagram of a system in which a mathematical problem answer evaluation method according to an embodiment of the present invention is used.

  As shown in FIG. 1, a system in which the mathematical problem answer evaluation method is used includes at least a server 1, a network 2, and a user terminal 3.

  The server 1 refers to a computer or software on the service providing side in a client / server type system. For example, the server includes a problem generation unit 11, a correct answer generation unit 12, a problem display unit 13, an answer input unit 14, a correct / incorrect determination unit 15, a determination result display unit 16, question data 1a, and correct answer data 1b. The answer data is received and correct / incorrect determination of the answer is made.

  The problem generation means 11 is a means for generating a mathematical descriptive exercise problem on a computer, and the generated problem is stored in the problem data 1a. The question sentence can be created by a computer. For example, prepare a set of methods (here [□□□]) and arguments (here [00]]), extract elements one by one from the method set and argument set, and particles Using “no”, create a question sentence alongside “[□□□]” of [[00]]. Furthermore, a question sentence created by a person may be input and registered in the question data. The problem data 1a will be described in detail later.

The correct answer generating means 12 is a means for generating only one correct answer of the exercise problem, and the correct answer is stored in the correct answer data 1b. The correct answer data can be derived by using the structure analysis of the question sentence. For example, "[thousand] of [□□□]""<□□□>(<thousand>)" from the syntax of preparing a syntax rewritten to T _{E X} format, ability to process the computer Is prepared, the processing result automatically becomes the correct answer to the exercise. The correct answer data 1b will be described in detail later.

  The problem display means 13 is a means for displaying a problem on a computer. For example, a mathematical descriptive exercise problem registered in the problem data 1 a is displayed on the display unit of the user terminal 3.

  The answer input means 14 is a means for a user to input an answer to an exercise.

  The correctness / incorrectness determination means 15 is means for recognizing the correct answer and the answer, calculating a result obtained by substituting numerical values in both, and comparing the results. For example, using a standard function match determination method, whether two expressions are equal is determined by the equality of numerical values at a certain point. A certain numerical value is a rational number, and the lowest value is 10 and a relatively prime number. For example, 1.1, 1.3, 1.7, 1.11, 1.33, 1.77, etc.

  The determination result display means 16 is a means for displaying a correct answer when the results of the correct / incorrect determination means 15 match, and for displaying an incorrect answer on the display unit of the user terminal 3 when the results do not match.

  The question data 1a is information on a math practice question and is stored in the storage unit of the server.

  The correct answer data 1b is correct answer information of the question data 1a and is stored in the storage unit of the server.

  The network 2 is a state in which computers are connected for the purpose of sharing hardware, software, data, and the like. For example, LAN (Local Area Network) is used to connect computers on the same floor, the same building or nearby buildings, or WAN (Wide Area Network) is used to connect computers in remote locations to public lines. Connect using the net.

  The user terminal 3 is a terminal that can use the system of the mathematical problem answer evaluation method, and includes at least an input unit, an output unit, a display unit, and a storage unit.

  Next, FIG. 2 is a flowchart for explaining a mathematical problem answer evaluation method according to an embodiment of the present invention.

  First, the creator generates a mathematical descriptive exercise (Step S1). The exercises may be automatically generated by passing methods and arguments to the computer, or the exercises created by the creator may be registered directly in the problem data.

  Then, only one correct answer for the exercise problem is generated (step S2). The generated correct answer is stored in the correct answer data 1b in the storage unit of the server.

  Then, the exercise problem is displayed on the user terminal 3 (step S3). The user reads the displayed exercise and asks for an answer by himself.

  Then, the user enters the answer in the answer field (step S4). There are five answer formats: (1) constant, (2) integer coefficient polynomial, (3) rational coefficient polynomial, (4) rational function, and (5) cases other than 2-4 above. The five answer patterns will be described in detail later.

  Then, correctness determination is performed by assigning a certain numerical value to both the correct answer and the answer (step S5). If the correct / incorrect determination results match (YES in step S5), the user terminal 3 is displayed and informed that the user's answer is correct (step S6). On the other hand, when the result of correct / incorrect determination does not match (NO in step S5), it is displayed on the user terminal 3 to notify that the user's answer is incorrect (step S7).

  Next, the correctness determination of the correctness determination means will be described in detail for each answer pattern with reference to FIGS.

Example 1
FIG. 3 is an example of a display screen showing exercise questions whose answers are constants and their answer description columns.

  For example, as shown in FIG. 3, it is assumed that the question “Find the limit value of the next function” is displayed on the display screen, and the user describes “1/2” in the answer column. The correct answer prepared is “1/2”.

  Then, the correctness determination means 15 determines whether the user's answer is correct or incorrect. For example, Table 1 shows the result of correct / incorrect determination with a certain numerical value x set to x = 1.11.

