CN112289086A

CN112289086A - Teaching appliance for understanding expression relation

Info

Publication number: CN112289086A
Application number: CN202011309841.2A
Authority: CN
Inventors: 陈清华; 陈雨青; 范林
Original assignee: Beijing Normal University
Current assignee: Beijing Normal University
Priority date: 2020-11-20
Filing date: 2020-11-20
Publication date: 2021-01-29

Abstract

The invention discloses a teaching apparatus for systematically cultivating primary and secondary school students to understand important mathematical contents such as constants, variables, expressions, quantitative relationships, equations, inequalities, solutions, functions, and function images. Through students' hands-on operation of tools and interactive and intuitive display, students' interest in learning is stimulated, so that students can better understand and consolidate relevant mathematical knowledge. The teaching apparatus can be an independent device, and the method can also be run on a common computer or a tablet computer in the form of computer software to obtain the same teaching effect.

Description

Teaching appliance for understanding expression relation

Technical Field

The invention belongs to teaching appliances, and essentially implements advanced teaching methods and concepts through proper equipment. The specific method relates to mathematics, education, psychology, information technology and the like.

Background

In mathematical learning, there are some basic concepts including constants, variables, expressions, quantitative relationships, equations, inequalities, simplifications, solutions, functions, etc., students generally have difficulty in understanding and mastering, and often encounter obstacles in the analysis and calculation processes, and some teachers feel difficult to describe clearly in teaching. But the grasp of the basic content of the part is closely related to the flexible application of the mathematical knowledge and the further learning of the mathematical knowledge in the future. Learning to successfully solve and break through this section is extremely important.

An important feature of mathematical knowledge is that they tend to be abstract. The advantage of abstraction is that a mathematical object can correspond to infinite actual objects, and a mathematical method can be applied to solve infinite actual problems, which is the strong point of mathematics. However, abstraction poses a great challenge to primary and secondary school education, because the thinking characteristics of the young students take concrete image thinking as a main form, the form of intuitive action thinking is kept, and the mathematical thought and the mathematical thinking method are difficult to be grasped only by the explanation of teachers in the cognitive process. Abstract, rather than intuitive, content can make it difficult for many students to accept, not to mention that teachers want students to achieve a true fusion.

For better education, the mental characteristics of primary and secondary school students need to be started, and the knowledge points which need to be mastered by the students are displayed in an intuitive way of actual images. Many of kindergarten and elementary school's teaching process are counting concrete objects, just so doing. Practice proves that students can feel natural, intimate and real to learn and are not afraid of mathematics by closely relating to the life reality of the students in mathematical education.

The mathematics teaching process is a special cognition process, and the key for learning good mathematics is that students actively participate in the learning process. The famous psychologist Piyaje says: the thinking of children is started from actions, and the children can not develop thinking by cutting off the connection between the actions and the thinking. "british educational house roche also states: the primary skill of educating children is to change the things that children should do into a game. Not only children, teenagers, even adults learn, but also the knowledge obtained by the mode of experience of hands-on can be faster and firmer, and the use can be smoother.

A good mathematical teaching aid is just required to present knowledge to users in an intuitive mode by enabling the users to operate the teaching aid by themselves, and obstacles brought by abstract information are broken. The invention integrates basic concepts and knowledge of constants, variables, expressions, quantitative relations, equalities, inequalities, simplifications, solutions, functions and the like into a numerical-based relation design teaching aid, and promotes a user to really understand and master the knowledge.

The main technical parts are as follows:

the fusion of mathematical knowledge, constants, variables, expressions, quantitative relationships, equality, inequality, simplification, solution, functions, and the like, seems to be fragmented. There are actually profound relationships between them, which are essentially relationships with numbers, and there are three basic relationships: relationships that are equal, greater than or less than, greater than or equal to, less than or equal to, and not equal to are not determinative are derivatives of the primary relationship, and may be achieved by discussing the primary relationship. The relationship between constants does not change, there may be a change in the relationship between variables, they may remain the same or in some cases change. Reduction refers to obtaining simpler mathematical relationships by operating on equality and inequality, solving to reduce equality or inequality to a specific form, with the unknowns (variable symbols) in one segment only. The function is the relationship between two variables, a mapping, an input and an output.

