Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Wednesday, April 2, 2014

Looking through the eyes of New Technology

By Dolores Luna Hogan
The Learning and Neuro-Development Research Center is so  happy because we have another international interview today, we will share some ideas from Japan, because we have the honor to talk with Mineshima Takayuki. Mineshima who graduated from high school after the 3 year information processing program, later graduated from University of Nebraska at Omaha with Bachelor’s degree in geography specializing in USSR.

After he came back to Japan, he used to work as a teacher at a private school in Iwakuni for 5 years this gave him the light to reconstructed my career to assimilate knowledge and skills in education and technology at NTT (Nipon Telegraph and Telephone). Thanks this he received an endorsement from Educational Board of Hiroshima City to work at Fujinoki Elementary School as an ICT (Information and Communication Technology) specialist to help accomplish Japanese ICT educational policies including so called “Future School Project” and “Learning Innovation Project” for 3 years respectively.; with this background he established Learn For Japan to help learners and educators with ICT educational policies of Japanese ministry of Education and let us say that we are front a innovation leader.

LNDRC: Thank you so much Mineshima for sharing so deeply information about you, our first question is one we ask to every foreigner we met, how is Educational System in your country, Japan?

Mineshima: Japan is trying to getting out of criticism about its legacy educational system in which more academic emphasis is put on goal oriented approaches to accumulate knowledge, and now is trying to develop towards process oriented approaches to nourish abilities and skills such as critical thinking, creativity, communication, and collaboration with using the cutting edge use of technology for the 21st century learning as a national educational policy.  This is exactly what is happening in Japan today and innovations in learning are getting part of its big driving force to nourish global citizens who are well adaptable to changing societies in the world, successful in international contexts, and confident about where they should go.

On the contrary, geographically isolated conditions have oddly allowed Japan to be committed to conservative tendencies towards educational uniformity and Japanese as a dominant language in the country has often lead to non-internationally educational systems resulting only to struggle with poor communication with foreign people, clumsy collaboration for building international understandings and consensus, and embarrassment in solving worldwide problems in different languages.  Japanese conservative educators tend to prefer being part of their local communities and exclusive decision-making trying not to contribute to advancement of globalization.

It is, however, true that Japan has become more enthusiastic to give it a change to be part of the 21st century society where global awareness plays a key role in learning from and working collaboratively with individuals representing diverse cultures, religions and lifestyles in a spirit of mutual respect and open dialogue in personal, work and community context.  Japan is looking for a better way to a new educational system as technology finds new possibilities in classrooms.



LNDRC: What are the pros and cons of Japan Educational System?

     Mineshima: As shown in PISA test results, Japanese Ministry of Education puts great importance on international academic achievement to confirm effectiveness and reasonableness of its educational system while making progress with remediation and improvement from a global view point.  This inspires Japanese leading educators to be more confident about what new pedagogical approaches and learning methods play a key role in breaking through difficulties and limitations whose solutions were left unclear under existing learning conditions and environment.  As Japanese educational policies of using technology in classrooms show evidences of their effectiveness and usefulness, educators in the country gradually pays more attention to technology and expects its growing possibilities to apply them to development of the Japanese educational system.

   
  On the other hand, conservative educators in Japan still don’t pay much attention to exploratory possibilities or advantageous options of technology use in classrooms along with their academic effects or pedagogical value in the advanced educational system.  Many of them advocate traditional learning environment already include effective pedagogical philosophies which are good enough to meet conditions to build the 21st century educational system.  They point out the small number of computers in classrooms and limited vindication to contradict the PISA test results so Japan should wait for more explanatory evidence for diffusion of technology use in Japanese classrooms.

