WO2022018780A1 - Arithmetic learning computer program - Google Patents
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- WO2022018780A1 WO2022018780A1 PCT/JP2020/027980 JP2020027980W WO2022018780A1 WO 2022018780 A1 WO2022018780 A1 WO 2022018780A1 JP 2020027980 W JP2020027980 W JP 2020027980W WO 2022018780 A1 WO2022018780 A1 WO 2022018780A1
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- G09B19/02—Counting; Calculating
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- the present invention relates to a computer program for learning mathematics for learning mathematics.
- "13 can be divided into 8 and 5" is equivalent to "combining 8 and 5 into 13". Dividing and compositing can be learned in the same way, but it is better to be aware of one large number first and learn to divide it so that a large number is synthesized first by being aware of two small numbers. It was more efficient than learning. It is thought that this is because small numbers that are easy to understand can be understood without difficulty by first conscious of large numbers that are more difficult to understand through vision.
- the above division can be understood visually, for example, by arranging a card with 8 circles and a card with 5 circles side by side. This facilitates understanding.
- the figure to be drawn is not limited to a circle, and any shape may be used as long as it has the same shape, such as a star shape. Alternatively, the number may be identified by filling the frame itself.
- Patent Document 1 Various computer programs that assist in learning arithmetic are known, for example, as disclosed in Patent Document 1. However, it does not aid a rudimentary understanding that the division of small numbers is the basic concept of addition and subtraction. Since this learning step is omitted, it becomes difficult to understand by the quantity image of addition and subtraction, and it is remembered as an operation of a symbol called a number.
- the computer program for arithmetic learning of the present invention is S pieces of frames with figures are displayed side by side in one direction from one end.
- a division guide indicating between the N-th frame and the (N + 1) -th frame from one end is displayed.
- a computer program for arithmetic learning that displays N figures of the frame and M figures of the other frames in different colors by operating the division guide. It is characterized in that it is possible to perform operations for all S and N where S ⁇ 18 and N ⁇ 9.
- the computer program for arithmetic learning of the present invention is When displaying the figure of the frame of N pieces from one end and the figure of the other frame in different colors, between the frame Nth from the one end and the frame (N + 1) th.
- the feature is that the boundary is displayed.
- N frames and M frames are separated by a boundary, and each looks like one card, and it looks like two cards in total.
- the learning effect can be enhanced.
- the computer program for arithmetic learning of the present invention is It is characterized in that the voice of "S is N plus M" or "S is N and M" is output by the operation to the division guide.
- the computer program for arithmetic learning of the present invention is By operating the division guide, the voice "N plus M is S" is output.
- addition can be understood as a quantity operation opposite to the division of numbers, that is, the composition of numbers. It can also be understood as a combination of two specific numbers as in the case of division. It was
- the computer program for arithmetic learning of the present invention is It is characterized in that the voice of "S pulling N is M" or "S pulling M is N" is output by the operation to the division guide.
- subtraction is a quantity operation excluding one of the divided numbers. It can also be understood as a combination of two specific numbers as in the case of division.
- the computer program for arithmetic learning of the present invention is The figure of the frame of N from one end, which is displayed by the operation to the division guide, is displayed in achromatic color, and the figure of the other M frames is displayed in chromatic color, or the figure is displayed in chromatic color.
- the figure of the frame of N from one end is displayed in chromatic color, and the figure of the other frame of M is displayed in achromatic color.
- the computer program for arithmetic learning of the present invention is The division guide is displayed, and after the operation for the operation to the displayed division guide, the next division guide is displayed, and the learning is sequentially performed.
- the value of N is sequentially increased by 1 and learned sequentially.
- N 1 ROUNDUP (S / 2)
- N 2 MIN (S-1, 9) It is characterized by being.
- ROUNDUP (X) is a value obtained by rounding up X to an integer if X is an integer, and X is a value rounded up to an integer if X is not an integer, and MIN (X, Y) is the smaller value of X and Y. be.
- N 1 ROUNDDOWN (S / 2)
- N 2 MAX (S-9,1) May be.
- ROUNDDOWN (X) is a value obtained by devaluing X to an integer if X is an integer
- X is a value obtained by devaluing X to an integer if X is not an integer
- MAX (X, Y) is the larger value of X and Y. be.
- N 1 is a number close to half of S.
- S odd
- S odd
- N 1 is a number close to half of S. It makes you understand that.
- the computer program for arithmetic learning of the present invention is When displaying S frames, a boundary is displayed between the tenth frame and the eleventh frame from one end.
- the computer program for arithmetic learning of the present invention is When displaying the S frames, the boundary is displayed between the fifth frame and the sixth frame from one end and between the fifteenth frame and the sixteenth frame. It is a feature.
- the card for learning arithmetic of the present invention can be easily created.
- FIG. 1 is a diagram illustrating processing of a computer program.
- FIG. 2 is a diagram illustrating a transition of display.
- FIG. 3 is a diagram illustrating a transition of the display.
- FIG. 4 is a diagram illustrating a transition of the display.
- Example 2 is a diagram illustrating a transition of the display.
- Example 3 is a diagram illustrating a transition of the display.
- Example 3 is a diagram illustrating a transition of the display.
- Example 2 is a diagram illustrating a transition of the display.
- FIG. 4 is a diagram illustrating a transition of the display.
- Example 3 is a diagram illustrating a transition of the display.
- Example 3 is a diagram illustrating a transition of the display.
- Example 3 is a diagram illustrating a transition of the display.
- Example 3 is a diagram illustrating a transition of the display.
- Example 4 is a diagram illustrating a transition of the display.
- Example 3 is a diagram illustrating a transition of
- FIG. 1 is a diagram illustrating the processing of a computer program.
- the computer program 1 for arithmetic learning first determines S (1a) and performs initial display (FIG. 2A) (1b).
- the computer program 1 for arithmetic learning determines the position of the division guide 4 (1c) and displays it (1d). Determining the position of the split guide 4 is almost equivalent to determining N.
- the computer program 1 for arithmetic learning performs division display (FIG. 2 (D)) (1e).
- the "operation” confirms that the learner is aware of the division, and may be any operation such as clicking the displayed division guide, pressing the enter key, or any other operation. Further, even when there is no operation by the learner, the passage of time (for example, 10 seconds) may be regarded as an operation.
- the computer program 1 for arithmetic learning performs mathematical expression display (division) (1f) and voice output (division) (1g). Both the mathematical expression display (division) and the audio output (division) may be performed, only one may be performed, or none may be performed at all. It may be designed according to the learning purpose. When both are performed, the screen display and the audio output can be performed at the same time.
- the computer program 1 for arithmetic learning displays mathematical expressions (addition / subtraction) (1h) and audio output (addition / subtraction) (1i) instead of mathematical expression display (division) (1f) and audio output (division) (1g). You may go.
- both "mathematical expression display (division)” (1f) and “mathematical expression display (addition / subtraction)” (1h) are referred to as “mathematical expression display”
- audio output (division) (1g) audio output (addition / subtraction) Both 1i) are described as "voice output” and are distinguished by a code.
- the computer program 1 for arithmetic learning determines whether or not the learning is completed (1j), and if it is not completed, the learning is performed again from the initial display (1b). The next learning is performed by changing N.
- N When determining the position of the division guide 4 (1c), the value of N is changed. For example, it is conceivable to increase N by 1 from the previous time. For one value of S, N is changed for learning. Since learning is performed sequentially while increasing N by 1, it can be seen that when N increases by 1, M decreases by 1, and learning can be performed effectively.
- next learning may be performed not from the initial display (1b) but from the determination of S (1a).
- FIG. 2 (A) shows the initial display (1b).
- Five frames 2 are arranged in the horizontal direction, and the figure 3a is arranged in each frame. Further, the shape and color of the figure 3a may be arbitrary. In the figure, it is shown in black, but it can be, for example, a red circle (the same applies to the figures 3b1 and 3c described later).
- the boundary line of the frame 2 is indicated by a broken line in the figure, it does not necessarily have to be indicated. The number of "5" can be understood only by the five figures 3a.
- the division guide 4 shows the third frame 2 instead of the boundary of the frame 2.
- the division guide 4 shows between the third frame 2 and the fourth frame 2.
- FIGS. 2B and 2C are the same. In this case, the display of FIG. 2B is omitted.
- the display of FIG. 2 (B) is performed. Since the portion indicated by the division guide 4 is not between the two frames 2, the division guide 4 does not indicate the division portion, but it is preferable to display the division guide 4 having the same shape as the display of FIG. 2C. It shows exactly half of S, and by moving the division guide 4 from here to the state of FIG. 2 (C), it is shown that the division is performed at a value close to half of S.