ｘ＝１．１１で記述された解答と用意された正解の評価を行う。表より明らかなように、両者の値はそれぞれ０．５となり、同じものであることが判定できる。

The answer described by x = 1.11 and the prepared correct answer are evaluated. As is apparent from the table, both values are 0.5, and it can be determined that they are the same.

  If the user's answer is the same as the prepared correct answer, it will be the same regardless of what x is evaluated. That is, it is possible to make a correct / incorrect determination using an evaluation value of a certain numerical value x. A certain numerical value x is a rational number, and the lowest value is preferably a relatively prime number with 10.

(Example 2)
FIG. 4 is an example of a display screen showing an exercise problem whose answer is an integer coefficient polynomial and its answer description column.

For example, "find the derivative of the next function." As shown in FIG. 4 are displayed on the display screen problem, the user shall be described as "2 + 2x + 35x ⁶ -12x ^3" to the answer column. The correct answer prepared is “35x ⁶ −12x ³ + 2x + 2”.

  Then, the correctness determination means 15 determines whether the user's answer is correct or incorrect. For example, Table 2 shows the results of correct / incorrect determination with a certain numerical value x set to x = 1.11.

ｘ＝１．１１で記述された解答と用意された正解の評価を行う。表より明らかなように、両者の値はそれぞれ５３．２７２９３７３３となり、同じものであることが判定できる。

The answer described by x = 1.11 and the prepared correct answer are evaluated. As is apparent from the table, both values are 53.27393733, and it can be determined that they are the same.

  In the case of the conventional evaluation method, it is necessary to prepare all correct patterns. However, if the evaluation of the function at a certain numerical value is used, it is possible to determine whether the user's answer is correct or not simply by substituting a certain numerical value x (in this case, x = 1.11) and evaluating the user's answer and the correct answer. It becomes possible.

(Example 3)
FIG. 5 is an example of a display screen showing an exercise problem in which the solution is a rational coefficient polynomial and its answer description column.

For example, as shown in FIG. 5, the question “Find the derivative of the next function” is displayed on the display screen, and the user writes “x + 2x ⁶ + 1 / 3-4 / 5x ³ ” in the answer column. Suppose that The correct answer prepared is “2x ⁶ −4 / 5x ³ + x + 1/3”.

  Then, the correctness determination means 15 determines whether the user's answer is correct or incorrect. For example, Table 3 shows the result of correct / incorrect determination with a certain numerical value x set to x = 1.11.

ｘ＝１．１１で記述された解答と用意された正解の評価を行う。表より明らかなように、両者の値はそれぞれ４．０９００５７６３８となり、同じものであることが判定できる。

The answer described by x = 1.11 and the prepared correct answer are evaluated. As apparent from the table, both values are 4.0090057638, and it can be determined that they are the same.

Example 4
FIG. 6 is an example of a display screen showing an exercise problem whose answer is a rational function and its answer description column.

For example, as shown in FIG. 6, it is assumed that the question “Find the derivative of the next function” is displayed on the display screen, and the user describes “2x / (1 + x ² )” in the answer column. The correct answer prepared is “2x / (x ² +1)”.

  Then, the correctness determination means 15 determines whether the user's answer is correct or incorrect. For example, Table 4 shows the results of correct / incorrect determination with a certain numerical value x set to x = 1.11.

ｘ＝１．１１で記述された解答と用意された正解の評価を行う。表より明らかなように、両者の値はそれぞれ０．９９４５７９０９５９となり、同じものであることが判定できる。

The answer described by x = 1.11 and the prepared correct answer are evaluated. As apparent from the table, both values are 0.9945579959, and it can be determined that they are the same.

  If the answer is an advantageous function, the correctness / incorrectness determination means 15 first arranges the answer and the correct answer denominator. When attention is paid to both numerators, since both become polynomials, it is possible to make a correct / incorrect determination as in the second or third embodiment.

(Example 5)
FIG. 7 is an example of a display screen showing a practice question whose answer is other than a polynomial of a positive coefficient or rational coefficient, and a rational function, and its answer description column.

For example, as shown in FIG. 7, it is assumed that the question “Find the derivative of the next function” is displayed on the display screen, and the user describes “9 cosx−9 cos ³ x + 2 + 2x” in the answer column. The correct answer prepared is “9 sin ² xcosx + 2x + 2”.

  Then, the correctness determination means 15 determines whether the user's answer is correct or incorrect. For example, Table 5 shows the results of correct / incorrect determination with a certain numerical value x set to x = 1.11.

ｘ＝１．１１で記述された解答と用意された正解の評価を行う。表より明らかなように、両者の値はそれぞれ７．４３０６７１９０９となり、同じものであることが判定できる。

The answer described by x = 1.11 and the prepared correct answer are evaluated. As apparent from the table, both values are 7.43071909, and it can be determined that they are the same.