Friendly Interface design, User Interface (UI) refers to the integral design of man-machine interaction, operation logic and attractive Interface of software. The good UI design not only enables the software to become individual and tasteful, but also enables the operation of the software to become comfortable, simple and free, and fully embodies the positioning and characteristics of the software. The interface is designed for primary and middle school students, and particularly, the interface is simple and convenient, simple to operate, capable of interacting in real time, clear and visual in result, and free of operation and pleasure for the students to use.

In practice, the method may exist as a stand-alone hardware device. The design content can also be realized through computer programming and run on a common computer, a tablet personal computer or even a mobile phone in the form of APP.

Disclosure of Invention

The invention provides a set of mathematical teaching tools which integrate knowledge points such as constants, variables, expressions, quantitative relations, equalities, inequalities, simplifications, solutions, functions and the like. From the aspects of education and psychology, abstract mathematical knowledge is displayed in an intuitive graphic mode, and the method is suitable for classroom teaching and knowledge consolidation after class.

The invention provides a set of mathematical teaching apparatus, which comprises a machine body, a shell, keys, a screen and the like. The housing covers and protects the entire body. The front surface of the shell is provided with a screen and a key part. The keys include switches, reset clear operations, and some example buttons.

And the coordinate position is modified on the screen in an interactive mode, the result of the expression is operated in real time and is visually represented by the movement of the point on the axis. The modified mathematical expression may be clicked and saved as an example after the modification is completed.

The invention can also be directly operated on a common computer, a tablet personal computer and a mobile phone in the form of APP. The operation is performed by a mouse or a touch screen.

Advantageous effects

1. The basic mathematical knowledge points are systematically fused together and displayed in an intuitive mode, so that teaching activities are facilitated.

2. The method can be operated manually, dynamically reflect the relation between the two numbers in real time, and promote the real understanding of students.

3. Mathematical calculations and common mathematical functions are supported, including exponential functions, trigonometric functions, absolute values, and the like.

4. The adoption is alone teaching aid equipment or at the APP of computer or cell-phone, and is nimble convenient, is fit for the consolidation and the exploration after classroom teaching and student's class.

Drawings

FIG. 1 is a front view of the apparatus;

FIG. 2 sets the values of the current basic variables x and y through a touch screen;

FIG. 3 results display area;

FIG. 4 soft keyboard schematic;

FIG. 5 is a solution of different expression relationships.

Detailed Description

The following describes in detail a specific embodiment of the mathematical education apparatus provided by the present invention with reference to the accompanying drawings.

The present embodiment provides a mathematical teaching aid, particularly suitable for primary and secondary school students, and fig. 1 is a schematic diagram of the present embodiment.

As shown in fig. 1, the whole teaching aid is an object 1 similar to a tablet computer, the periphery of the object is covered and protected by a shell 2, and the front of the object is provided with a plurality of keys 3 and a screen 4. The key 3 includes a power switch 31, a clear reset key 32 and some

example keys

331, 332, 333, 334, 335, 336. When the power switch is turned on for a long time, after an example key of a certain number is pressed, the corresponding position of the screen 4 can have a set or stored expression, and the calculation result and the relation of the expression are displayed. The number of example keys may be varied as desired.

Long press of the power switch 31 switches the switch state. When the power switch 31 is pressed for a long time and turned on, the screen is lighted up, and a coordinate input area 41 and a result display area 42 (composed of a plurality of unit display areas 421,422,423, 424, 425, 426, 427, 428, 429, etc.) are displayed. A further long press of the power switch 31 will turn off the device and the screen 4 will have no display.

As shown in fig. 2, when the finger slides on the coordinate input area 41 and the current finger touches the point 411, the corresponding x position is 412 and the y position is 413. The value of x can be changed by directly sliding left and right, and the value of y can be changed by sliding up and down. The current value of x is shown on abscissa 414 and the current value of y is shown on ordinate 415. When the finger clicks or slides, the result display area 42 will be updated in real time, the corresponding value changes, the position of the point on the corresponding numerical axis changes, and the numerical relationship of the mathematical expression is updated at the same time. The finger-click set coordinate range 416 may modify the current coordinate range, with a minimum set to 1, meaning that x and y are both limited to the range of [ -1, +1], a maximum set to 10000, meaning that x and y have values limited to the range of [ -10000, +10000 ].