- the division guide 4 is operated (the division guide 4 is clicked, the enter key is pressed, the time (for example, 10 seconds) elapses, and other things specified by the design are performed. ) And split display is performed.
- FIG. 2 (D) shows a divided display (1e).
- Boundary 5a makes it look like an N-width card and an M-width card. It is easy to understand that the width of S is obtained by two cards and S is divided into N and M.
- the figure 3b1 and the figure 3c are shown by shading different from the figure 3a. It is preferable that the figures 3b1 and the figure 3c have colors different from those of the figure 3a. For example, when the figure 3a is red, it is conceivable that the figure 3b1 is blue and the figure 3c is yellow. By setting the color so that the figure 3b1 and the figure 3c can be clearly distinguished in this way, it is ensured that the card looks like an N-width card and an M-width card. In addition, either one of the figure 3b1 and the figure 3c may have the same or similar color as the figure 3a.
- FIG. 2 (E) represents a mathematical expression display (1f).
- FIG. 2 (F) represents an audio output (1 g).
- the balloon 7 in the figure is an audio output (not displayed on the screen).
- the audio output is an audio output 7a of "5 is 3 and 2" according to the mathematical formula. Alternatively, it may be an audio output of "5 is 3 plus 2". It is shown that 5 is divided into 3 and 2, but since it appears in the order of 5, 3 and 2 in the mathematical expression display, this voice can be easily understood. As a result, it is possible to learn by associating division with addition.
- FIG. 3 is a diagram for explaining the transition of the display. It is written as (E) (F) in the figure, and there is no (A) (B) (C) (D), but it is the same (A) (B) (C) (D) as in FIG. That is, the mathematical expression display (1h) and the audio output (1i) are represented by (E) and (F) corresponding to FIG.
- the audio output is the audio output 7b with "3 plus 2 is 5".
- FIG. 4 is a diagram for explaining the transition of the display.
- (E) (F) are shown in the figure, and there is no (A) (B) (C) (D), but the same (A) (B) (C) (D) as in Example 1 (FIG. 2). Is. That is, the display up to the operation of the division guide is the same as that of the first embodiment, and the subsequent display is represented by (E) and (F) corresponding to FIG.
- FIG. 4 (E) shows a divided display (1e).
- the figure 3b1 is changed to the figure 3b2.
- the figure 3b2 is not shaded, the figure 3b2 is achromatic so as to reduce the impression given to the learner.
- the figure 3c is a chromatic color as in the first embodiment (FIG. 2 (D)).
- the figure 3a and the figure 3c may be the same color.
- figure 3b2 may be a chromatic color as in the first embodiment.
- FIG. 4 (F) represents an audio output (1i).
- the balloon 7 in the figure is an audio output (not displayed on the screen).
- the audio output is an audio output 7c with "5 minus 3 is 2" according to the mathematical formula.
- S exceeds 10. Detailed description of the same parts as those of Examples 1 and 2 will be omitted.
- S 13.
- (A), (C), and (D) are written, and (B), (E), and (F) are not present, but (B), (E), and (F) are the same as in Example 1 (FIG. 2). That is, the display of the division guide to the fractional position shown in FIGS. 2 and 4, the mathematical expression displayed in (E) and (F), and the audio output are the same as those in Examples 1 and 2. be.
- the number of frames 2 differs depending on the difference in the value of S.
- the boundary 5b is displayed between the 5th frame and the 6th frame, between the 10th frame and the 11th frame, and between the 15th frame and the 16th frame. It is possible to make the learner aware of 5 as a delimiter, and to perform learning with 5 as a delimiter, for example, 7 is 5 and 2. In addition, in order to perform learning with 10 as a delimiter instead of 5, the boundary 5b is displayed only between the 10th frame and the 11th frame, and the 15th frame is displayed between the 5th frame and the 6th frame. The boundary 5b may not be displayed between the frame and the 16th frame.
- FIG. 5C shows the display (1d) of the division guide.
- FIG. 5 (D) shows a divided display (1e).
- the figure uses a chromatic figure 3b1 as in FIG. 2 (D). It corresponds to addition. Similar to FIG. 4D, the achromatic figure 3b2 may be used (corresponding to subtraction).
- Boundary 5a is also displayed at the right end of the S-th frame. As a result, it seems as if two cards, an N-width card and an M-width card, are displayed. The learner visually understands that S is divided into N and M.
- the computer program for learning arithmetic of the present invention can easily understand the division of small numbers and brings about a high learning effect of arithmetic. It can be used by many educational institutions and individuals.
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Abstract
[Problem] To provide an arithmetic learning computer program for learning a quantity operational concept of addition and subtraction and a combination of determined numbers in conjunction with the division of a small number through understanding via the vision. [Solution] Provided is an arithmetic learning computer program 1 which can: display drawn frames 2 of a figure sequentially in parallel in one direction from S ends; display a division guide 4 that indicates a space between an N-th frame and an (N+1)-th frame from one end; display, in different colors, a figure 3 of N frames 2 from the one end and a figure 3 of the other M frames 2 by means of an operation for the division guide 4; and perform actions on all S and N where S≦18 and N≦9.
Description
本発明は、算数を学習するための算数学習用コンピュータプログラムに関する。
The present invention relates to a computer program for learning mathematics for learning mathematics.
算数を学習する際、初期の段階で小さな数の足し算及び引き算を学習する。小さな数とは、N+M=Sという足し算、これと同等なS-M=Nという引き算(N,M,Sはいずれも正の整数)において、N、Mが共に1桁の数である(N≦9、M≦9)ものを言う。
When learning mathematics, learn the addition and subtraction of small numbers at the initial stage. A small number is a one-digit number for both N and M in the addition of N + M = S and the equivalent subtraction of SM = N (N, M, and S are all positive integers). ≤9, M≤9) Say something.
学習が進んで、例えば2桁の数同士の足し算、引き算を学習する場合にも、筆算を行う際には、1桁の数同士の足し算N+Mを行うことが基本となる。また、引き算では、18以下の数から1桁の数を引く引き算S-Mを行うことが基本となる。ここで、Sは、繰り下がりがある場合に上位の桁の1が10となるため、最大で18となる。
As learning progresses, for example, even when learning addition or subtraction between two-digit numbers, when performing long division, it is basic to perform addition N + M between one-digit numbers. Further, in subtraction, it is basic to perform subtraction SM by subtracting a one-digit number from a number of 18 or less. Here, S is 18 at the maximum because 1 of the upper digit is 10 when there is a carry.
N≦9、M≦9であり、N,Mの組み合わせは81通りのみであるので、足し算、引き算を合わせた162通りについて、掛け算の九九のように暗記しても、小さな数の足し算及び引き算をすることができる。しかし、出願人が小学生に教えたところ、例えば「8+5=13」と「13-8=5」とを暗記させるよりも、「13が8と5に分割できる」ことを理解させるほうが学習効率が高かった。ここで、「13が8と5に分割できる」ことは、「8と5を合成して13になる」ことと等価である。分割と合成とは、同様に学習できるが、先に1つの大きな数を意識し、それが分割されることを学ぶほうが、先に2つの小さな数を意識して大きな数が合成されることを学ぶよりも効率が良かった。視覚を介した理解のより難しい大きな数を先に意識することで、理解の易しい小さな数が苦労なく理解できるためと考えられる。
Since N ≤ 9 and M ≤ 9 and there are only 81 combinations of N and M, even if you memorize 162 combinations of addition and subtraction like multiplication table, you can add a small number and add them. You can do subtraction. However, when the applicant taught elementary school students, it is more efficient to understand that "13 can be divided into 8 and 5" than to memorize "8 + 5 = 13" and "13-8 = 5", for example. it was high. Here, "13 can be divided into 8 and 5" is equivalent to "combining 8 and 5 into 13". Dividing and compositing can be learned in the same way, but it is better to be aware of one large number first and learn to divide it so that a large number is synthesized first by being aware of two small numbers. It was more efficient than learning. It is thought that this is because small numbers that are easy to understand can be understood without difficulty by first conscious of large numbers that are more difficult to understand through vision.
上記の分割は、例えば、8つの円が描かれたカードと5つの円が描かれたカードとを並べることで、視覚を介した理解が可能である。これによって、理解が容易になる。なお、描かれる図形は円に限らず、すべて同じ形のものであれば星型などでもよく、形を選ばない。または、枠そのものが塗りつぶされることで数が識別される方法でもよい。
The above division can be understood visually, for example, by arranging a card with 8 circles and a card with 5 circles side by side. This facilitates understanding. The figure to be drawn is not limited to a circle, and any shape may be used as long as it has the same shape, such as a star shape. Alternatively, the number may be identified by filling the frame itself.