  In the case of the conventional evaluation method, the following six patterns were prepared as correct answers to this problem.

・ 2x + 9sin ² xcosx + 2
・ 2 + 9sin ² xcosx + 2x
・ 2 + 2x + 9sin ² xcosx
・ 2x + 2 + 9sin ² xcosx
・ 9sin ² xcosx + 2 + 2x
・ 9sin ² xcosx + 2x + 2
Since sin ² x can also be expressed as 1-cos ² x, cos ² x-cos 2x, and (1-cos 2x) / 2, 6 × 4 = 24 correct answers are prepared even if only listed here. It was necessary and inefficient.

  However, if the evaluation of the function at a certain numerical value is used, it is possible to determine whether the user's answer is correct or not simply by substituting a certain numerical value x (in this case, x = 1.11) and evaluating the user's answer and the correct answer. It becomes possible.

  In the following, it will be described in detail that the correctness / incorrectness determination performed using the above-described function matching by one point is sufficiently practical.

  First, a case where the solution of the second embodiment is an “integer coefficient polynomial” will be proved.

Assume that the coefficients of the polynomials f (x) and g (x) of two integer coefficients are between −10 ^l and 10 ^l .

d (m) = 0 satisfying gcd (d _i , 10) = 1. In d ₁ d ₂ ... d _m , l ≦ m, there is the following theorem. Note that gcd (d _i , 10) = 1 indicates that the greatest common divisor of d _i and 10 is 1.
(Theorem) If f (d (m)) = g (d (m)), nm + l ≦ k,
f (x) = g (x) is established.

Here, from f (d (m)) = g (d (m)), the end of the maximum order a _n (d (m) ⁿ ) and the end of b _n (d (m) ⁿ ) are compared.

From l ≦ m and nm + l ≦ k, the end of a _n (d (m) ⁿ ) and the end of b _n (d (m) ⁿ ) are not affected by any other term and are equal.

Furthermore, since the end of d (m) ⁿ is relatively prime with 10, a _n = b _n . Similarly, a _i = b _i for all i.

Since the number of digits nm + 1 of a _n (d (m) ⁿ ) is less than k, f (x) = g (x) with zero error. That is, f (x) = g (x) is established.

  For example, when d (m) = 1.11, the result of comparing the answer of Example 2 and the correct answer for each order from the maximum order is shown in Table 6.

表からも明らかなように、各次数の値がそれぞれ一致すれば、総和は一致する。また、最大次数から順番に比較していき、不一致となる次数が出現した場合には、これ以上判定を行っても両者が一致することは無いと判断される。そして、正誤判定の処理は終了となる。

As is clear from the table, if the values of the orders match, the sums match. In addition, when the orders that do not match appear in order from the maximum order, it is determined that they do not match even if the determination is further made. Then, the correctness / incorrectness determination process ends.

  Note that a certain numerical value is a rational number and the least significant is a relatively prime number with 10, and the order of comparison from the maximum order is the least significant of the calculated value of the maximum degree (for example, n) of a certain numerical value. This is because it is not affected by the calculated values of other orders (for example, n-1, n-2, ..., 1).

  In addition, the lowest value of a certain numerical value (for example, 1.11) is 10 and a relatively prime number. The lowest value is obtained by multiplying 10 and a relatively prime number by any two numbers from 1 to 9. This is because they are always different. For example, when a certain numerical value is 1.22 or 1.44 and any two numbers from 1 to 9 such as 11 and 16 are multiplied, the calculated lowest value (2 in the case of 1.22 is 2, In the case of 1.44, 4) is the same and correct / incorrect determination cannot be made. Therefore, if a certain numerical value is 1.11, 1.33, or 1.77, correct / incorrect determination can be made.

  Next, the case where the solution of the third embodiment is a “rational coefficient polynomial” will be proved.

Suppose that the coefficients numerator and denominator of the polynomials f (x) and g (x) of the two rational number coefficients are between −5 ^l and 5 ^l .

d (m) = 0 satisfying gcd (d _i , 10) = 1. In d ₁ d ₂ ... d _m , l ≦ m, there is the following theorem.

（定理） ｆ（ｄ（ｍ））＝ｆ（ｄ（ｍ））かつ数１かつ数２ならば、
ｆ（ｘ）＝ｇ（ｘ）が成り立つ。

(Theorem) If f (d (m)) = f (d (m)) and Equation 1 and Equation 2,
f (x) = g (x) is established.

ｆ（ｘ）とｇ（ｘ）の有理数係数の分母の最小公倍数をｌｃｍとし、数３のように表す。

The least common multiple of the denominator of the rational coefficient of f (x) and g (x) is assumed to be 1 cm, and expressed as Equation 3.