As shown in fig. 3, which is the case of one specific unit region 428,

mathematical expressions

4281 and 4282 are displayed, values of the mathematical expressions are calculated, and are expressed on corresponding

axes

4283 and 4284. The current positions are 4285 and 4286, respectively, and the corresponding numerical values are 4287 and 4288. Different colors are set according to the position relationship of the points, such as a point located on the right side of the numerical axis as a large solid point (indicating a large value, and a color such as red can also be added), and a point located on the left side of the numerical axis as a small hollow point (indicating a small value, and another color such as blue can be added). If the two dots are at the same position, black dots having the same size are set. The relationship 4289 of the mathematical expression has three types: equal to, greater than or less than. If the value of the mathematical expression is out of the range of the number axis, it is not displayed.

Clicking on the mathematical expression (e.g., 4281 or 4282) pops up the soft keyboard 43, containing the numeric and alphabetic keys, may modify the set mathematical expression (e.g., 4281 or 4282). The functions that support numeric values and general use include cos (), sin (), exp (), abs (), and the like. As shown in fig. 4, functions and operators may be augmented or modified as desired.

The specific unit display area can be pressed for a long time or double-click to display the solving condition of the relational expressions in the coordinate interaction area, different colors are used for representing corresponding areas of different relations, the black color represents that the two expressions are equal, the red color represents that the first expression is larger than the second expression, and the blue color represents that the first expression is smaller than the second expression. Fig. 5 shows the relationship between the results of the two expressions y and 2 × x +20 in the area shown in 427, where y is 2 × x +20 at the position of the black line, so that the black line is actually the function image. The red region y >2 x +20 to the left of the black line and the blue region y <2 x +20 to the right of the black line. The relation of the expressions displayed on the appropriate region check result region can still be touched with a finger at this time (red indicates that the above expression is larger than the below expression).

If the method is realized on a common computer APP, a computer keyboard can be directly used without popping up a soft keyboard. A mouse may be used instead of a finger to set the coordinate positions, i.e., the current values of the basic variables x and y.

Claims

1. A mathematical teaching apparatus comprising: the device comprises a machine body (1), a shell (2), keys (3) and a screen (4). If the software APP form is adopted, the software APP form only comprises a screen (4), and the keys (3) are also realized on the screen (4).

2. Mathematical education instrument according to claim 1 characterized in that the case (2) covers the whole body (1) and the body is powered by normal dry cell or by power adapter with rectified change, the back of the case (2) is left with battery box or power jack on the side.

3. The mathematical education apparatus as set forth in claim 1, wherein the keys (3) include a switch key (31), a clear key (32), and a plurality of example keys (33) such as an example 1 key (331), an example 2 key (332), an example 3 key (333), an example 4 key (334), an example 5 key (335), and an example 6 key (336).

4. Mathematical teaching aid as claimed in claim 1, characterized in that the screen (4) is a touch interactive screen comprising a touch screen coordinate input area (41) and a result display area (42).

5. Mathematical teaching aid according to claim 4, wherein the result display area (42) comprises a plurality of unit output areas (421,422,423, etc.), each unit area containing a single output or a plurality of comparison outputs, such as 428 comprising a mathematical expression (4281, 4282), a number axis (4283, 4284), a value of the expression (4287, 4288), a point corresponding to the value of the expression (4285, 4286) and an expression relation (4289); when interaction occurs in the touch screen coordinate input area (41), the values of the current basic variables x and y are changed, so that the numerical values and the relations of the unit areas (421,422,423 and the like) in the result display area (42) are correspondingly changed, the position relations of the points are expressed by colors, for example, a red point is on the right, a blue point is on the left, and if the positions of the points are the same, black is used.

6. The apparatus for teaching mathematical expressions as claimed in claim 5, wherein a soft keyboard is popped up after touching the mathematical expression part (e.g. 4281, 4282), the setting is modified interactively to a new expression, the relative value and the position of the point are updated instantly, and after setting the new expression, a certain example key can be pressed for a long time to be stored for reproducing the current setting after pressing the example key in the future.

7. A mathematical teaching aid according to claim 5, wherein upon touching the expression relationship area, the areas resulting in different relationship results are displayed in different colours in the touch screen coordinate input area (41), for example black indicating equal results, red indicating greater results for the first expression and blue indicating lesser results for the first expression.

8. The mathematical education apparatus as claimed in claims 1-7, wherein the number of keys, the interaction mode and the color can be adjusted according to the situation, and the method can be implemented on software and operated with a computer, a tablet computer and a mobile phone.