算数の学習を補助するコンピュータプログラムが、例えば特許文献1に開示されたように、種々知られている。しかし、小さい数の分割が、足し算と引き算の基礎概念であるという初歩的な理解を補助するものではない。この学習ステップが抜けているため、足し算と引き算の数量イメージによる理解が困難になり、数字という記号の操作として覚えてしまう。
Various computer programs that assist in learning arithmetic are known, for example, as disclosed in Patent Document 1. However, it does not aid a rudimentary understanding that the division of small numbers is the basic concept of addition and subtraction. Since this learning step is omitted, it becomes difficult to understand by the quantity image of addition and subtraction, and it is remembered as an operation of a symbol called a number.
本発明は、視覚を介した理解を通じて、小さい数の分割との関連で、足し算と引き算の数量操作概念と、定まった数の組み合わせを学習するための算数学習用コンピュータプログラムを提供することを課題とする。
It is an object of the present invention to provide a computer program for arithmetic learning for learning a fixed number combination and a quantity manipulation concept of addition and subtraction in relation to division of a small number through visual understanding. And.
本発明の算数学習用コンピュータプログラムは、
図形の描かれた枠をS個、一端から1方向に順に並べて表示し、
前記一端からN番目の前記枠と(N+1)番目の前記枠との間を指示する分割ガイドを表示し、
前記分割ガイドへの操作によって、前記一端からN個の前記枠の前記図形と、他のM個の前記枠の前記図形とを異なる色で表示する算数学習用コンピュータプログラムであって、
S≦18、かつ、N≦9である全てのS、Nについての動作を行うことが可能であることを特徴とする。 The computer program for arithmetic learning of the present invention is
S pieces of frames with figures are displayed side by side in one direction from one end.
A division guide indicating between the N-th frame and the (N + 1) -th frame from one end is displayed.
A computer program for arithmetic learning that displays N figures of the frame and M figures of the other frames in different colors by operating the division guide.
It is characterized in that it is possible to perform operations for all S and N where S ≦ 18 and N ≦ 9.
図形の描かれた枠をS個、一端から1方向に順に並べて表示し、
前記一端からN番目の前記枠と(N+1)番目の前記枠との間を指示する分割ガイドを表示し、
前記分割ガイドへの操作によって、前記一端からN個の前記枠の前記図形と、他のM個の前記枠の前記図形とを異なる色で表示する算数学習用コンピュータプログラムであって、
S≦18、かつ、N≦9である全てのS、Nについての動作を行うことが可能であることを特徴とする。 The computer program for arithmetic learning of the present invention is
S pieces of frames with figures are displayed side by side in one direction from one end.
A division guide indicating between the N-th frame and the (N + 1) -th frame from one end is displayed.
A computer program for arithmetic learning that displays N figures of the frame and M figures of the other frames in different colors by operating the division guide.
It is characterized in that it is possible to perform operations for all S and N where S ≦ 18 and N ≦ 9.
この特徴によれば、S個の枠が、N個の枠とM個の枠(M=S―N)に分割されることを、視覚を介して学習することができる。
According to this feature, it is possible to visually learn that S frames are divided into N frames and M frames (M = SN).
本発明の算数学習用コンピュータプログラムは、
前記一端からN個の前記枠の前記図形と、他の前記枠の前記図形とを異なる色で表示する際に、前記一端からN番目の前記枠と(N+1)番目の前記枠との間に境界が表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
When displaying the figure of the frame of N pieces from one end and the figure of the other frame in different colors, between the frame Nth from the one end and the frame (N + 1) th. The feature is that the boundary is displayed.
前記一端からN個の前記枠の前記図形と、他の前記枠の前記図形とを異なる色で表示する際に、前記一端からN番目の前記枠と(N+1)番目の前記枠との間に境界が表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
When displaying the figure of the frame of N pieces from one end and the figure of the other frame in different colors, between the frame Nth from the one end and the frame (N + 1) th. The feature is that the boundary is displayed.
この特徴によれば、N個の枠とM個の枠が境界によって分離され、それぞれが1枚、全体で2枚のカードのように見える。学習効果を高めることができる。
According to this feature, N frames and M frames are separated by a boundary, and each looks like one card, and it looks like two cards in total. The learning effect can be enhanced.
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドへの操作によって、「S=N+M」とのテキストを表示することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the text "S = N + M" is displayed.
前記分割ガイドへの操作によって、「S=N+M」とのテキストを表示することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the text "S = N + M" is displayed.
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドへの操作によって、「SはNたすM」又は「SはNとM」との音声を出力することを特徴とする。 The computer program for arithmetic learning of the present invention is
It is characterized in that the voice of "S is N plus M" or "S is N and M" is output by the operation to the division guide.
前記分割ガイドへの操作によって、「SはNたすM」又は「SはNとM」との音声を出力することを特徴とする。 The computer program for arithmetic learning of the present invention is
It is characterized in that the voice of "S is N plus M" or "S is N and M" is output by the operation to the division guide.
これら2つの特徴によれば、分割を2つの特定の数の組み合わせとして理解することが促進される。
These two features facilitate the understanding of division as a combination of two specific numbers.
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドへの操作によって、「N+M=S」とのテキストを表示することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the text "N + M = S" is displayed.
前記分割ガイドへの操作によって、「N+M=S」とのテキストを表示することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the text "N + M = S" is displayed.
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドへの操作によって、「NたすMはS」との音声を出力することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the voice "N plus M is S" is output.
前記分割ガイドへの操作によって、「NたすMはS」との音声を出力することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the voice "N plus M is S" is output.
これら2つの特徴によれば、足し算を、数の分割と逆の数量操作、すなわち数の合成として理解することができる。また、分割と同様に2つの特定の数の組み合わせとして理解することも可能である。
According to these two characteristics, addition can be understood as a quantity operation opposite to the division of numbers, that is, the composition of numbers. It can also be understood as a combination of two specific numbers as in the case of division. It was
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドへの操作によって、「S-N=M」又は「S-M=N」とのテキストを表示することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the text "SN = M" or "SM = N" is displayed.
前記分割ガイドへの操作によって、「S-N=M」又は「S-M=N」とのテキストを表示することを特徴とする。 The computer program for arithmetic learning of the present invention is
By operating the division guide, the text "SN = M" or "SM = N" is displayed.
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドへの操作によって、「SひくNはM」又は「SひくMはN」との音声を出力することを特徴とする。 The computer program for arithmetic learning of the present invention is
It is characterized in that the voice of "S pulling N is M" or "S pulling M is N" is output by the operation to the division guide.
前記分割ガイドへの操作によって、「SひくNはM」又は「SひくMはN」との音声を出力することを特徴とする。 The computer program for arithmetic learning of the present invention is
It is characterized in that the voice of "S pulling N is M" or "S pulling M is N" is output by the operation to the division guide.
この特徴によれば、引き算が、分割された数のうち一つを除く数量操作であることを理解できる。また、分割と同様に2つの特定の数の組み合わせとして理解することも可能である。
According to this feature, it can be understood that subtraction is a quantity operation excluding one of the divided numbers. It can also be understood as a combination of two specific numbers as in the case of division.
ここで、「S=N+M」の分割の式と音声は、共通の図を見ながら、足し算/引き算の式と連続して表記および音声出力されることで容易に比較され、足し算の式「N+M=S」では右辺と左辺が共通することにより、引き算の式「S-N=M」では数字の並び順が共通することにより、分割との関連を理解することが促進される。
Here, the division formula of "S = N + M" and the voice are easily compared by notating and outputting the voice continuously with the addition / subtraction formula while looking at the common figure, and the addition formula "N + M". In "= S", the right side and the left side are common, and in the subtraction formula "SN = M", the order of the numbers is common, which facilitates understanding the relationship with the division.
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドへの操作によって表示される、前記一端からN個の前記枠の前記図形は無彩色で表示され、他のM個の前記枠の前記図形は有彩色で表示されること、または前記一端からN個の前記枠の前記図形は有彩色で表示され、他のM個の前記枠の前記図形は無彩色で表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
The figure of the frame of N from one end, which is displayed by the operation to the division guide, is displayed in achromatic color, and the figure of the other M frames is displayed in chromatic color, or the figure is displayed in chromatic color. The figure of the frame of N from one end is displayed in chromatic color, and the figure of the other frame of M is displayed in achromatic color.