ｆ（ｄ（ｍ））＝ｇ（ｄ（ｍ））より、数４となる。

From f (d (m)) = g (d (m)), Equation 4 is obtained.

  Here, the end of the maximum order is equal to that in Equation (1). Further, from Equation 2, f (x) and g (x) do not include the factor xd (m).

更に、ｄ（ｍ）^ｎの末尾は１０と互いに素であるから、数５となる。

Further, since the end of d (m) ⁿ is relatively prime with 10, Equation 5 is obtained.

同様にして、すべてのｉにおいてもａ_ｉ＝ｂ_ｉとなる。また、数６の桁数である数７はｋより少ないので、誤差０でｆ（ｘ）＝ｇ（ｘ）である。

Similarly, a _i = b _i for all i. Further, since the number 7 of the number 6 is less than k, the error is 0 and f (x) = g (x).

  That is, f (x) = g (x) is established.

  Finally, the case where the solution of Example 5 is “standard mathematical function other than polynomial” will be proved.

  From Lindermann and Baker's theorem, it is known that all values of standard functions that do not contain powers of x are transcendental numbers except for obvious algebraic numbers. Transcendental numbers are all irrational numbers and complex numbers that do not become solutions to algebraic equations, for example, pi.

  That is, if the value of h (d) = f (d) −g (d) in the unclear algebraic number d is 0, it can be said that f (x) = g (x).

Since h (x) = f (x) −g (x) is not a polynomial, if polynomial approximation is performed, h (x) ≈c ₀ + c ₁ x +... + c _n x ⁿ .

If | h (0.1) | ≦ 10 ^−k , then c ₀ = c ₁ =... = C _k = 0.

Therefore, d (m) = 0. _{d 1} d ₂ ... d m, when l ≦ m | f (d ( m)) - g (d (m)) | ≦ 10 -k If, in the error ^{10 -k} below f (x) = g ( x).

That is, the probability that f (x) = g (x) is satisfied is 1-10 ^−k or more.

  As described above in detail, by using the mathematical problem answer evaluation method of the present invention, for example, in the creation of mathematical exercises of standard mathematical functions other than integer coefficient polynomials, rational number coefficient polynomials, rational functions, and polynomials, problems and correct answers can be obtained. It can be automatically generated, and the correctness of the entered answer and the prepared correct answer can be determined using a match of a certain numerical value, thereby reducing the burden on the problem creator. Therefore, it can be used to provide a wide range of problems in the final exams.

It is a block diagram of the system by which the mathematical problem-answer evaluation method which is one embodiment of this invention is utilized. It is a flowchart explaining the mathematical question answer evaluation method which is one embodiment of this invention. It is an example of the display screen showing the practice question and the answer description column in which the solution is an embodiment according to the present invention. It is an example of the display screen showing the exercise problem in which the solution which is one embodiment of this invention becomes an integer coefficient polynomial, and its answer description column. It is an example of the display screen showing the exercise problem in which the solution which is one embodiment of this invention becomes a rational coefficient polynomial, and its answer description column. It is an example of the display screen showing the exercise problem in which the solution which is one embodiment of this invention becomes a rational function, and its answer description column. It is an example of the display screen showing the exercise problem in which the solution which is one embodiment of this invention becomes a positive coefficient or a polynomial of a rational coefficient, and other than a rational function, and its answer description column.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Server 2 Network 3 User terminal 11 Problem generation means 12 Correct answer generation means 13 Problem answer means 14 Answer input means 15 Correct / incorrect determination means 16 Determination result display means 1a Problem data 1b Correct answer data

Claims (5)

A problem generation means for generating a mathematical descriptive exercise on a computer;
Correct answer generating means for generating only one correct answer of the exercise,
Problem display means for displaying the exercise on the computer;
An answer input means for the user to enter an answer;
Recognizing the correct answer and the answer, calculating a result calculated by substituting numerical values in both, correctness determination means for comparing the results,
5. A mathematical problem answer evaluation method comprising: a determination result display means for displaying a correct answer or an incorrect answer depending on whether the result in the correctness / incorrectness determination means matches or does not match.   2. The mathematical problem answer evaluation method according to claim 1, wherein the correct answer and the answer are displayed as a function formula.   2. The mathematical problem answer evaluation method according to claim 1, wherein the correct answer generation means is automatically generated by inputting a question.   The mathematical problem answer evaluation method according to claim 1, wherein the certain numerical value is a rational number, and the lowest value is a relatively prime number with 10.   2. The mathematical problem answer evaluation method according to claim 1, wherein the correctness / incorrectness determination means can perform determination in the case of a standard mathematical function other than an integer coefficient polynomial, a rational number coefficient polynomial, a rational function, or a polynomial.

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