MATHEMATICS

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Rabu, 13 Maret 2013

Open Learning

Creative Learning - Week 5

Video: Audrey Watters, Mako Hill (Moderator: Philipp Schmidt). Opened discussing peoples teaching/learning videos which they did by Hangout. People noted the courage needed to document publicly your learning or teaching. Then on to Open Learning.  Ultimately there was acknowledgement that these methods might not be for all, but they're important.

Audrey started to think about it because of blogging and the way she was doing professional learning. She blogs to learn, but it's also about how she licenses her work. It requires being willing to put out half-baked ideas and to then collaborate on them. Worries that so much of online learning is replicating traditional lecture. (Hmm.)  Mako does open programming on a number of big projects. He sums up his unlearning experiences in a post at his site.

They discuss how blogging is similar to open programming. We need a way to fork with attribution. Audrey is even trying putting work up on github. Mako notes how a big part of the open programming idea is that the user owns the work. I think similar to the idea of student-centered learning. Both this and the Learning Web article talk about the benefits of systems being hackable. If education is not a blackbox, then we can adjust and understand what's going on. (Previously in the course this was a point about technology for learning, that if it's inscrutable there's no learning, and if it's hackable it leads to creation.)

At 54 min in response to a question about the classroom application, Audrey makes a strong statement of collaboration as the first step towards openness. Mako echoes, encouraging students to document learning not just for themselves but in an open space where others can engage. Actually, let's clip that.





Reading: "Minds on Fire: Open Education, the Long Tail, and Learning 2.0" (pdf) by John Seely Brown and Richard P. Adler.; Ivan Illich: Deschooling Society (Chapter 6: Learning Webs); Eric Steven Raymond, The Cathedral and the Bazaar a essay on the development of fetchmail for Linux. (links are all pdf)

Minds on Fire: an advocacy piece pushing for online, social learning. Nothing constructive, I think, but pretty descriptive of the hopes of the backers of this. I liked the pictures.



Learning Webs: "In school registered students submit to certified teachers in order to obtain certificates of their own; both are frustrated and both blame insufficient resources--money, time, or buildings--for their mutual frustration." The article gets into the difference between schooling and learning. It is literally radical and often rambling, which might be off-putting to some readers, but I found it thought provoking. On people's desire to have Aristotle for their Alexander: "The person who can both inspire students and demonstrate a technique is so rare, and so hard to recognize, that even princelings more often get a sophist than a true philosopher." Illich is advocating liberation pedagogy.

Cathedral and the Bazaar: interesting as an analogy for curriculum development. This is what I would like to see; I think it's what tends to happen with Dan Meyer's projects/movements. What does debugging mean? In the midst of writing this, Michael Pershan led a Global Math session to fix his broken Complex Numbers unit. He's put a lot of work into where it is now, but 20-30 teachers put in a good hour to discuss and revise. Great experience. In the video debugging is contracted with the 'you learned it or you didn't' vision of education.

Recommendation: watch the video, skip the parts irrelevant to you. If you're ramble and revolution tolerant, read the Learning Webs article.

AssignmentTeach & Learn = Ask & Answer
1) Go to stackexchange.com/sites and choose a site that you find interesting
2) Post (at least) one question and answer someone else’s question (at least one)
3) Reflect: What aspects of the experience contribute to a sense of a learning community? What aspects limit a sense of community?
Learning match (extra activity): Offer to teach something & sign-up to learn something from someone else - Post it here

I'm new to Stack Exchange, but there is a large Mathematics section with 115,000 questions. The questions on the front page were math major or grad student level questions, with some research level questions. Fascinating. I chose to answer a question about mathematically related online games. There was some frustration with posting, getting used to the editor, etc. But not too bad. Here's the question and answer. They wouldn't let me put more than 2 links, so I put them into a Tumblr post

Harder to think about what I would ask. I wound up asking about those Escher spirals I never finished (Tumblr posts one and two) and my secondary sabbatical project, a common core sharing framework. The reputation bit reminds me of Cory Doctorow's Down and Out in the Magic Kingdom... "them that's got shall get, them that's not shall lose."

It's an interesting site, and I'd love to hear from people who like it how they like it. How does it compare to Quora for example? It feels more focused and less social, but that's an initial impression. (I'm not a big Quora user, either, though.)

Jumat, 20 Juni 2008

Animated mathematical figures

In an e teaching workshop organised by CII Shiksha, I got to know about a cool animation tool UnFREEz. The addition of this e software to my directory helped me to add life to still mathematical figures. I experimented with this software in creating some animated mathematical stuff.
Have a look.
The following three figures are created to explain the properties of a rectangle viz. both pairs of opposite sides of a rectangle are equal, each angle of a rectangle is a right angle and diagonals of a rectangle are equal.
The figure given below may be used to understand the concept of vertices of a cube. Observe the pink dots. My students were making mathematics project on optical illusion . I thought of creating animated illusions using UnFRRez. Two parallel lines turning into a pair of intersecting lines ... Two equal lines turning into unequal lines...

