POSSIBILITIES OF USING OF COMPUTER IN MATHEMATICS

AND OTHER APPLICATIONS IN INCLUSIVE EDUCATION

Alsu Gibadullina, math teacher

Secondary and high school # 57, Kazan, Russia

In recent years Russia actively promoted and implemented the so-called inclusive education (IE). According to the materials of Alliance of human rights organizations “Save the children”: "Inclusive or included education is the term used to describe the process of teaching children with special needs in General (mass) schools. In the base of inclusive education is the ideology that ensures equal treatment for everybody, but creates special conditions for children with special educational needs. Experience shows that any of the rigid educational system some part of the children is eliminated because the system is not ready to meet the individual needs of these children in education. This ratio is 15 % of the total number of children in schools and so retired children become separated and excluded from the overall system. You need to understand that children do not fail but the system excludes children. Inclusive approaches can support such children in learning and achieving success. Inclusive education seeks to develop a methodology that recognizes that all children have different learning needs tries to develop a more flexible approach to teaching. If teaching and learning will become more effective as a result of the changes that introduces Inclusive Education, all children will win (not only children with special needs)."

There are many examples of schools that have developed their strategy implementation of IE, published many theoretical and practical benefits of inclusion today. All of them have common, immaterial character. There is no description of specific techniques implementing the principles of IO in the teaching of certain disciplines, particularly mathematics. In this paper we propose a methodology that can be successfully used as in “mathematical education for everyone", also for the development of scientific creativity of children at all age levels of the school in any discipline.

According to the author, one of the most effective methodological tools for education is a computer mathematics (SCM, SSM). Despite the fact that the SCM were created for solving problems of higher mathematics, their ability can successfully implement them in the school system. This opinion is confirmed by more than 10–year-old author's experience of using the package Maple in teaching mathematics. At first it was just learning the system and primitive using its. Then author’s interactive demonstrations, e-books, programs of analytical testing were created by the tools packages. The experience of using the system Maple in teaching inevitably led to the necessity to teach children to work with it. At first worked a club who has studied  the principles of the package’s work, which eventually turned into a research laboratory for the use of computer technology. Later on its basis there was created the scientific student society (SSS) “GEODROMhic" which operates to this day. The main idea and the ultimate goal of SSS – individual research activities on their interests with the creation of the author electronic scientific journals through the use of computer mathematics Maple. The field of application of the package was very diverse: from mathematics to psychology and cultural phenomena. SSS’s activity is very high: they are constantly and successfully participate in intellectual high-level activities (up to international). Obviously, not every SSS’s member reaches high end result. However, even basic experience in scientific analysis, modeling, intelligent  using of the computer teaches the critical thinking skills, evokes interest to new knowledge, allows you to experience their practical value, gives rise to the development of creative abilities. As a result, the research activity improves intellectual culture, self-esteem and confidence, resistance to external negative influence. It should be noted, however, that members of the scientific societies are not largely the so-called "gifted", than ordinary teenagers with different level of intellectual development and mathematical training. With all this especially valuable is that the student is dealing with mathematical signs and mathematical models, which contributes to the development of mathematical thinking.

From 2007 to 2012. our school (№. 57 of Kazan) was the experimental platform of the Republican study SKM (Maple) and other application software in the system of school mathematical education under the scientific management of Professor Yu. G. Ignatyev of Kazan state University (KF(P)U).

Practical adaptation of computer mathematics and other useful information technologies to the educational process of secondary schools passed and continues to work in the following areas:

1. The creation of a demonstration support of different types of the lessons;
2. The embedding of computing to the structure of practical trainings;
3. In the form of additional courses - studying of computer applications through which you can conduct a research of the mathematical model and create animated presentation videos, web-pages, auto-run menu;
4. Students’ working on individual creative projects:

• construction of computer mathematical models;
• creating author's programs with elements of scientific researches;
• students create interactive computer-based tutorials;
• creation of an electronic library of creative projects;

1. The participation of students  in the annual competitions and scientific conferences for students;
2. The accumulation and dissemination of new methodological experience.