前記分割ガイドへの操作によって表示される、前記一端からN個の前記枠の前記図形は無彩色で表示され、他のM個の前記枠の前記図形は有彩色で表示されること、または前記一端からN個の前記枠の前記図形は有彩色で表示され、他のM個の前記枠の前記図形は無彩色で表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
The figure of the frame of N from one end, which is displayed by the operation to the division guide, is displayed in achromatic color, and the figure of the other M frames is displayed in chromatic color, or the figure is displayed in chromatic color. The figure of the frame of N from one end is displayed in chromatic color, and the figure of the other frame of M is displayed in achromatic color.
この特徴によれば、分割を引き算として理解する際に、減数(N個の枠)が印象弱く、差(M個の枠)が印象強く表示されるので、被減数(S個の枠)から、減数(N個の枠)を消して、差(M個の枠)となるような印象を得ることができる。減数がNとMが入れ替わる場合も同様である。
According to this feature, when the division is understood as subtraction, the subtrahend (N frames) is weakly impressed and the difference (M frames) is strongly displayed. Therefore, from the minuend (S frames), You can get the impression that the subtraction (N frames) is erased and the difference (M frames) is obtained. The same applies when N and M are interchanged in the subtraction.
本発明の算数学習用コンピュータプログラムは、
前記分割ガイドを表示し、表示された分割ガイドへの操作に対する動作の後に次の分割ガイドを表示する形式で逐次に学習させ、
1つのSに対して、N=N1から、N=N2まで、Nの値を1ずつ順番に増やして逐次に学習させ、
N1=ROUNDUP(S/2)
N2=MIN(S-1,9)
であることを特徴とする。 The computer program for arithmetic learning of the present invention is
The division guide is displayed, and after the operation for the operation to the displayed division guide, the next division guide is displayed, and the learning is sequentially performed.
For one S, from N = N 1 to N = N 2 , the value of N is sequentially increased by 1 and learned sequentially.
N 1 = ROUNDUP (S / 2)
N 2 = MIN (S-1, 9)
It is characterized by being.
前記分割ガイドを表示し、表示された分割ガイドへの操作に対する動作の後に次の分割ガイドを表示する形式で逐次に学習させ、
1つのSに対して、N=N1から、N=N2まで、Nの値を1ずつ順番に増やして逐次に学習させ、
N1=ROUNDUP(S/2)
N2=MIN(S-1,9)
であることを特徴とする。 The computer program for arithmetic learning of the present invention is
The division guide is displayed, and after the operation for the operation to the displayed division guide, the next division guide is displayed, and the learning is sequentially performed.
For one S, from N = N 1 to N = N 2 , the value of N is sequentially increased by 1 and learned sequentially.
N 1 = ROUNDUP (S / 2)
N 2 = MIN (S-1, 9)
It is characterized by being.
この特徴によれば、S(=N+M)の分割を、Nを1ずつ増やしながら逐次に学習するので、Nが1だけ増加するとMが1だけ減少するととがわかり、理解が容易になる。ここで、ROUNDUP(X)はXが整数であればX、Xが整数でない場合にはXを整数に切り上げた値であり、MIN(X,Y)は、XとYの小さい方の値である。
According to this feature, since the division of S (= N + M) is learned sequentially while increasing N by 1, it is understood that when N increases by 1, M decreases by 1, which makes it easier to understand. Here, ROUNDUP (X) is a value obtained by rounding up X to an integer if X is an integer, and X is a value rounded up to an integer if X is not an integer, and MIN (X, Y) is the smaller value of X and Y. be.
Sの半分に近い数であるN1からNを増やしていくが、9を超えてNを増やさないのは、10進法の学習において、N又はMの一方が10以上であれば、(S―10)の分割によってSの分割が理解できる(15=12+3に替えて5=2+3を学習すればよい)ため、重複学習をなくして学習量を減らすものである。
N is increased from N 1, which is a number close to half of S, but N is not increased beyond 9, if either N or M is 10 or more in decimal learning (S). Since the division of S can be understood by the division of -10) (5 = 2 + 3 may be learned instead of 15 = 12 + 3), duplicate learning is eliminated and the amount of learning is reduced.
なお、Nを1ずつ増やしながら逐次に学習するのみでなく、他の学習を併用してもよい。例えば、N=N1から、N=N2まで、Nの値を1ずつ順番に増やして逐次に学習させた後に、N=N1-1から、Nの値を1ずつ順番に減らして逐次に学習させ、
N1=ROUNDDOWN(S/2)
N2=MAX(S-9,1)
としてもよい。 In addition to learning sequentially while increasing N by 1, other learning may be used in combination. For example, the N = N 1, to N = N 2, after is trained successively increased in the order value of N by one, from the N = N 1 -1, successively reducing in turn the value of N by one To learn
N 1 = ROUNDDOWN (S / 2)
N 2 = MAX (S-9,1)
May be.
N1=ROUNDDOWN(S/2)
N2=MAX(S-9,1)
としてもよい。 In addition to learning sequentially while increasing N by 1, other learning may be used in combination. For example, the N = N 1, to N = N 2, after is trained successively increased in the order value of N by one, from the N = N 1 -1, successively reducing in turn the value of N by one To learn
N 1 = ROUNDDOWN (S / 2)
N 2 = MAX (S-9,1)
May be.
この特徴によれば、S(=N+M )の分割を、Nを1ずつ減らしながら逐次に学習するので、Nが1だけ減少するとMが1だけ増加するととがわかり、理解が容易になる。ここで、ROUNDDOWN(X)はXが整数であればX、Xが整数でない場合にはXを整数に切り下げた値であり、MAX(X,Y)は、XとYの大きい方の値である。
According to this feature, since the division of S (= N + M) is learned sequentially while decreasing N by 1, it is understood that when N decreases by 1, M increases by 1, which makes it easier to understand. Here, ROUNDDOWN (X) is a value obtained by devaluing X to an integer if X is an integer, and X is a value obtained by devaluing X to an integer if X is not an integer, and MAX (X, Y) is the larger value of X and Y. be.
本発明の算数学習用コンピュータプログラムは、
Sが奇数である場合に、N=N1に対応する前記分割ガイドを表示する際に、前記分割ガイドを前記一端からN1番目の前記枠を指示して表示し、その後にN1番目の前記枠と(N1+1)番目の前記枠との間を指示する位置に前記分割ガイドを移動させることを特徴とする。 The computer program for arithmetic learning of the present invention is
When S is an odd number, when displaying the division guide corresponding to N = N 1 , the division guide is indicated by indicating the N first frame from one end of the division guide, and then the N first frame is displayed. It is characterized in that the division guide is moved to a position indicating between the frame and the (N 1 + 1) th frame.
Sが奇数である場合に、N=N1に対応する前記分割ガイドを表示する際に、前記分割ガイドを前記一端からN1番目の前記枠を指示して表示し、その後にN1番目の前記枠と(N1+1)番目の前記枠との間を指示する位置に前記分割ガイドを移動させることを特徴とする。 The computer program for arithmetic learning of the present invention is
When S is an odd number, when displaying the division guide corresponding to N = N 1 , the division guide is indicated by indicating the N first frame from one end of the division guide, and then the N first frame is displayed. It is characterized in that the division guide is moved to a position indicating between the frame and the (N 1 + 1) th frame.
この特徴によれば、N1がSの半分に近い数であることが、容易に理解できる。Sが奇数の場合には、分割ガイドの左右に同数(S/2)の枠があるので半分であることが理解しやすいが、Sが奇数の場合にもN1がSの半分に近い数であることを理解させるものである。
According to this feature, it can be easily understood that N 1 is a number close to half of S. When S is odd, it is easy to understand that it is half because there are the same number (S / 2) frames on the left and right of the division guide, but even when S is odd, N 1 is a number close to half of S. It makes you understand that.
本発明の算数学習用コンピュータプログラムは、
S個の枠を表示する際に、前記一端から10番目の前記枠と11番目の前記枠との間に境界が表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
When displaying S frames, a boundary is displayed between the tenth frame and the eleventh frame from one end.
S個の枠を表示する際に、前記一端から10番目の前記枠と11番目の前記枠との間に境界が表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
When displaying S frames, a boundary is displayed between the tenth frame and the eleventh frame from one end.
この特徴によれば、境界によって、10を区切りとして意識した学習を行うことができる。(詳細は後述の実施例3を参照)
According to this feature, it is possible to perform conscious learning with 10 as a delimiter depending on the boundary. (See Example 3 below for details)
本発明の算数学習用コンピュータプログラムは、
S個の枠を表示する際に、前記一端から5番目の前記枠と6番目の前記枠との間及び15番目の前記枠と16番目の前記枠との間に境界が表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
When displaying the S frames, the boundary is displayed between the fifth frame and the sixth frame from one end and between the fifteenth frame and the sixteenth frame. It is a feature.
