Articles

ARTIFICIAL INTELLIGENCE AND MATHEMATIC EDUCATION IN PRIMARY AND SECONDARY SCHOOL

Muhammet KULUŞ

mkulush@gmail.com

Sinan ERASLAN

Kazakh-Turkish High School For Gifted Boys, Karaganda, Kazakistan

            sinan.eraslan@gmail.com

ABSTRACT

Teachers and educators aim full effective education.This difficult job needs many different processes and time.

With the classical problems for education in this century we have many possibilities as computer, internet and something which combines them as 3D programs and Artificial Intelligent applications.

The software engineers are focused on many complicated problems in science and technological events. They want to create artificial intelligence for their own area. Some software engineers want to invent for education, but it is very hard because every subject except mathematics has discussible answers or not absolute answers. Mathematic education has this opportunity as countable and calculable solutions.

We believe that any progressive step in AI for mathematics education gives significant results for general research in AI. In near future we can see some good applications of ARTIFICIAL INTELLIGENCE ( AI )  for mathematics education.

Key words: Discussible answers, artificial intelligence, countable and calculable solutions.

Абстракт

Оқытушылар мен білім саласындағы қызметкерлердің негізгі мақсаты толық білім беру. Бұл салаға қажымас қайрат пен көп уақыт талап етеді.

Кешенді қиыншылықтармен қатар жаңа мүмкіндіктер пайда болды мысалға ғалам тор, компьютер және 3D қолданылатын бағдарламалар, жоғары ойдағы қолданбалы бағдарламалар.

Компьютер инженерлер ғылыми және технологиялық салада өте күрделі мәселелерді шешуді көздеген.

Өз ортасындағы ең керекті бағдарламаны табуға тырысады.Бірақ бұл процесс өте күрделі. Математикадан тыс ғылымдардың шешімдерінде нақты жауап жоқ немесе жаңа жауаптар туындатады. Математика ғылымы нақты шешімімен  жеңілдік тудырады.

Болашақта тез дамып келе жатырған компьютер әлемі математика саласында өз ізін қалдырады, жақында осы салада математика ғылымы үшін жаңа бағдарламалар ойлап табылады.

Абстракт

Учителя и воспитатели стремятся к полному и эффективному обучению. Эта трудная работа нуждается во многих различных процессах и времени.

Наряду с классическими проблемами в области образования, у нас есть много возможностей, таких как компьютер, интернет и то, что объединяет их как 3D программы и приложения искусственного интеллекта.

Разработчики программного обеспечения ориентированы на многие сложные проблемы в области науки и технологических мероприятий. Они хотят создать искусственный интеллект для их собственной области. Некоторые разработчики программного обеспечения также хотят придумать и в обдасти образования, но это очень трудный шаг, потому что каждый предмет, кроме математики, имеет дискуссионные или не определенные ответы. Математическое образование имеет такую возможность, так как счетно и имеет вычислительные решения.

Мы считаем, что любой прогрессивный шаг в области искусственного интеллекта для математического образования дает значительные результаты для общих исследований в области искусственного интеллекта. В ближайшее время мы можем увидеть некоторые хорошие применения искусственного интеллекта (AI) для математического образования.

ABSTRACT

Eğitimciler  ve öğretmenler tam verimli eğitimi amaç edinirler.Bu zor iş değişik bir çok işlem ve zaman gerektirir. Çağımızda eğitime ait birçok klasik problemler olmasına rağmen,bilgisayar,internet, 3 boyutlu programlar ve yapay zeka gibi bir çok kullanılmayı bekleyen imkanlara sahibiz.

Bilgisayar mühendisleri birçok bilimsel ve teknolojik olaylara odaklanmış

durumdalar. Onlar kendi sahalarında hemen hemen gerçek bir zeka elde etmeye

çalışıyorlar. Bazıları ise bunu eğitim sahasında istiyorlar. Fakat bu oldukça zor.Çünkü matamatik dışındaki branşlar tartışılabilir veya kesin olmayan cevaplara sahipler.Matamatik eğitimi ise sayılabilir veya hesaplanabilir çözümlere sahip.

Biz  yapay zeka konusunda matamatik eğitimi için kaydedilen gelişmelerin, genel manada yapay zeka çalışmalarında da dikkate değer sonuçlar vereceğine inanıyoruz. Ve yakın gelecekte matamatik eğitiminde kullanılan gelişmiş yapay zeka uygulamalarını görebileceğiz.

Anahtar kelimeler.: Tartışılabilir cevaplar, ,Yapay zeka, sayılabilir ve hesaplanabilir çözümler.

INTRODUCTION

SOME APPROACHES TO AI

The main contribution of artificial intelligence ( A I ) to mathematics education is to provides concepts,methods and tools for the design of flexible and relevant computer- based system for teaching and learning purposes.Such systems convey great expectations as: directmanipulation of abstract objects,customized explanations,intelligent micro worlds allowing learning by discovery.(1)

Another approach  to AI from Oliver Knill, Johnny Carlsson, Andrew Chi and Mark Lezama in 2003 (2) The goals  of  the  (AI) project  which was  to  gain  insight  into  the  mechanisms  of  teaching  and  learning  by  playing  and experimenting  with some existing  AI tools.