Traditionally, the training system has the structure: explanation of a new →  the solution of tasks→ check, self-test and control → planning of the new unit  with using analysis. However, the main task types: 1) elementary, 2) basic, 3) combined, 4) integrated, 5) custom. With the increasing the level of training a number of basic tasks are growing and some integrated tasks become a class of basic. Thus, the library for basic operations is generated. The decision of the educational task occurs on the way of mastering the theoretical knowledge of mathematical modeling: 1) analysis of conditions (and construction drawing), 2) the search for methods of solution, 3) computation, 4) the researching.

To introduce computer mathematics in this training system, you can:

• At demonstrations. For example, with Maplе facilities you can create a step-by-step interactive and animated images, which are essentially the exact graphic interpretation of mathematical models.
• If we have centralized collective control.
• If students have individual self-control.
• In the analysis of the conditions of the problem, for the construction and visualization of its model, the study of this model.
• In the computations.
• In practical training of different forms.
• In individual projects with elements of research.

In the learning process with the use of computer mathematics in the school a library of themed demonstrations, tasks of different levels and purpose, programs, analytical testing, research projects is generated. With all this especially valuable is that the student is dealing with mathematical signs and mathematical models. Addiction to them processed in the course of working with them it’s unobtrusive, naturally, organically.

Mathematical modelling (MM) is increasingly becoming an important component of scientific research. Today's powerful engineering tools allow to carry out numerous computer experiments, deep and full enough of exploring the object, without significant cost painless. Thus provided the advantages of theoretical approach, and experiment. The integration of information technology and      MM method is effective, safe and economical. This explains its wide distribution and makes unavoidable component of scientific and technical progress.

Modeling is a natural process for people, it is present in any activity. The introduction with nature by man occurs through constant  modeling of situation, comparing with the basic models and past experience by them. Method for modeling, abstraction as a method of understanding the world is therefore  an effective method of learning. Training activities associated with the creative transformation of the subject. The main feature of educational training activities is the systematic solution of the educational problems. The connection of the principles of developmental education, mathematical modeling, neurophysiological mechanisms of the brain and experience with Maple leads to the following conclusions: the method of mathematical modeling is not only scientific research but also the way of development of thinking in general; computer and mathematical environment (Maple), which is a powerful tool for scientific simulation can be considered as the elementary analogue of the brain. These qualities of computer mathematics led to the idea of using it not only as an effective methodological tool but as a means of nurturing the thinking and development of mental functions of the brain. To study this effect the school psychologist conducted a test, which confirm the observations: the dynamics of intellectual options students  who working with Maple compares favorably with peers. In the process of doing computer math, in particular Maple, are involved in complex different mental functions. It is in the inclusion of all mental functions is the essence of integration of learning, its educational character. And this, in turn, contributes to the solution of moral problems.

Long-term work with computer mathematics led to the idea to use it as a tool for psychological testing. One of the projects focuses on the psychology and contains authors Maple–tests to identify the degree of development of different mental functions. Interactive mathematical environment  gives a wide variability and creative testing capabilities. Moreover, Maple–test can be used not only as diagnostic but also as educational, and corrective. This technology was tested in one of psycho neurological dispensaries a few years ago.

Currently, one of the author's students, the so-called "homeworkers", the second year is a young man with a diagnosis, categories F20, who does not speak and does not write independently. It was         impossible to get feedback from him and have basic training until then author have begun to apply computer-based tools, including system Maple. Working with the computer tests and mathematical objects helps to see not only the mental and even the simplest thinking movement, but also emotional movement!

In general, the effectiveness of the implementation in the structure of educational process of secondary school of new organizational forms of the use of computers, based on the application of the symbolic mathematics package Maple, computer modeling and information technology, has many aspects, here are some of them:

• goals of education and math in particular;
• additional education;
• methodical and professional opportunities;
• theoretical education;
• modeling;
• scientific creativity;
• logical language;
• spatial thinking, the development of the imagination;
• programming skills;
• the specificity of technical translation;
• differentiation and individualization of educational process;
• prospective teaching, the continuity of higher and secondary mathematics education;
• development of creative abilities, research skills;
• analytical thinking;
• mathematical thinking;
• mental diagnosis;
• mental correction.