S個の枠を表示する際に、前記一端から5番目の前記枠と6番目の前記枠との間及び15番目の前記枠と16番目の前記枠との間に境界が表示されることを特徴とする。 The computer program for arithmetic learning of the present invention is
When displaying the S frames, the boundary is displayed between the fifth frame and the sixth frame from one end and between the fifteenth frame and the sixteenth frame. It is a feature.
この特徴によれば、10に加えて5を区切りとした学習も行うことができる。5は10の半分なので、10進法を学習する上で、5を区切りとすることもできる。特に6~9について視覚を介した理解がうまくできない場合には、5を区切りとしてそれを補助することができる。
According to this feature, it is possible to perform learning with 5 as a delimiter in addition to 10. Since 5 is half of 10, it is possible to use 5 as a delimiter when learning the decimal system. In particular, if the visual understanding of 6 to 9 is not good, 5 can be used as a delimiter to assist it.
本発明の算数学習用コンピュータプログラムによれば、本発明の算数学習用カードを容易に作成することができる。
According to the computer program for learning arithmetic of the present invention, the card for learning arithmetic of the present invention can be easily created.
以下、本発明の実施例について説明する。
Hereinafter, examples of the present invention will be described.
図1は、コンピュータプログラムの処理を説明する図である。算数学習用コンピュータプログラム1は、S=N+Mを学習するため、まず、Sを決定し(1a)、初期表示(図2(A))を行う(1b)。
FIG. 1 is a diagram illustrating the processing of a computer program. In order to learn S = N + M, the computer program 1 for arithmetic learning first determines S (1a) and performs initial display (FIG. 2A) (1b).
算数学習用コンピュータプログラム1は、次に、分割ガイド4の位置を決定し(1c)、それを表示する(1d)。分割ガイド4の位置の決定は、Nを決定することとほぼ等価である。
Next, the computer program 1 for arithmetic learning determines the position of the division guide 4 (1c) and displays it (1d). Determining the position of the split guide 4 is almost equivalent to determining N.
学習者が、分割ガイド4の操作を行うと、算数学習用コンピュータプログラム1は、分割表示(図2(D))を行う(1e)。ここで、「操作」は、学習者が分割を意識していることを確認するものであり、表示された分割ガイドをクリックする、エンターキーを押下する、その他いかなる操作としてもよい。また、学習者の操作がない場合にも時間(例えば10秒)の経過を操作とみなしてもよい。
When the learner operates the division guide 4, the computer program 1 for arithmetic learning performs division display (FIG. 2 (D)) (1e). Here, the "operation" confirms that the learner is aware of the division, and may be any operation such as clicking the displayed division guide, pressing the enter key, or any other operation. Further, even when there is no operation by the learner, the passage of time (for example, 10 seconds) may be regarded as an operation.
その後、算数学習用コンピュータプログラム1は、数式表示(分割)(1f)及び音声出力(分割)(1g)を行う。数式表示(分割)及び音声出力(分割)は両方を行ってもよく、一方のみを行ってもよく、全く行わなくてもよい。学習目的に応じて設計すればよい。なお、両方を行う場合には、画面表示と音声出力なので、同時に行うこともできる。
After that, the computer program 1 for arithmetic learning performs mathematical expression display (division) (1f) and voice output (division) (1g). Both the mathematical expression display (division) and the audio output (division) may be performed, only one may be performed, or none may be performed at all. It may be designed according to the learning purpose. When both are performed, the screen display and the audio output can be performed at the same time.
算数学習用コンピュータプログラム1は、数式表示(分割)(1f)及び音声出力(分割)(1g)に替えて数式表示(足し算/引き算)(1h)及び音声出力(足し算/引き算)(1i)を行ってもよい。以後、「数式表示(分割)」(1f)及び「数式表示(足し算/引き算)」(1h)を共に「数式表示」と記し、音声出力(分割)(1g)音声出力(足し算/引き算)(1i)を共に「音声出力」と記し、符号によって区別する。
The computer program 1 for arithmetic learning displays mathematical expressions (addition / subtraction) (1h) and audio output (addition / subtraction) (1i) instead of mathematical expression display (division) (1f) and audio output (division) (1g). You may go. Hereinafter, both "mathematical expression display (division)" (1f) and "mathematical expression display (addition / subtraction)" (1h) are referred to as "mathematical expression display", and audio output (division) (1g) audio output (addition / subtraction) ( Both 1i) are described as "voice output" and are distinguished by a code.
算数学習用コンピュータプログラム1は、学習が終了したか否かを判断し(1j)、終了していない場合には、改めて初期表示(1b)から学習を行わせる。Nを変更して次の学習を行うものである。分割ガイド4の位置を決定する(1c)時に、Nの値を変化させる。例えば、Nを前回よりも1だけ増やすことが考えられる。1つのSの値について、Nを変化させて学習するものである。Nを1ずつ増やしながら逐次に学習するので、Nが1だけ増加するとMが1だけ減少することがわかり、効果的に学習できる。
The computer program 1 for arithmetic learning determines whether or not the learning is completed (1j), and if it is not completed, the learning is performed again from the initial display (1b). The next learning is performed by changing N. When determining the position of the division guide 4 (1c), the value of N is changed. For example, it is conceivable to increase N by 1 from the previous time. For one value of S, N is changed for learning. Since learning is performed sequentially while increasing N by 1, it can be seen that when N increases by 1, M decreases by 1, and learning can be performed effectively.
なお、学習が終了していない場合については、次の学習において、Nの値のみならずSの値を変化させることも考えられる。その場合には、初期表示(1b)からでなくSの決定(1a)から次の学習を行えばよい。
If the learning is not completed, it is conceivable to change not only the value of N but also the value of S in the next learning. In that case, the next learning may be performed not from the initial display (1b) but from the determination of S (1a).
図2は、表示の推移を説明する図である。S=5の場合について表したものである。図2(A)から図2(F)の順に表示が推移する。
FIG. 2 is a diagram for explaining the transition of the display. It shows the case of S = 5. The display changes in the order of FIG. 2 (A) to FIG. 2 (F).
図2(A)は、初期表示(1b)を示す。5つの枠2が横方向に並べられ、各々の枠に図形3aが配置されている。また、図形3aの形状、色彩は任意のものでよい。図では、黒色で示したが、例えば赤色の円形とすることができる(後述の図形3b1、3cについても同様)。なお、図には枠2の境界線を破線で表示したが、必ずしも表示しなくともよい。5つの図形3aのみによっても「5」の数が理解できる。
FIG. 2 (A) shows the initial display (1b). Five frames 2 are arranged in the horizontal direction, and the figure 3a is arranged in each frame. Further, the shape and color of the figure 3a may be arbitrary. In the figure, it is shown in black, but it can be, for example, a red circle (the same applies to the figures 3b1 and 3c described later). Although the boundary line of the frame 2 is indicated by a broken line in the figure, it does not necessarily have to be indicated. The number of "5" can be understood only by the five figures 3a.
図2(B)(C)は、分割ガイドの位置決定及び表示(1b、1c)を示す。図2(B)は、S=5であるところ、S/2=2.5の位置に分割ガイド4を表示したものである。枠2の境界ではなく、3番目の枠2を分割ガイド4が示している。
2 (B) and 2 (C) show the position determination and display (1b, 1c) of the division guide. FIG. 2B shows the division guide 4 displayed at the position of S / 2 = 2.5 where S = 5. The division guide 4 shows the third frame 2 instead of the boundary of the frame 2.
図2(C)は、S=5であるところ、ROUNDUP(S/2)=3の位置に分割ガイド4を表示したものである。3番目の枠2と4番目の枠2の間を、分割ガイド4が示している。
FIG. 2C shows the division guide 4 displayed at the position of ROUNDUP (S / 2) = 3 where S = 5. The division guide 4 shows between the third frame 2 and the fourth frame 2.
ここで、Sが5でなくて偶数である場合には、図2(B)と(C)とが同一である。この場合には、図2(B)の表示を省略する。
Here, when S is not 5 but an even number, FIGS. 2B and 2C are the same. In this case, the display of FIG. 2B is omitted.
Sが奇数の場合には、N=ROUNDUP(S/2)であれば、図2(B)の表示を行う。分割ガイド4の示す箇所が2つの枠2の間ではないので、分割ガイド4が分割箇所を示していないが、図2(C)の表示と同一形状の分割ガイド4を表示することが好ましい。Sのちょうど半分の箇所を示すものであり、ここから分割ガイド4を移動して図2(C)の状態とすることで、Sの半分に近い値での分割であることが示される。
If S is an odd number and N = ROUNDUP (S / 2), the display of FIG. 2 (B) is performed. Since the portion indicated by the division guide 4 is not between the two frames 2, the division guide 4 does not indicate the division portion, but it is preferable to display the division guide 4 having the same shape as the display of FIG. 2C. It shows exactly half of S, and by moving the division guide 4 from here to the state of FIG. 2 (C), it is shown that the division is performed at a value close to half of S.