They hoped that they could use the experiments  to  shed light on basic questions in education like:

• How do we teach effectively?

• How do students learn?

They hoped also to produce ”agents” which are of practical value.  The knowledge base can be used to produce glossaries or help to build calculus problems of a certain type.

Their  goal were to

• Build an online partner for mathematical conversations.

• Have an interface to computer algebra systems.

• Learn about artificial intelligence.What is possible and what not?

• Explore new features in mathematical communication.

• Understand the teaching process from an otherperspective.

• Reflect on the process, how we learn mathematics.

According to G. Tecuci (3)  for the interaction between computer and human we need anintelligent agent as AI. In his estimation a different type of interaction is realized by an ”intelligent agent”.  It can be used as an interface to other tools or agents.  An intelligent agent should by definition contain a

• knowledge base

• a problem solvingcomponent

• an interface to the user as well as

• a knowledge acquisition and

• a learning component.

Under these approaches and our experience of  general education we can state the sentence below

TRUE EXPECTATIONS FOR MATHEMATICS EDUCATION CAN BE ANSWERED BY COMPUTER WITH  ITS ADDITIONS IN PRIMARY AND SECONDARY SCHOOL.

For understanding of expectations in education the separation will have four main titles.

*Teacher expectations

*Student expectations

*Parents expectations

*Expectations of  schooladministration

Some expectations for teachers are:

-Showing good examples in our life as short films ,slide show and more visual examples.

-Checking exams very fast and analyzing marks and results for hole class.

-Saving lectures.

-Giving more questions or solved problems  without paper and books.

-Reaching easily to which is the pastsaved documents and similar educational materials.

-Giving homework and checking duties  out of school.

-Electronic library ….

-Contact to the teachers and students if  necessary

-Individual requirements ( cv,electronic annual plans,time table…)

-Questionnaires as electronic pages.

-And more…

Some expectations for students are:

-Repeating some lessons or topics

-Giving homework which finished by the student  to the teacher  anytime.

-Writing and saving without paper and else

-Taking results of exams or duties without waiting for time of the subject teacher or lessons.

-Watching more videos, demonstrations and visual materials.

-Reaching easily to which is the  past saved documents and similar educational materials.

-Comparing own results or performance with the class mates.

-Contact to the teachers and students if necessary

-Electronic library.

-Individual requirements ( cv, exams or midterms dates,time table…)

-Requests and complements about  subject or conditions.

-Distance education

-And more…

( We don`t write last two  titles in this section )

If we look which we gave as expectations for teacher and students they are common expectations for general educations.And also we should find specialexpectations of  mathematics education.

Some special expectations for mathematic education.

-Drawing graphs

-Understanding geometric elements ( 3D shaped objects,volume, area….)

–Finding mistake (s) of solution***

-Formulas and equations

-Mathematics in practice or in our life

-…

Today some software programs can recognize hand writing and they change our hand type letters to digital letters.And some mobile computer which means tablet pc has same process for simple math expressions.(The name of one of the program is Script calculator.)

In the expectations above the third title (***) is the most important part of the good math education in my estimation. Because individual education needs to find mistake of the solution.The teachers who expect real learning of math topics must show all details and methods.After this the teacher must check one by one all students then repeating of misunderstanding part.It takes time as a waste for some teachers.We don’t investigate pedagogical behavior but it is reality. May be some teachers want to help but sometimes conditions also don’t allow the individual helping.

Basic mathematics for primary school and secondary schools (except 11-12 grades ) can be understand by computer programs today. We want to give a simple and understandable example in the fallowing sentence for the proof.

A simple math question:

Find the X in the expression:

3X+13=28

Some possible mistakes of the students:

–               3X=13-28  ( sign mistake )

–               X+13=28/3 (division mistake )

–               3X=28/13    (division mistake )

Some programs can understand simple math questions without exceptions.(it is not about complexprograms which works for height technologies.) This is already that we have.The next step understanding of solutions which is solved by the students.There for we can speak about Artificial Intelligent software for students as an ARTIFICIAL TEACHER.

Another subject teacher has different difficulties.Some answer of the questions has not got clear answer as numbers or countable results.Most part of mathematics topics for primary and secondary school are not having such kind difficulty.That is why we believe in a few years we can see some Artificial Teacher for mathematic education.The artificial  teacher as software program can analyzing question and can decide or find solution (s).After it can compare its solution and solutions of the student then it can find which is  mistake part (s).It can also show as we gave above some possible mistake(s)

Finally we should understand technological developing is very fast and we need to combine with mathematics education in practice.

(1) Balacheff N. (1993) Laboratoire IMAG-LSD2 CNRS et Université Joseph Fourier

Grenoble, FRANCE

(2) An artificial intelligence experiment in college math education

Oliver Knill, Johnny Carlsson, Andrew Chi and Mark Lezama 11/17/2003, latest edit: 4/19/2004

(3)  G. Tecuci. Building Intelligent Agents. Academic Press, San Diego, London, Boston, New York, Sydney,     Tokyo, Toronto, 1998

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