The purpose of the Paperless Math project is not necessarily to introduce teachers to a bunch of technology tools they can use to teach math. Fundamentally Paperless Math is about introducing the notion that mathematics has never really been done on paper, the paper is the medium through which we communicate math, and it also acts as a medium between our former selves, and our current selves (also known as our memory). In this sense, computer math is not really about computers either, but about the affordances of the digital medium. One can communicate mathematics more broadly than every before through digital mediums, but significantly, a computer acts as a aid to memory in much the same way as paper has done for millenia.
I wrote this as the opening for a keynote presentation in Alberta in February of 2012.
There is a technology our students use which is destroying their ability to learn actual mathematics.
This technology is so advanced that you can use it to find any formula. In fact, almost every all of mathematics we know is available via this technology. Some students, lacking the resources at home, are able to go to the library and use this technology and learn all of the mathematics we teach ahead of time, thus destroying our lessons during the year. Other students can even access this technology from home!
When using this technology, students don't need to think. It can record every step they do during a problem so they don't need to actually remember where they are. In fact, if they have done a similar problem before, they just can just copy the steps from the previous time.
Students are using this technology to share ideas outside of class, and plagiarism and cheating is rampant because of the ease of sharing provided by this technology. This technology is inequitable because not all students have equal access to it at home. Some of our homeless students, for example, do not have access to this technology at all.
Further, the production of this technology is damaging our ecosystem, and we throw millions of tonnes of it away each year. It is an environmental catastrophe in our schools, and something must be done.
Yes folks, it's time. We need to stop using paper in our mathematics classes. (Wees, 2011)
Satire aside, there are those that believe that there is no place for technology in learning; that it is an unnecessary extravagance. To these people, I point out that everything we currently use to teach mathematics is a form of technology, and was contested when it was introduced. We learn mathematics from books, and the written word was contested both by Socrates, who claimed that writing would destroy thinking. The printing press itself had its detractors. The introduction of every new form of communication tool will naturally have its detractors.
However both the book and the printing press that followed it help democracize information, and bring it to the masses. Before the printing press, formal academic education was only for the elite classes. Today we expect that nearly every child in world will have some degree of formal education. In much the same way, I think the computer can democracize a particular type of education - mathematical reasoning.
In our current system, how much mathematical reasoning people develop before they leave school is dependent on their experiences before they enter school, and their experiences during school. Many people who have parents who do not use much mathematical reasoning in their lives, and teach their children even less mathematical reasoning. This leads to an extremely wide range of ability before children enter school, which tends to widen as these children pass through school. In school, children have very different experiences depending on their teachers.
Technology may allow for children to have opportunities to develop mathematical reasoning, particularly through games.
(to be continued)
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