WO2022018780A1 - Arithmetic learning computer program - Google Patents

Arithmetic learning computer program Download PDF

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Publication number
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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frame
displayed
computer program
learning
division guide
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PCT/JP2020/027980
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French (fr)
Japanese (ja)
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明子 直井
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明子 直井
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Priority to JP2022538491A priority Critical patent/JPWO2022018780A1/ja
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Publication of WO2022018780A1 publication Critical patent/WO2022018780A1/en

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    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B19/00—Teaching not covered by other main groups of this subclass
    • 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

算数学習用コンピュータプログラムComputer program for arithmetic learning
　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.
特開２０１４－１７４２７７号公報Japanese Unexamined Patent Publication No. 2014-174277
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
　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.
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。（実施例１）FIG. 1 is a diagram illustrating processing of a computer program. (Example 1) 図２は、表示の推移を説明する図である。（実施例１）FIG. 2 is a diagram illustrating a transition of display. (Example 1) 図３は、表示の推移を説明する図である。（実施例１）FIG. 3 is a diagram illustrating a transition of the display. (Example 1) 図４は、表示の推移を説明する図である。（実施例２）FIG. 4 is a diagram illustrating a transition of the display. (Example 2) 図５は、表示の推移を説明する図である。（実施例３）FIG. 5 is a diagram illustrating a transition of the display. (Example 3)
　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 2 Frame 3 Figure 3a Figure (initial)
3b1 figure (left side)
3b2 figure (left side)
3c figure (right side)
4 Division guide 5 Boundary 5a Boundary (numerical dependence)
5b boundary (multiple of 5)
6 text 6a text (split)
6b text (addition)
6c text (subtraction)
7 Voice 7a Voice (split)
7b Voice (addition)
7c voice (subtraction)

Claims (14)

  1. 　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.
  2. 　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.
  3. 　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.
  4. 　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.
  5. 　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.
  6. 　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.
  7. 　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.
  8. 　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. ..
  9. 　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.
  10. 　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.
  11. 　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.
  12. 　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.
  13. 　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.
  14. 　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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