     This, however, doesn’t mean that Japanese educators are insecure about where they should go, but there is room for both sides of the educators to discuss and share ideas about what the essential nature and definition of Japanese educational systems should be today and tomorrow.  To understand this situation more clearly, one possible explanation could be the fact that the newest knowledge and experiences harvested from the technology-based educational policies are not well shared or understood to arrive at reasonable conclusions for both of them.  Today it is often seen in Japan to discuss pros and cons over technology use in classrooms.  Pros insist that learning in classroom with technology should effectively enhance academic advancement and quality education while cons maintain that technology should distort and mislead the intrinsic nature of traditional Japanese education only to result in much more burden and confusion left for teachers and students.


LNDRC: You designed an application, especially for teachers to engage children with mathematics; this application is Digital Block, why did you decide this application was necessary in Japanese classrooms?

Mineshima: Digital Block actually has shown good evidence in Japanese educational policies with technology in the 21st century classrooms.  As a student-centered learning tool for knowledge building through communication and collaboration with classmates, Digital Block is necessary for children to make mutual understandings and consensus so they can arrive at mathematical conclusions while finding a way to grow their learning skills by themselves.

In fact, Japanese educators put more emphasis on learning than on teaching because they think it is highly important for children to become aware of their own learning processes with consistency and reasonableness so they can develop their own learning skills by themselves.  Teachers play an important role in nourishing their learning skills, as they grow intelligent in learning. 

As often seen in Japanese classrooms, for example, concrete materials are used to help children easily understand abstract concepts of mathematics while assimilating their real experience and simultaneous feeling through manipulating concrete materials.  This makes a lot of sense as long as their behavioral and cognitive development stages correspond to each other.  Otherwise, children would use a lot of time to find analog materials they may lose, find more space to put them back on their untidy desks, and find friends to talk about their clumsiness.

One of the biggest roles of Digital Block is help children to assimilate their instinctive sense and thinking processes through simulated experience and intuitive cognition in a calculating area of mathematics.  They can correlate the concrete and abstract concepts, bind them together, and make structured knowledge and systematical understanding by providing them with a framework of ideas they make without losing precious time to learn at higher stages of mathematical processes they would consequently deserve.  This makes their learning processes more efficient and exploratory in understanding abstract concepts of mathematics and acquiring subordinate procedural knowledge while they feel it is not easy to understand mathematical logic through limited time, space, functions presented in the Japanese 20th century classrooms as pictures below explain.

LNDRC: When you invite to teachers to use Digital Blocks, what is the most important to you?

   
Mineshima:  What matters most to me is see how children learn how to learn by themselves.  It is not necessarily difficult for children to gather information, put up ideas, and build knowledge, but learning the way they learn is much more meaningful and important.  Learning how to learn is one of the biggest goals children should accomplish as long as they are life-long learners.  So I would like teachers to use Digital Block as a learning tool rather than a teaching tool to help children nourish their learning skills, which are flexible and useful for fluid problem solving in their entire life.  

LNRC: Do you think new generations are less interesting on learning?

    Mineshima:  I don’t think new generations are less interesting on learning because children are bone with intellectual curiosity.  Children have intellectual appetite for extending the range of their behavioral and cognitive application as they grow while absorbing information from environment that surrounds them.  If there is a concern about their willingness and interest to their learning, you can find some aspects of the problem in educational systems and the way they include children.  In other words, educational systems define the way children learn.  Well designed educational systems and curriculum, indeed, can be effective in improving the performance of children learning.  It is, however, true in a way that the educational systems don’t always secure children their willingness or motivation to learn.  The educational systems rather tend to restrict the range of the way they learn.  So I think that is when educators need to rethink about what results from the education systems involved if new generations are less interesting on learning.

LNDRC: What is your perception about New Technologies in the classrooms?

     Minesima: Today we are living in an era of transitional technologies.  With development of information society, global citizens are required to have demanding skills to create new value and contribute it to global society where the way they live and work has to be multidimensional and trans cultural.  If education plays an important part in creating the new era, NEW Technologies should not merely be something that encourages children to acquire knowledge and skills as a goal of their learning, but something that inspires children to transform from students in classrooms to learners in society.
    