Do you want to download it?
Here is the link.

Selasa, 17 Juni 2008

Mathematics and image editing

Technology has given a magical toy in the hands of teachers and students to explore and learn interesting facts with ease. I have been exploring the internet based tools and softwares from past 2 years and had deeply felt its power in enriching learning level of students.
In our mathematics laboratory, we have been exploring on mathematics based activities using pictures. It is interesting to note that by using tech tools and softwares , we can do many mathematical experiments with a click of a mouse button. There are image editing tools and online programmes which can add/remove effects to a picture . This can bring in an incredible change in the existing image/picture leading to unusual results. I believe , a teacher or a student must take advantage of this facility . It would surely inculcate in learners the interest in the subject and developing creative skills. May be one day we may find a hidden mathematician.
Here I am sharing some interesting observations
  • Transforming a tangram to a curvy tangram. I talked about this experiment in my previous post on image editing.
  • Experimenting with illusions is an interesting activity which may be performed easily using image editors. Observe the given pictures... This is an optical illusion
In the above picture ,there are pink squares bounded by white and green squares. The presence of white and green boundaries around pink squares has changed the tone of pink shade. It is observed that when pink squares are bounded by green squares then they appear to be darker in shade. And when we remove all the green squares then we found that all the pink coloured squares are of same tone.
I was astonished to see this illusion. But you know, I wanted to try it for some other colour combinations. Manually, it is quite impossible to check on drawing, shading and then observing. So, an idea came to my mind to try using image editing tools. And here is the result...
I first tried with turning all pink squares to orange.
then to blue and so on I experimented with 5 different colours.The I tried to remove the green squares using eraser tool and got actually verified the result. In the figure given below, observe the part from where the green squares are completely removed. You will find that tone of blue colour is same . Ans there is a change in the tone of blue shade in the portion which is bounded by green squares.
The following pictures are edited using irfan view , a wonderful image editing tool. I took the following picture. I wanted to change the green coloured squares to some other colour to verify the experiment. Through Irfan view it was made posible. I edited the picture successfully.
Here is the result. I was amazed to see the fact that when green squares are turned to black, then also the illusion effect in yellow squares was there.Using a swap colour option, just by a click of mouse button, Yellow coloured squares are changed to blue. Exploring and learning the wonderful facts using technology is an enriching experience for me.
Check this one which I posted on Figures Speak.

Rabu, 14 Februari 2007

Open Source Software

Open source softwares are creating waves in education. I am exploring and working on it since December 2006. I have realised that it has a lot of potential to transform the traditional methods of teaching/learning mathematics. I believe learning in life ia a never ending process. The time has arrived that we teachers have to take up bold initiatives to take a turn in educating the students only through chalk and talk. I have tried working on various math tools like Geogebra, C.a.R , Graph sketcher and many more .These tools are really effective.
1.Graph Sketcher lets you make elegant and precise graphs in seconds, simply by sketching what you want.I think if we incorporate technology in math education it can create miracles. As you all know it is very tedious to draw graphs on a board if done manually.With the help of these kind of softwares we can create graphs in fraction of seconds .
2. GeoGebra is a free and multi-platform dynamic mathematics software for schools that joins geometry, algebra and calculus.
What is GeoGebra? See About.
What does GeoGebra look like? See Screenshots and Examples.
What can I do with GeoGebra? See Help and GeoGebraWiki.
Where do I get GeoGebra? See WebStart and Download.
Chek out the following link for more details.
http://www.geogebra.org/cms/
You can explore the following links to see the readymade lessons.
http://math247.jot.com/GeoGebrahttp://math247.jot.com/WikiHome/Library/How%20to%20Mathcasts/Learn%20and%20Use%20GeoGebra
3. Graph is an open source application used to draw mathematical graphs in a coordinate system. Visit its official site and know more about it.http://www.padowan.dk/graph/I find this software very interesting and useful in doing analysis of graphs. It saves time and the students would be able to analyse so many graphs in one period of duration 35 minutes.
4. Free mind Mapping software
This one is really a very interesting and useful software. Know about it in detail from the following link.http://freemind.sourceforge.net/wiki/index.php/Main_PageI think for recapitulation of a topic in mathematics, we teachers can prepare mind maps using this software and also it would help us in keeping a track of what all we have done in a chapter and what is left uncovered? Also, mindmaps may be utilised while teaching the history of a topic, suggesting useful study links to the students, organising lesson plans etc. I find it very interesting and useful.
5.SpeQ
SpeQ is a small, extensive mathematics program with a simple, intuitive interface. All calculations are entered in a sheet. In there you can freely add, edit and execute all calculations. You can define variables and functions, and plot graphs of your functions. You can save your calculations for later re-use.
Know more about it...
http://www.speqmath.com/