Observing Children’s Mathematical Problem Solving with 21st C Technology

Here is a conversation with an old friend, Prof dr Heinrich Bauersfeld, a mathematician at the University of Bielefeld.

His concern about "Lonely Learning" seemed to me to be important and worth sharing. My guess is that his sentiments are widely held.

I would very much welcome other views from members of this community.

Tom O'Brien

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1.

From: Tom O'Brien
Date: March 21, 2006 11:04:49 PM CST
To: Heinrich Bauersfeld
Subject: from Tom O'Brien: Forming an international community

Dear Henry,

I am happy to tell you that one of O'Brien's papers on the use of handheld computers to promote inferential thinking in children is currently the lead article on the international Handheld Learning Forum (http://www.handheldlearning.co.uk) that is based in London. The Forum is the leading community of academics and educators working in the field of handheld and mobile computing in learning. As such it has become an invaluable resource that I am pleased to have contributed to. The Forum and its associated annual conference (the largest of its kind in Europe) was the brainchild of Graham Brown-Martin, one of the leaders in this emergent field of educational computing. Please take a look and add your reactions to my paper on this Forum to keep the discussions flowing.

My paper may be found at:

http://www.handheldlearning.co.uk/content/view/24/2/

Ciao.

Tom O'Brien

2.

From: Heinrich Bauersfeld
Subject: Re: from Tom O'Brien: Forming an international community
Date:    March 25, 2006 4:58:58 AM CST
To: Tom O'Brien

Your tasks are marvellous, no doubt. The/my problem is with how to use/apply these.

My extending experiences with mathematically highly gifted kids convince me more and more about how important for them cooperation and competition is. Keeping a little machine in your hands and hacking on it may be fascinating for them, yet it is not what these kids are in need of: exchange, active languaging, commenting, analyzing, defending hypotheses, checking other folks' alternatives, extending self-reflexion in interaction etc. etc.

Lonesome learning the longer it lasts is an illusion, there is not enough progress, no deeping of experiences, no performing in language. Permanent change, challenge, and cheating (defending against as well as doing it effectively and clandestinely) are necessary. You should see my kids when I open my box of tasks and ask them for to choose a partner for some work in pairs! Well, how do you install these nice things?

Aside of such special and clearly marginal experiences and more general I doubt the stories about "interactive programs" and "interactive computer environments" etc. These machines can react only to a limit realm of statements and events, - and this non-sensitively in spite of large DVD's . So far I have not come across serious realizations of really "intelligent computer environments".

3.

From: Tom O'Brien
Date: March 25, 2006 9:30:01 AM CST
To: "Heinrich Dr. Bauersfeld"
Subject: Re: from Tom O'Brien: Forming an international community

Henry,

Wonderfully well said!!!

>>>... exchange, active languaging, commenting, analyzing, defending hypotheses, checking other folks' alternatives, extending self-reflexion in interaction etc. etc.<<<

No question about it! These things are at the heart of the issue! The little pda has the role of posing the problems and giving feedback ("How far is box A-1 from the missing Emerald? " "It is 3 boxes away.")

The REAL stuff happens with children's interactions, No such thing as (what a lovely phrase) lonesome learning.

And, I'm sure that this is no surprise to you: not only does the exchange, active languaging, commenting, analyzing, defending hypotheses, checking other folks' alternatives, extending self-reflexion in interaction etc. etc. lead to very important and very complex mathematical thinking, the relations between children are supportive. respectful, collaborative and friendly (Something not always the case with 11 year old kids) and thus the kids become more confident and more successful. See the two papers from Mathematics Teaching in my web site, www.professortobbs.com.

You are absolutely right about the foolishness of lonesome learning and the importance of kids' working in concert with one another.

Warmest regards,

Tom

4.

From: Tom O'Brien
Subject: Afterthoughts
Date:    March 26, 2006 8:01:05 PM CST
To: Heinrich Bauersfeld

Henry,

I thought more about what you said and it seems more and more to me that you have said exactly what needs to be said.

Many people, I am sure, feel that learning situations involving computers must be Lonely Learning (or parrot learning) or worse.

I am happy to say that there is nothing lonely about the work children have been doing with the logic games delivered by a pda. The children work together and construct ideas and learn a lot from one another. No teaching whatsoever takes place - by the computer or by the teacher - but a vast amount of learning takes place.

It's the heart of what I see as constructivist learning - learning takes place by provoked adaptation; i.e., children constructing important ideas in the face of a problem situation.

I enclose part of one of the early articles (in a three-year series of articles, still under way) in which NO Lonely Learning is involved. Rather, there's lots of Friendly Learning. I think you will find our findings in complete harmony with what you say.

Warmest regards.

Tom

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Handheld Learning - learning with mobile and ubiquitous technologies

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