In other words, the essential value of New Technologies in education must be in the process to help children acquire knowledge, experience, and skills required to lead their entire life as a member of ever-changing society.

LNDRC: In your opinion, what is the role of New Technology in learning process?

    Mineshima:  The role of New Technology in learning is discover New Learning.  This means learners can become aware of their own cognitive activities and make an objective evaluation on which the process of nourishing their problem solving skills is based.

    
In recent years, many international educational institutions such as ATC21S (Assessment & Teaching of the 21 Century Skills) place special emphasis upon problem solving skills required for children to play a successful role in an international society in the future.  It is highly important for children to plan, analyze, evaluate, and adjust what to learn with their classmates, not just to learn respectively with efficiency.

     Naomi Miyake, professor at Tokyo university, points out as follows; Learning skills were mainly defined as skills for individuals to comprehend knowledge exactly and solve given problems efficiently so educators could set goals and design education to reach them.  But today massive informational environment is created and information is updated all any one time.  Goals are regarded more like something that reset themselves as you get closer to them so goals need to take care of every situation.  For this reason, it is important for children to find problems and answers at the same time, share methods of solution among groups, and remake their knowledge building processes, not for teachers to teach what is supposed to be taught.  For this purpose, goals need tools to trigger these processes.  At the same time, New Learning requires a new evaluation method.  The new evaluation method is not something that measures achievement of learning but something that keeps track of progress of learning and generates clues to go on to next levels of learning by deciding on how to modify what is actually happening there.  In order to make this kind of evaluation in accordance with progress of learning, teachers need a strong IT infrastructure to record, analyze, and share learning processes for next steps.  If the IT infrastructure is strong enough, teachers can concentrate on innovating New Learning without being distracted by maintenance of IT environment and the evaluation method.

    
Since the role of New Technology depends on how we can define the applicable range of learning processes, there is no expected answer in advance.  This way a lot of attention and expectation have been paid to a rapidly-growing technology society where the effective way of utilizing technology in education is mainly on the table.  In conclusion, if it is children who create a technology society in the future, it will be self-evident what the role of New Technologies in their learning processes is.

LNDRC: If you had all the money of the world, and no restriction to take decision to design a school, what would you include in it?

   Mineshima: If I had all the money of the world, and no restriction to take decisions to design a school, I would provide all the children in the world with equal opportunity to learn.  Children should be given an equal opportunity and the right to become successful in their entire life through learning.

    
As discussed earlier, international educational institutions and their organically mutual cooperation has been facilitating international consensus and standardization regarding a modern education method and learning process.  However, there are still many children who do not have an opportunity to enjoy modern and idealistic education because of a variety of factors such as politics, economy, and culture in the world. Furthermore, problems about academic achievement gap among countries and thus negative effects on education have been frequently pointed out.

    
Therefore, it is extremely important for educators to build an international educational platform and lead collaborative innovations in trans cultural education so children as global citizens who are living in a modern society can live a better life beyond borders with success by nourishing their intelligence and skills that will be useful when they grow up.  I believe everyone can be happy if everyone hopes for a global educational consortium for everyone.  And this is just what I am trying to do in my country with Learn For Japan and I believe this leads to the first step toward Learn For the World.

Don't forget to watch some videos to understand Digital Blocks: 
 http://youtu.be/_17oYPkB0oM
http://youtu.be/WCGR0mJKoXg
http://youtu.be/ablNj6-sPmw

You can find Digital blocks in Itunes Store: https://itunes.apple.com/us/app/digital-block-for-vertical/id797538471?mt=8

And Learning for Japan is an wonderful resource: http://learnforjapan.org/learning-tool/math/place-value/english/index.html

Finally we share another Interview to Mineshima: http://dailyedventures.com/index.php/2012/05/06/japan/

Friday, January 24, 2014

When Nash theory brings into play some love


  By Alma Dzib Goodin

Daniel is a Russian physicist ready to conquer the world with his ideas, but in the midst of publications filled with Greek letters and numbers, he has failed to atract a beautiful girl’s love of the lab at the other side of the campus. That girl that walks around with the sweetest smile and when she meets Daniel in the cafeteria, smiles even more broadly, knowing that he is a foreigner so she does not want to say something wrong... that girl who ... does she make him sweat?... perhaps so much that he has even asked her name...
 
