Education ∪ Math ∪ Technology

Day: December 20, 2010 (page 1 of 1)

Are computers dangerous?

Socrates would definitely think that computers are dangerous. He would see them as weakening men’s minds so that the learner needs to know nothing and can rely on the box in front of them to provide all answers. After all, he thought the same thing about writing.

"…this discovery of yours will create forgetfulness in the learners’ souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves."

Socrates as quoted by Plato in Phaedrus, 500 BC.

Obviously our minds have not become weak. Instead what has happened is that our society has transformed and writing has become an invaluable tool for remembering what past discoveries have been made. It allows us to build upon previous generations’ knowledge and experience and to move into uncharted territories. Our minds have become strong as we have to now digest centuries worth of written knowledge in order to be able to add to the new pool of knowledge. In fact the specialization required to add to the knowledge pool in some disciplines is so great that most people will never achieve it.

As Kurzweil points out, our total knowledge is increasing at an enormous rate, an exponential rate, and that we are nearing a singularity after which we have no idea what our species will even look like past this point. We have no idea what lies beyond the singularity. 

We do have a choice. We could decide that this unknown future is too frightening and uncertain to entertain, that we should abandon our current rate of progress and put aside our tools. If we all agreed that we know enough, that our world has moved far enough, then we might slow down this race toward a possible oblivion as a species.

Oblivion is a possible future, as the alarmist theories present in such modern day nightmares as the Terminator series suggest. If you look at many of the science fiction movies that exist today, you see examples of dystopian futures which surely emanate from legitimate concerns about the future of our race and planet. However, fear sells. Maybe these nightmare futures are just created to because they scare us into watching them…

Maybe our species has a chance. Perhaps the progress we have made, and yet to make is worth the risk? We have not yet solved all the world’s problems. We are too reliant on fossil fuels for energy, and our social justice, although rapidly improving, still lingers in many parts of the world. We need to solve the environmental, economic, and political problems previous generations have foisted upon us, and find a better way for the future.

It is not hard to argue that our use of computers is enabling the current acceleration in change. They allow us to compute faster, more collaboratively, and analyze information in ways never before possible. In effect a single computer, connected to the Internet, has access to vast quantities of the world’s information. In effect, you can know anything you want within seconds at the least, and possibly minutes depending on how open the data structure is. Access to a computer allows us to calculate quantities millions of orders faster than the human mind can do alone.

A computer should be the ultimate disaster for thinking in the framework of Socrates. After all, one does not even need to remember which book a piece of knowledge lies. Google and other search engines can organize the world’s information for us, allowing even the task of cognitive categorization to disappear. However, it is through the computing devices we have that amazing discoveries are made. People can collaborate from around the planet, and the ability to communicate with each other about any issue is unprecedented. Perhaps it is this communication that turns the crutch into a tool? 

Writing is after all a form of communication. It is through the writings of his student Plato that we know anything of Socrates at all. Writing has allowed us to communicate across generations. Computers and the world wide web allow us to remove other barriers to communication. It is the ability to communicate what we know that makes these devices transformative for our culture.

Where Socrates was right is that writing does weaken our memories as we rely on the crutch and so too will computers. What he failed to recognize is that it greatly strengthens our collective mind, which is far more valuable than any individual could hope to be. Computers aren’t going to destroy our society, we will, through our indifference, our inaction, and our inattention to the ample warning signs of a planet in distress.

Finding examples of reasons to learn math is easy

Here’s an example from the maintenance committee for our housing coop. Basically, our budget was off by thousands of dollars, and we were trying to figure out why. The explanation is below in the screen-shot I took of our email exchange.

Emails about budget discrepancy

"What a difference a dot makes."

Finding examples for using mathematics in the real world is this easy. We should find more examples like this one. Imagine you gave the spreadsheet to students (in paper form or otherwise) and said, "Okay, you find the error," and see what the kids come up with.


Essential tools I use for teaching mathematics

I’ve moved country a fair number of times and had to bring my teaching supplies with me. I started collecting my own supplies when I taught in NYC, and my collection has grown over the years. What follows are some of the essential tools I use when teaching middle school and high school mathematics.


A graphing calculator

These devices let students quickly generate graphs, do calculations on lists of numbers, and a huge amount of other mathematical operations. I tend to focus on the things we can do with the mathematics we know, and treat mathematical calculations as tools for solving problems. As far as I know, so far no single computer program is as easy to use and does as much as the modern graphing calculator.

Graphing calculator


Decks of cards

You can use these in probability simulations, learning mathematical card games and tricks, or just choosing which group is going to present next.

Decks of cards



We use dice for more probability simulations, choosing partners for groups (occasionally, I usually let students choose their own group members), and playing board games. Yes, we play games in math class.

Graphing calculator



Whether you are using the string as a tool for more interesting mathematical phenomena (like pendulum motion), using it to tie parts of a project together, or studying the pattern of knots tied in the string, this is an invaluable tool in mathematics class.

Graphing calculator


Scissors and rulers

I have a class set of these very useful devices. Being able to construct models from shapes cut out of paper helps bring mathematics alive for students.

Graphing calculator


Compass and protractor

I also have a class set of a compass and protractor. I ask students to buy one of each of these things as part of their supplies for class, but provide them for students as well. I don’t want my lesson floundering because some 13 year old forgot his supplies for class…

Graphing calculator


Golf (and other similarly bouncy) balls

You can bounce them, roll them down inclines, and throw them through the air. All of these result in interesting mathematical models for students to inspect and analyze.

Graphing calculator



These are great for counting, using as markers, keeping track of positions of frogs jumping past each other on lily pads, and loads of uses I haven’t even thought of yet.

Graphing calculator


Long measuring tape

I have 8 of these. At one point I had 10, but they are such an incredibly useful device, they sometimes go missing. I use these to test the Pythagorean theorem out on the soccer field, or apply trigonometry to finding heights of things, to testing that our measures of distances using parallax are accurate. I can’t imagine not having these measuring tapes, they’ve been to 4 different countries with me. When my wife (while we were packing for Thailand) asked me if I really needed these, I just gave her the most incredulous look. Of course!

Graphing calculator


Paper clips 

It’s amazing what you can do with paperclips if you see them as something other than a paper clip. