Paul's notation collection project

[Maria Droujkova]

http://wiki.math-bridge.org/display/ntns/Home

This link came from the epic language discussion thread. I wanted to pull it out because comparing notations from different countries has a lot of pedagogical value. It basically empowers students. Instead of viewing notation as something set in stone, magically powerful and unchangeable, they see it as a human endeavor, created by human authors and used differently by different people.

I wonder if an educator portal can be made on the basis of this wiki, making it more visual?

Cheers,
Maria Droujkova

Make math your own, to make your own math.

 

[Paul Libbrecht]

On 3 nov. 2010, at 12:27, Maria Droujkova wrote:

http://wiki.math-bridge.org/display/ntns/Home

This link came from the epic language discussion thread. I wanted to pull it out because comparing notations from different countries has a lot of pedagogical value. It basically empowers students. Instead of viewing notation as something set in stone, magically powerful and unchangeable, they see it as a human endeavor, created by human authors and used differently by different people.

I wonder if an educator portal can be made on the basis of this wiki, making it more visual?

Maria,

thanks for the question. I fully with agree with the vision of a human endeavor. Saying "it's all a matter of culture" does go on some people's nerves though!

I think the current approach to realize such learning material would be to use the census as a source for cross-notation learning material. That's the reason we also try to keep clean licenses.

I like this idea very much, I have to say, and it may impose a bit on the census, for example the fact that the context of the observation is more important because it helps understanding "what these bizarre guys are doing".

Do you have an example at hand?

I know some teachers like to do notation-journeys, but I only know few that really do and I've never seen something explicitly indicated.

For example the german and french long divisions have each their advantage which I would be able to show to some learners but the risk of confusing them remains pretty high. As a father I experienced several time sharp rejection of my kids because I tried to explain it with the notations I knew and not the ones of teacher.

paul

[Dani Novak]

This is very interesting but when I looked at the formulas they looked different and it is clear why.  the notations were tken off the web and not done by real people who share.  Imagine that from every language there is a volunteer who writes the notation for the exact expression and then that can actually be a basis for class discussions and interesting sharing situations as Paul hinted to.

(one can also do it based on the current information of course but more work...)

--Dani

 

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[Paul Libbrecht]

Our source, currently, are textbooks... this represents for many an official source of writing way. Would you suggest we need to add all the hand-written world especially black-boards?

paul

[Maria Droujkova]

On Thu, Nov 11, 2010 at 4:51 AM, Paul Libbrecht <pa...@activemath.org> wrote:

On 3 nov. 2010, at 12:27, Maria Droujkova wrote:

http://wiki.math-bridge.org/display/ntns/Home

This link came from the epic language discussion thread. I wanted to pull it out because comparing notations from different countries has a lot of pedagogical value. It basically empowers students. Instead of viewing notation as something set in stone, magically powerful and unchangeable, they see it as a human endeavor, created by human authors and used differently by different people.

I wonder if an educator portal can be made on the basis of this wiki, making it more visual?

Maria,

thanks for the question. I fully with agree with the vision of a human endeavor. Saying "it's all a matter of culture" does go on some people's nerves though!

I think the current approach to realize such learning material would be to use the census as a source for cross-notation learning material. That's the reason we also try to keep clean licenses.

I like this idea very much, I have to say, and it may impose a bit on the census, for example the fact that the context of the observation is more important because it helps understanding "what these bizarre guys are doing".

Do you have an example at hand?

A couple of weeks ago, I worked with a student on a problem that came up, 50:60
We did it "like the Ancient Greeks" (with fractions), then "like the Arabs" (partial quotient decimal) and then "like the Ancient Egyptians" (base two fractions), though we used the modern visual "computer registry" (ones and zeroes in columns) visual notation for the latter.


 

I know some teachers like to do notation-journeys, but I only know few that really do and I've never seen something explicitly indicated.

For example the german and french long divisions have each their advantage which I would be able to show to some learners but the risk of confusing them remains pretty high. As a father I experienced several time sharp rejection of my kids because I tried to explain it with the notations I knew and not the ones of teacher.

paul

Children typically dislike exploration activities in the middle of fluency activities, and for a very good reason - the two interfere with one another! If the kids just learned a multiple-step algorithm and are trying to memorize it better, exploring alternatives will mess them up.

There are quite a few existing collections, in books and sites, unfortunately NOT aggregated in one place yet, of lesson plans devoted to children inventing notation. John van de Walle had written about it, for example. "Living Math" community, led by Julie Brennan, has a lot of discussions about this. I do this activity routinely, with all my students in most of the topics. When this is going on, students LOVE to look at multiple historical or modern notations, which we usually do after they've invented their own. This way, they see themselves as a part of the long continuum of math creators.

For the purposes of such an activity, my wish list is:
- a place like your wiki available (check!)
- a place just like that, but for student- and teacher-invented notations
- a cross-linked depository of lessons/activities using the above census items (somewhat like Joel's http://geogebramath.org/lms/nav/index.jsp); that is, aggregation of links to activities where each notation is used on notations' pages, and links back to the notation census from activities' pages
- a way of commenting back and forth with people who are contributing activities (like blog comments)

The next step toward my wish list is to start a sister wiki for student notation. Your work is so inspiring, Paul!