N≠ROUNDUP(S/2)の場合、例えばS=5、N=4の場合には、図2(B)の表示を行わない。Sの半分に近い値での分割ではないためである。
When N ≠ ROUNDUP (S / 2), for example, when S = 5 and N = 4, the display of FIG. 2B is not performed. This is because it is not a division with a value close to half of S.
図2(C)の表示において、分割ガイド4が操作される(分割ガイド4がクリックされる、エンターキーが押下される、時間(例えば10秒)が経過する、その他設計で定めたものが行われる)と分割表示が行われる。
In the display of FIG. 2C, the division guide 4 is operated (the division guide 4 is clicked, the enter key is pressed, the time (for example, 10 seconds) elapses, and other things specified by the design are performed. ) And split display is performed.
図2(D)は、分割表示(1e)を示す。図2(A)と比較すると、N=3に対応して3番目の枠と4番目の枠との間に境界5aが表示されていることと、図形3aの左の3つが図形3b1に、右の2つが図形3cに変更されていることとが相違している。
FIG. 2 (D) shows a divided display (1e). Compared with FIG. 2A, the boundary 5a is displayed between the third frame and the fourth frame corresponding to N = 3, and the three on the left of the figure 3a are in the figure 3b1. It is different from the fact that the two on the right are changed to the figure 3c.
境界5aによって、Nの幅のカードとMの幅のカードのように見える。2枚のカードによってSの幅となり、SがNとMに分割されることが理解しやすい。
Boundary 5a makes it look like an N-width card and an M-width card. It is easy to understand that the width of S is obtained by two cards and S is divided into N and M.
図において、図形3b1及び図形3cを、図形3aとは相違する網掛けで示した。図形3b1及び図形3cを、図形3aと相違する色彩とすることが好ましい。例えば、図形3aが赤色の場合、図形3b1を青色、図形3cを黄色とすることが考えられる。このように、図形3b1と図形3cとを明確に区別できる色彩とすることで、Nの幅のカードとMの幅のカードのように見えることが確実になる。なお、図形3b1と図形3cとのいずれか一方は、図形3aと同一のあるいは類似した色彩であってもよい。
In the figure, the figure 3b1 and the figure 3c are shown by shading different from the figure 3a. It is preferable that the figures 3b1 and the figure 3c have colors different from those of the figure 3a. For example, when the figure 3a is red, it is conceivable that the figure 3b1 is blue and the figure 3c is yellow. By setting the color so that the figure 3b1 and the figure 3c can be clearly distinguished in this way, it is ensured that the card looks like an N-width card and an M-width card. In addition, either one of the figure 3b1 and the figure 3c may have the same or similar color as the figure 3a.
図2(E)は、数式表示(1f)を表す。図2(D)の表示に加えて「5=3+2」とのテキスト表示6aを行う。なお、図2(D)の表示を省略して、分割ガイド4が操作されたことで図2(E)の表示を行ってもよい。
FIG. 2 (E) represents a mathematical expression display (1f). In addition to the display of FIG. 2D, the text display 6a of "5 = 3 + 2" is performed. Note that the display of FIG. 2 (D) may be omitted and the display of FIG. 2 (E) may be performed by operating the division guide 4.
図2(F)は、音声出力(1g)を表す。図中の吹き出し7が音声出力である(画面に表示されない)。音声出力は、数式に合わせた「5は3と2」との音声出力7aとする。又は「5は3たす2」との音声出力としてもよい。5が3と2に分割されることを示すが、数式表示に5,3,2の順に表れるので、この音声を容易に理解することができる。これにより、分割と足し算とを関連付けて学習させることができる。
FIG. 2 (F) represents an audio output (1 g). The balloon 7 in the figure is an audio output (not displayed on the screen). The audio output is an audio output 7a of "5 is 3 and 2" according to the mathematical formula. Alternatively, it may be an audio output of "5 is 3 plus 2". It is shown that 5 is divided into 3 and 2, but since it appears in the order of 5, 3 and 2 in the mathematical expression display, this voice can be easily understood. As a result, it is possible to learn by associating division with addition.
図3は、表示の推移を説明する図である。図に(E)(F)と記され、(A)(B)(C)(D)がないが、図2と同一の(A)(B)(C)(D)である。すなわち、数式表示(1h)と音声出力(1i)を、図2に対応させて(E)(F)で表している。
FIG. 3 is a diagram for explaining the transition of the display. It is written as (E) (F) in the figure, and there is no (A) (B) (C) (D), but it is the same (A) (B) (C) (D) as in FIG. That is, the mathematical expression display (1h) and the audio output (1i) are represented by (E) and (F) corresponding to FIG.
テキスト表示を6a「5=3+2」に替えて6b「3+2=5」とする。図2に比して左辺と右辺が入れ替わったことにより、通常の足し算の計算表示となっている。
Replace the text display with 6a "5 = 3 + 2" and set it to 6b "3 + 2 = 5". Since the left side and the right side are exchanged as compared with FIG. 2, the calculation display of normal addition is obtained.
音声出力は、「3たす2は5」との音声出力7bとする。
The audio output is the audio output 7b with "3 plus 2 is 5".
以上詳細に説明したように、本実施例の算数学習用コンピュータプログラム1は、図2(A)に示す初期表示から、分割ガイド4に示される箇所で分割して、SがNとMに分割されることの理解を経て、NとMがSに合成されることが、N+M=Sという足し算の形式で、視覚を介して効率的に学習される。
As described in detail above, the computer program 1 for arithmetic learning of this embodiment is divided from the initial display shown in FIG. 2A at the points shown in the division guide 4, and S is divided into N and M. After understanding that N and M are combined into S, it is efficiently learned through vision in the form of addition of N + M = S.
本実施例は、SがNとMに分割されることを、足し算(N+M=S)でなく引き算(S―N=M)で示すものである。実施例1と同一の部分については、詳細な説明を省略する。
This embodiment shows that S is divided into N and M by subtraction (SN = M) instead of addition (N + M = S). Detailed description of the same parts as in the first embodiment will be omitted.
図4は、表示の推移を説明する図である。図に(E)(F)と記され、(A)(B)(C)(D)がないが、実施例1(図2)と同一の(A)(B)(C)(D)である。すなわち、分割ガイドの操作までの表示は実施例1と同一であり、その後の表示を、図2に対応させて(E)(F)で表している。
FIG. 4 is a diagram for explaining the transition of the display. (E) (F) are shown in the figure, and there is no (A) (B) (C) (D), but the same (A) (B) (C) (D) as in Example 1 (FIG. 2). Is. That is, the display up to the operation of the division guide is the same as that of the first embodiment, and the subsequent display is represented by (E) and (F) corresponding to FIG.
図4(E)は、分割表示(1e)を示す。図2(D)と比較すると、図形3b1が図形3b2に変更されている。図形3b2には網掛けを施していないが、図形3b2は、が学習者に与える印象を小さくするように無彩色である。これに対し、図形3cは、実施例1(図2(D))と同様に有彩色である。
FIG. 4 (E) shows a divided display (1e). Compared with FIG. 2D, the figure 3b1 is changed to the figure 3b2. Although the figure 3b2 is not shaded, the figure 3b2 is achromatic so as to reduce the impression given to the learner. On the other hand, the figure 3c is a chromatic color as in the first embodiment (FIG. 2 (D)).
以上の表示によれば、図形3aで示された表示から、図形3b2で示されたN個が削除されたような印象を学習者に与えることができる。この印象を強調するために、図形3aと図形3cとを同色にしてもよい。
According to the above display, it is possible to give the learner the impression that N pieces shown in the figure 3b2 are deleted from the display shown in the figure 3a. In order to emphasize this impression, the figure 3a and the figure 3c may be the same color.
なお、図形3b2を、実施例1と同様に有彩色としてもよい。
Note that the figure 3b2 may be a chromatic color as in the first embodiment.
図4(E)は、数式表示(1h)を表す。「5-3=2」とのテキスト表示6cを行う。
FIG. 4 (E) represents a mathematical expression display (1h). The text display 6c with "5-3 = 2" is performed.