       According to the author, the unique experience of the Kazan 57–th school suggests that computer mathematics (Maple) is the most effective also universal tool of new methods of inclusion. In recent decades, there are more children with a specific behavior, with a specific perception, not able to focus, with a poor memory, poor thinking processes. There are children, emotionally and intellectually healthy, or even ahead of their peers in one team together with them. High school should provide all the common core learning standards. It needed a variety of programs and techniques, as well as specialists who use them. Due to its remarkable features, computer mathematics, in particular Maple, can be used or be the basis of the variation of methods of physico-mathematical disciplines of inclusive education.

Good evening all,

How can I plot a straightline with points 

LogAt = - 0.097,  -0.20, -0.22, -0.25, -0.30 ,-0.40, -0.45, -1.01 and

t = 0, 20, 40, 60, 80, 100, 120, 140

Where LogA[t] on y-axis and t on x-axis. 

I have try this before . 

plot([[0,-0.097], [20,-0.20], [40,-0.22], [60,-0.25], [80,-0.30], [100,-0.40],  [120,-0.45],  [140,-1.01]]);

Couldn't any question with title beginning with http be removed automatically? There has been quite a few containing nothing but spam.

> restart;
> a := -10; b := 10; ps := seq(plot([i, t, t = -20 .. 20], x = -10 .. 10, y = -20 .. 20, color = red, style = point), i = a .. b);

plots[display](ps, insequence = true); p := plots[display](ps, insequence = true);

restart:
with(plots):
y=sin(x);
p:=implicitplot(y=sin(x),x=-10..10,y=-2..2,thickness=4,color=red,scaling=constrained,numpoints=1000):
plots[display](p);

y=sin(3*x);
p0:=implicitplot(y=sin(x),x=-10..10,y=-5..5,thickness=3,color=red,scaling=constrained,numpoints=1000,linestyle=2,style=POINT,symbol=CROSS):
p1:=implicitplot(y=sin(3*x),x=-10..10,y=-5..5,thickness=4,color=blue,numpoints=10000):
plots[display](p0,p1);
y=sin(1/3*x);
p11:=implicitplot(y=sin(1/3*x),x=-10..10,y=-5..5,thickness=4,color=navy,numpoints=10000):
plots[display](p0,p11);

y=2*sin(x);
p2:=implicitplot(y=2*sin(x),x=-10..10,y=-5..5,thickness=4,color=blue,numpoints=10000):
plots[display](p0,p2);
y=1/2*sin(x);
p22:=implicitplot(y=1/2*sin(x),x=-10..10,y=-5..5,thickness=4,color=navy,numpoints=10000):
plots[display](p0,p22);

y=2+sin(x);
p3:=implicitplot(y=2+sin(x),x=-10..10,y=-5..5,thickness=4,color=blue,numpoints=10000):
plots[display](p0,p3);
y=sin(x)-2;
p33:=implicitplot(y=sin(x)-2,x=-10..10,y=-5..5,thickness=4,color=navy,numpoints=10000):
plots[display](p0,p33);

y=sin(x+2);
p4:=implicitplot(y=sin(x+2),x=-10..10,y=-5..5,thickness=4,color=blue,numpoints=10000):
plots[display](p0,p4);
y=sin(x-2);
p44:=implicitplot(y=sin(x-2),x=-10..10,y=-5..5,thickness=4,color=navy,numpoints=10000):
plots[display](p0,p44);

y=-sin(x);
p7:=implicitplot(y=-sin(x),x=-10..10,y=-5..5,thickness=4,color=blue,numpoints=10000):
plots[display](p0,p7);
y=sin(-x);
p77:=implicitplot(y=sin(-x),x=-10..10,y=-5..5,thickness=4,color=navy,numpoints=10000):
plots[display](p0,p77);

y=abs(sin(x));
p00:=implicitplot(y=sin(x),x=-10..10,y=-5..5,thickness=3,color=red,scaling=constrained,numpoints=1000,linestyle=2,style=POINT,symbol=BOX):
p5:=implicitplot(y=abs(sin(x)),x=-10..10,y=-5..5,thickness=4,color=blue,numpoints=10000):
plots[display](p00,p5);
plots[display](p5,scaling=constrained);

y=sin(abs(x));
p00:=implicitplot(y=sin(x),x=-10..10,y=-5..5,thickness=3,color=red,scaling=constrained,numpoints=1000,linestyle=2,style=POINT,symbol=BOX):
p6:=implicitplot(y=sin(abs(x)),x=-10..10,y=-5..5,thickness=4,color=navy,numpoints=10000):
plots[display](p00,p6);
plots[display](p6,scaling=constrained);

I found useful to use the email address of a relative I live with, to create my own account on Maple Primes.
But I have just realized that his own account has disappeared.