Town was suffering the third winter storm of the season that evening, so Daniel went into the library, hiding as it was his habit to expect bad things to pass, it was his refuge for everything and everyone. 

He had been studying game theory during a while, especially from Nash’s perspective, and he was determined to publish an article about this topic, applying a proposal from economic and biological models. Although there is a lot of articles written on the subject, he wanted to innovate, he wanted to find something that no one else had seen, however he had to find  that something, there was no doubt he was going to find it there, or perhaps here... maybe in this journal... maybe...

He began to move from one side to another around 300 magazines on the table when one of them slid...... when he bent down to lift it without paying attention to the environment, he saw a hand taking his magazine. He was ready to shout do not touch my magazine, when his eyes followed a hand, and then an arm and then a shoulder... he came up to the neck and two brown eyes met with his blue eyes.

The smile was expanded as always... but this time she modulated carefully her words:
-Hey!, I found this!... What are reading?, she said.

-I'm reading Nash’s theory... He said as doubting whether those words came from his voice or if he was listening to through his headphones, he took them off to be able to distinguish between his voice and the music he was hearing, and they fell to the floor.

She hurried to help him to lift them up and while she did it put attention into the magazines on the table and reached to read one of them: game theory and their applications in biological models...
When she concluded reading, she gave him the headphones and then she stretched out her hand: 

-My name is Kathleen, Kat... I study nanotechnology applied to biological models, and try to explain evolutionary patterns... I see that you understand math... my advisor says that my proposal has no future... perhaps you can help me?... huh?, what do I say?, I’m sure you are very busy...

When she dropped his hand, he took it back and he said almost in a whisper:

-My name is Daniel... Dan... and yes!, in fact I want to design a model of application with game theory to economic and evolutionary models, although this  has been done before... I want to find a specific area that allows me to innovate a bit.

She moved a chair beside her and then more magazines fell, but this time he rose and offered her his chair,  he began cleaned the table a little and decided to talk about what he knew and loved so much with her... 

- Please,  sit down Kat, I think  I can explain you from mathematics how species have evolvied, however, remember that maths are only models that represent the reality.

-The science is that, isn't it? Kat, said smiling.

-Yes, yes... it is true... just explain the reality...

- What I know about game theory, is that studies the sharing of profits and therefore decision making among the players, if an entity can understand that it can win or lose during an exchange, it makes decisions based on its experience. I believe the same applies to biological models, as if we believe that species should take into account information from the environment and predators to survive, then they must apply decision-making on environmental responses.

Daniel further opened the eyes and arched eyebrows...

 -Exactly!, that's the idea... Game theory is much related to economic theory, where a zero-sum game is a mathematical representation of a situation in which a participant gains or loses profits and utility is exactly balanced by the gain or loss of the participant, as opposed to a non-zero sum game where both profits and losses are added to a situation in which players interact. To sum game zero resolves le with the Minimax theorem that is closely related to the theory of the Nash equilibrium.

-     I couldn’t understand that, could you explain it to me?, but used simple words, please.

-    It is a conceptual solution to the non-cooperative games that include two or more players, in which it is assumed that it is possible to know the balance of strategies of each player  since has something to gain by changing if strategy during the game.

-    It sounds complicated...

-    It is not, in fact it can be ridiculously simple: maybe if we try to understand biological systems... look, we will assume that you have a bee and a butterfly trying to obtain pollen from two flowers... do you work with biological systems at this level?, or perhaps... microbes, bacteria... 

-    Sounds like a cute example with bees and butterflies, please explain this and then maybe we can apply to spores...

-    Daniel looked at her very happy... well... I’ll explain it with butterflies... There are two flowers and one butterfly and one bee are trying to obtain the maximum pollen, if Butterfly makes it first movement, it can take all the pollen and thus the bee lost, and if the bee makes a first movement, butterfly lost, but both want to profit, so it is important to take a decision on the action and you can see it in simple way with a picture like this:

Bee takes pollen from a flower
Bee tries to take two flower
The butterfly takes pollen from a flower
Maximum common benefit
Bee gains and butterfly loses
Butterfly tries to take the pollen from two flowers
Butterfly gains and bee loses
Maximum common prejudice

- Crap!, it sounds so easy that even I can understand that, but surely there are a lot of numbers and things involved as I can see in your magazines.


-    I don’t understand it if I see it that way, but let me give you another example to see if I understood... Kat and Dan can learn from each other, and they both make decisions ... then if I do a matrix would be this:

Kat speaks with Dan
Kat does not speak with Dan
Dan speaks with Kat
Maximum common benefit
Kat goes home
Dan does not speak with Kat
Dan finishes his readings
Maximum common prejudice

-    Yes, more or less like that, but both must have the same level of profit, in this case the gain is different, you would have gone home and I would have read 2 or 3 magazines. 

-I want to study chaotic fluctuations in phenotypic frequency, specifically in those cases where it is necessary the adequacy of a heterozygote based on the measure of a recessive parent the next generation, which I think, is the measure of the adequacy of the homozygotes and heterozygotes would therefore have a destructive effect on the homozygotes and themselves, although to a lesser extent about themselves. This because if a behavior is associated with a low to reply to the environment and high fertility fitness gets a chaotic fluctuation.

Daniel's eyes were opened so much that his glasses were on ready to falling, when he could finally talk, began to mambling few words and then coughed a little to clarify his own ideas...

-Kat... I think that no doubt we both can gain from this talk, there are at least two possible explanations, even it would be possible to make predictions... I can apply my mathematical theories to everything you said,  however, the truth is  I did not understand a half of what you just said, but we can sit down and explain every thing with pears and apples, but I believe that we both would receive profits from all this and it is possible to balance our profits no doubt...

-  I want to know if it is possible to find patterns of adaptation and survival in living populations.

-    Have you ever read about the life of Conway game?

-     Yes, I do!, actually… that what gave me this idea, but I don't understand enough about math,  mmmm but I think that what you just explained and Conway model can help me a lot, now all are algorithms to create stable patterns, as the analysis of the databases, everything is math is our everyday lives, everything is about looking for patterns!.

-   Yes it is, yes... of course... I think you just increase our chances of achieving our dreams...Yes... can I invite a coffee?, I only need to ... collect all these magazines... and... I think it’s not snowing anymore... I can take you in my car, or do you have a car?

-    Let me help you with this… No, I do not have a car, only my bike, but I can leave it on campus, and I come tomorrow on the bus. Climatic variables, increases the probability of accidents as drivers change their behavior patterns...

-    Yes, it is true... well... we can put your bike in my car... I have a porta-bike that I use on weekends... well... only when there is no snow, because as you say... There are changes of patterns in the drivers... Yes... ohm... then if you put your bike in my car, can I take you home?... after coffee, of course...

-    Let me think... If I say yes, then we both get gains, then I should not take the bus tomorrow, and you know where to find me... but in such a case, there will be probably other decisions that each player goes, isn't it?

-    Yes, Yes... the pattern can be exponential... sure!

-    Yes, I figured that... can it become a chaotic fluctuation... the pattern could meet different conditions and therefore... change... evolve...

-    Yes, yes... it's true... yes...

-   Cool!, it seems that mathematics are not so complex!

-    No, no... they are not... they can explain many things and as you say... we apply them more and more everyday... I worked applying all this to economic models and I an algorithm to Google, so it seems that it can read your mind when you type something...

-    Amazing!... have you explained biological models?

-    No, but... apparently... I'm about to do it... If you allow it to me!.