図4(F)は、音声出力(1i)を表す。図中の吹き出し7が音声出力である(画面に表示されない)。音声出力は、数式に合わせた「5ひく3は2」との音声出力7cとする。また、「S-M=N」として、NとMを入れ替え、無彩色と有彩色の図形を入れ替えてもよい。これにより、分割と引き算とを関連付けて学習させることができる。
FIG. 4 (F) represents an audio output (1i). The balloon 7 in the figure is an audio output (not displayed on the screen). The audio output is an audio output 7c with "5 minus 3 is 2" according to the mathematical formula. Further, N and M may be exchanged as “SM = N”, and the achromatic and chromatic figures may be exchanged. This makes it possible to learn by associating division and subtraction.
以上詳細に説明したように、本実施例の算数学習用コンピュータプログラム1は、SがNとMに分割されることを、S-N=Mという引き算の形式で、視覚を介して効率的に学習できる。
As described in detail above, the computer program 1 for arithmetic learning of this embodiment efficiently indicates that S is divided into N and M in the form of subtraction of SN = M through vision. You can learn.
本実施例は、Sが10を超えるものである。実施例1、2と同様の部分については、詳細な説明を省略する。
In this embodiment, S exceeds 10. Detailed description of the same parts as those of Examples 1 and 2 will be omitted.
図5は、表示の推移を説明する図である。S=13の場合について表したものである。図に(A)(C)(D)と記され、(B)(E)(F)がないが、実施例1(図2)と同様の(B)(E)(F)である。すなわち、図2、図4に(B)で示された端数位置への分割ガイドの表示、(E)(F)で示された数式表示、音声出力については、実施例1、2と同様である。(Sの値の相違により、枠2の数は相違する。)
FIG. 5 is a diagram for explaining the transition of the display. It shows the case of S = 13. In the figure, (A), (C), and (D) are written, and (B), (E), and (F) are not present, but (B), (E), and (F) are the same as in Example 1 (FIG. 2). That is, the display of the division guide to the fractional position shown in FIGS. 2 and 4, the mathematical expression displayed in (E) and (F), and the audio output are the same as those in Examples 1 and 2. be. (The number of frames 2 differs depending on the difference in the value of S.)
図5(A)は、初期表示(1b)を表す。S=13であるため、S=5である実施例1,2と枠2の数が相違する。この他に、以下の相違がある。
FIG. 5 (A) represents the initial display (1b). Since S = 13, the number of frames 2 is different from that of Examples 1 and 2 where S = 5. In addition to this, there are the following differences.
図形を有さない枠が、図形を有する枠と合わせて全部で18個表示されている。学習対象の数が18(=9+9)以下なので、統一的に18個の枠としたものである。
A total of 18 frames without figures are displayed, including frames with figures. Since the number of learning objects is 18 (= 9 + 9) or less, the number of learning objects is unified to 18 frames.
5番目の枠と6番目の枠の間、10番目の枠と11番目の枠の間、15番目の枠と16番目の枠の間に、境界5bが表示されている。学習者に、5を区切りとして意識させ、例えば、7は5と2であるとういうように、5を区切りとした学習を行わせることができる。なお、5でなく10を区切りとした学習を行わせるために、10番目の枠と11番目の枠の間のみに境界5bを表示し5番目の枠と6番目の枠の間、15番目の枠と16番目の枠の間には境界5bを表示しないこととしてもよい。
The boundary 5b is displayed between the 5th frame and the 6th frame, between the 10th frame and the 11th frame, and between the 15th frame and the 16th frame. It is possible to make the learner aware of 5 as a delimiter, and to perform learning with 5 as a delimiter, for example, 7 is 5 and 2. In addition, in order to perform learning with 10 as a delimiter instead of 5, the boundary 5b is displayed only between the 10th frame and the 11th frame, and the 15th frame is displayed between the 5th frame and the 6th frame. The boundary 5b may not be displayed between the frame and the 16th frame.
図5(C)は、分割ガイドの表示(1d)を表す。分割ガイド4は、N=7(=ROUNDUP(13/2))の位置に表示されている。図に破線で示した、N=8、N=9の位置にも、2回目以降の学習で表示され得る。
FIG. 5C shows the display (1d) of the division guide. The division guide 4 is displayed at the position of N = 7 (= ROUNDUP (13/2)). The positions of N = 8 and N = 9 shown by the broken lines in the figure can also be displayed in the second and subsequent learnings.
以上のように、N=7、N=8、N=9の3つを学習することで、S=13の場合の学習は完結できる。13=7+6、13=8+5、13=9+4のみで、2つの1桁の数に分割される場合が網羅されるからである。これを、N=7、N=8、N=9の順で、Nを1ずつ増やしながら学習すると、Nが増えればその分Mが減ることが容易に学習できる。
As described above, by learning the three of N = 7, N = 8, and N = 9, the learning in the case of S = 13 can be completed. This is because only 13 = 7 + 6, 13 = 8 + 5, and 13 = 9 + 4 cover the case where the number is divided into two single-digit numbers. If this is learned while increasing N by 1 in the order of N = 7, N = 8, and N = 9, it is easy to learn that as N increases, M decreases by that amount.
上記に加えて、N=6、N=5、N=4を学習してもよい。N=7、N=8、N=9に比して、NとMとが入れ替わっただけなので、特に学習せずとも理解できると考えられるが、NとMを入れ替えて学習することも、学習者のレベルによっては効果的である。
In addition to the above, N = 6, N = 5, N = 4 may be learned. Compared to N = 7, N = 8, N = 9, N and M are just swapped, so it is thought that you can understand without special learning, but learning by swapping N and M is also learning. It is effective depending on the level of the person.
図5(D)は、分割表示(1e)を示す。図は、図2(D)と同様に有彩色の図形3b1を用いている。足し算に対応するものである。図4(D)と同様に無彩色の図形3b2を用いる(引き算に対応する)ものとしてもよい。
FIG. 5 (D) shows a divided display (1e). The figure uses a chromatic figure 3b1 as in FIG. 2 (D). It corresponds to addition. Similar to FIG. 4D, the achromatic figure 3b2 may be used (corresponding to subtraction).
境界5aが、S番目の枠の右端にも表示される。これにより、あたかも、Nの幅のカードと、Mの幅のカードの2枚が表示されているように見える。学習者は、SがNとMに分割されることを、視覚を介して理解する。
Boundary 5a is also displayed at the right end of the S-th frame. As a result, it seems as if two cards, an N-width card and an M-width card, are displayed. The learner visually understands that S is divided into N and M.
境界5bが表示されていることにより、学習者は、詳細な理解が可能となる。N=7=5+2、M=6=3+3であることが、境界5bによって理解できる。これにより、7と6を合成して得られる13の1の位が3であることが容易に理解される。
By displaying the boundary 5b, the learner can understand in detail. It can be understood from the boundary 5b that N = 7 = 5 + 2 and M = 6 = 3 + 3. From this, it is easily understood that the ones place of 13 obtained by synthesizing 7 and 6 is 3.
1の位の値を理解する目的では、境界5bを、10番目の枠と11番目の枠の間の間にのみ表示し、5番目の枠と6番目の枠の間、15番目の枠と16番目の枠の間に、表示しないことも考えられる。N=7、M=6=3+3であることが、境界5bによって理解できる。6~9の視覚を介した理解が進んだ学習者に適したものとなる。
For the purpose of understanding the value of the 1st place, the boundary 5b is displayed only between the 10th frame and the 11th frame, and between the 5th frame and the 6th frame, and the 15th frame. It is also conceivable that it will not be displayed between the 16th frames. It can be understood from the boundary 5b that N = 7 and M = 6 = 3 + 3. It is suitable for learners who have advanced understanding through 6 to 9 visions.
以上詳細に説明したように、本実施例の算数学習用コンピュータプログラム1は、Sが10以上の場合に、境界5bによって、1の位の値が、視覚を介して効率的に学習される。
As described in detail above, in the computer program 1 for arithmetic learning of this embodiment, when S is 10 or more, the value of the 1st place is efficiently learned through the visual sense by the boundary 5b.
本発明の算数学習用コンピュータプログラムは、小さな数の分割が容易に理解でき、算数の高い学習効果をもたらす。多くの教育機関や個人における利用が考えられる。
The computer program for learning arithmetic of the present invention can easily understand the division of small numbers and brings about a high learning effect of arithmetic. It can be used by many educational institutions and individuals.
1 算数学習用コンピュータプログラム
2 枠
3 図形
3a 図形(初期)
3b1 図形(左側)
3b2 図形(左側)
3c 図形(右側)
4 分割ガイド
5 境界
5a 境界(数値依存)
5b 境界(5の倍数)
6 テキスト
6a テキスト(分割)
6b テキスト(足し算)
6c テキスト(引き算)
7 音声
7a 音声(分割)
7b 音声(足し算)
7c 音声(引き算) 1 Computer program for learning arithmetic 2Frame 3 Figure 3a Figure (initial)
3b1 figure (left side)
3b2 figure (left side)
3c figure (right side)
4Division guide 5 Boundary 5a Boundary (numerical dependence)
5b boundary (multiple of 5)
6 text 6a text (split)
6b text (addition)
6c text (subtraction)
7Voice 7a Voice (split)
7b Voice (addition)
7c voice (subtraction)
2 枠
3 図形
3a 図形(初期)
3b1 図形(左側)
3b2 図形(左側)
3c 図形(右側)
4 分割ガイド
5 境界
5a 境界(数値依存)
5b 境界(5の倍数)
6 テキスト
6a テキスト(分割)
6b テキスト(足し算)
6c テキスト(引き算)
7 音声
7a 音声(分割)
7b 音声(足し算)
7c 音声(引き算) 1 Computer program for learning arithmetic 2
3b1 figure (left side)
3b2 figure (left side)
3c figure (right side)
4
5b boundary (multiple of 5)
6 text 6a text (split)
6b text (addition)
6c text (subtraction)
7
7b Voice (addition)
7c voice (subtraction)
Claims (14)
- 図形の描かれた枠をS個、一端から1方向に順に並べて表示し、
前記一端からN番目の前記枠と(N+1)番目の前記枠との間を指示する分割ガイドを表示し、
前記分割ガイドへの操作によって、前記一端からN個の前記枠の前記図形と、他のM個の前記枠の前記図形とを異なる色で表示する算数学習用コンピュータプログラムであって、
S≦18、かつ、N≦9である全てのS、Nについての動作を行うことが可能であることを特徴とする、算数学習用コンピュータプログラム。 S pieces of frames with figures are displayed side by side in one direction from one end.
A division guide indicating between the N-th frame and the (N + 1) -th frame from one end is displayed.
A computer program for arithmetic learning that displays N figures of the frame and M figures of the other frames in different colors by operating the division guide.
A computer program for arithmetic learning, characterized in that it is possible to perform operations for all S and N in which S ≦ 18 and N ≦ 9. - 前記一端からN個の前記枠の前記図形と、他の前記枠の前記図形とを異なる色で表示する際に、前記一端からN番目の前記枠と(N+1)番目の前記枠との間に境界が表示されることを特徴とする、請求項1に記載の算数学習用コンピュータプログラム。 When displaying the figure of the frame of N pieces from one end and the figure of the other frame in different colors, between the frame Nth from the one end and the frame (N + 1) th. The computer program for arithmetic learning according to claim 1, wherein a boundary is displayed.
- 前記分割ガイドへの操作によって、「S=N+M」とのテキストを表示することを特徴とする、請求項1又は2に記載の算数学習用コンピュータプログラム。 The computer program for arithmetic learning according to claim 1 or 2, wherein the text "S = N + M" is displayed by operating the division guide.
- 前記分割ガイドへの操作によって、「SはNたすM」又は「SはNとM」との音声を出力することを特徴とする、請求項1~3のいずれか1項に記載の算数学習用コンピュータプログラム。 The arithmetic according to any one of claims 1 to 3, wherein the voice of "S is N plus M" or "S is N and M" is output by the operation to the division guide. Computer program for learning.
- 前記分割ガイドへの操作によって、「N+M=S」とのテキストを表示することを特徴とする、請求項1又は2に記載の算数学習用コンピュータプログラム。 The computer program for arithmetic learning according to claim 1 or 2, wherein the text "N + M = S" is displayed by operating the division guide.
- 前記分割ガイドへの操作によって、「NたすMはS」との音声を出力することを特徴とする、請求項1、2、5のいずれか1項に記載の算数学習用コンピュータプログラム。 The computer program for arithmetic learning according to any one of claims 1, 2 and 5, characterized in that a voice of "N plus M is S" is output by operating the division guide.
- 前記分割ガイドへの操作によって、「S-N=M」又は「S-M=N」とのテキストを表示することを特徴とする、請求項1又は2に記載の算数学習用コンピュータプログラム。 The computer program for arithmetic learning according to claim 1 or 2, wherein the text "SN = M" or "SM = N" is displayed by operating the division guide.
- 前記分割ガイドへの操作によって、「SひくNはM」又は「SひくMはN」との音声を出力することを特徴とする、請求項1、2又は7に記載の算数学習用コンピュータプログラム。 The computer program for arithmetic learning according to claim 1, 2 or 7, wherein the voice of "S-subtracting N is M" or "S-subtracting M is N" is output by operating the division guide. ..
- 前記分割ガイドへの操作によって表示される、前記一端からN個の前記枠の前記図形は無彩色で表示され、他のM個の前記枠の前記図形は有彩色で表示されること、または前記一端からN個の前記枠の前記図形は有彩色で表示され、他のM個の前記枠の前記図形は無彩色で表示されることを特徴とする、請求項7又は8に記載の算数学習用コンピュータプログラム。 The figure of the frame of N from one end, which is displayed by the operation to the division guide, is displayed in achromatic color, and the figure of the other M frames is displayed in chromatic color, or the figure is displayed in chromatic color. The arithmetic learning according to claim 7 or 8, wherein the figures of the frame of N from one end are displayed in chromatic colors, and the figures of the other frames of M are displayed in achromatic colors. For computer programs.
- 前記分割ガイドを表示し、表示された分割ガイドへの操作に対する動作の後に次の分割ガイドを表示する形式で逐次に学習させ、
1つのSに対して、N=N1から、N=N2まで、Nの値を1ずつ順番に増やして逐次に学習させ、
N1=ROUNDUP(S/2)
N2=MIN(S-1,9)
であることを特徴とする、請求項1~9のいずれか1項に記載の算数学習用コンピュータプログラム。 The division guide is displayed, and after the operation for the operation to the displayed division guide, the next division guide is displayed, and the learning is sequentially performed.
For one S, from N = N 1 to N = N 2 , the value of N is sequentially increased by 1 and learned sequentially.
N 1 = ROUNDUP (S / 2)
N 2 = MIN (S-1, 9)
The computer program for arithmetic learning according to any one of claims 1 to 9, wherein the computer program is characterized by the above. - 前記分割ガイドを表示し、表示された分割ガイドへの操作に対する動作の後に次の分割ガイドを表示する形式で逐次に学習させ、
1つのSに対して、N=N1から、N=N2まで、Nの値を1ずつ順番に減らして逐次に学習させ、
N1=ROUNDDOWN(S/2)
N2=MAX(S-9,1)
であることを特徴とする、請求項1~9のいずれか1項に記載の算数学習用コンピュータプログラム。 The division guide is displayed, and after the operation for the operation to the displayed division guide, the next division guide is displayed, and the learning is sequentially performed.
For one S, from N = N 1 to N = N 2 , the value of N is sequentially reduced by 1 and learned sequentially.
N 1 = ROUNDDOWN (S / 2)
N 2 = MAX (S-9,1)
The computer program for arithmetic learning according to any one of claims 1 to 9, wherein the computer program is characterized by the above. - Sが奇数である場合に、N=N1に対応する前記分割ガイドを表示する際に、前記分割ガイドを前記一端からN1番目の前記枠を指示して表示し、その後にN1番目の前記枠と(N1+1)番目または(N1-1)番目の前記枠との間を指示する位置に前記分割ガイドを移動させることを特徴とする、請求項10、11に記載の算数学習用コンピュータプログラム。 When S is an odd number, when displaying the division guide corresponding to N = N 1 , the division guide is indicated by indicating the N first frame from one end of the division guide, and then the N first frame is displayed. and wherein the moving the divided guide position designated between the frame and the (N 1 +1) -th or (N 1 -1) th said frame, arithmetic learning of claim 10, 11 Computer program for.
- S個の枠を表示する際に、前記一端から10番目の前記枠と11番目の前記枠との間に境界が表示されることを特徴とする、請求項1~12のいずれか1項に記載の算数学習用コンピュータプログラム。 The invention according to any one of claims 1 to 12, wherein when displaying the S frames, a boundary is displayed between the tenth frame from one end and the eleventh frame. The described computer program for learning arithmetic.
- S個の枠を表示する際に、前記一端から5番目の前記枠と6番目の前記枠との間及び15番目の前記枠と16番目の前記枠との間に境界が表示されることを特徴とする、請求項13に記載の算数学習用コンピュータプログラム。 When displaying the S frames, the boundary is displayed between the fifth frame and the sixth frame and between the fifteenth frame and the sixteenth frame from one end. The computer program for learning arithmetic according to claim 13.
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