Is there a way to have two differents accounts with the same email address ??? 

If not I will create my own account on my private email addresss

Sorry for the mess

I have seen several animated avatars on MaplePrimes. How is this done? I tried to make an animated GIF file my avatar, but it only shows the first frame. Here is the animation:

Dear friends,

after looking through your site for some time I could not find any instructions on how to change my avatar (green caleidoscope pattern at this time). Could you advise me on this? Thank you.

Best regards,

Marko Riedel

PS: If you are answering this, when I enter my website into my profile it says the link is invalid, could that possibly be because there is a tilde in the link and therefore it fails to match a regular expression somewhere? Could we get a more precise error message from the profile validator?

I have a simple minded question :
How can I give an answer a Vote Up or select it as the Best Answer to a question ?

Is there a way to see just the titles of, say, the last 100 questions?  Looking into recent questions I see the full post, so that requires moving up and down multiple pages. Really painful.

I saw yesterday evening (at home) a very elegant answer to my question "Intersection of real intervals" .
Unfortunately I can't retrieve it this morning (I'm in the office)

It was something like  coulitbe('_x' ...) ... but I don't remember it entirely
I think it came from Carl Love or maybe Mac Dude

 Could you please send me it again ?

Thanks

Hello

I am a student of an engineering career

The math teacher is going to ask us to solve some exercises Matlab

The teacher is very hard and explains nothing of Matlab in class

We must learn to use the program on our own viewing internet watching tutorials

I was wondering if somebody could help solve some exercises.

Are only three exercises which are imposible to me

I would appreciate it greatly.

Thank you

My e-mail :

alessagosti1@gmail.com

For the last 24hrs or so I have found it almost impossible to upload worksheet files in response to questions.

My usual approach is

Big green up-arrow:
(uploader pop-up appears)

Browse files

(this still works)

Upload file

This is the problem step - I generally just get "waiting for Mapleprimes" in my browser's annunciator box: and I wait, and wait, (as in >5 minutes) and still this step does not complete. Just to be annoying, every once in a while the file will upload as normal, such but success is now the exception

I'm seeing the same issue in Firefox 45.0.2 and Chrome 50.0.2661.75mon Win 7, 64-bit.

Anyone else seeing the same issue?

I am currently working on FDM ,i have 2 coupled nonlinear pde ,i need help in solving these equation using maple code.

> restart:

> alias(f=f(tau,eta), theta=theta(tau,eta));

>

> PDE1:=S*diff(f,tau,eta)=eta^2*diff(f,eta)^2+(6*eta^2-2*f*eta)*diff(f,eta)+(6*eta^3-f*eta)*diff(f,eta,eta)-eta^4*diff(f,eta,eta,eta);

> PDE2:=eta^4*diff(theta,eta,eta)+2*eta^3*diff(theta,eta)-Pr*(f*eta^2*diff(theta,eta)+S*diff(theta,tau))=0;

The code I write is properly indented.  The operation of pasting it here strips the white space and makes it hard for the reader to comprehend the structure. Manually restoring the appropriate indentation is doable but tedious, made more so because the characters we see here are in a variable width font.  The rationale might be that, given a variable width font the indentation is going to be inconsistent, but that isn't the case if the preformatted style is used, which I do, for code.

Is there any way to turn off the white space stripping?  Presumably this is some ridiculous xml-based processing feature.

sqrt(5) gives

sqrt(1+sqrt(5)) gives "You have entered an invalid Maple expression"

sqrt(u) gives

sqrt(1+u); gives "You have entered an invalid Maple expression"

when using the Maple Math icon. How can I get the correct input for the two expressions?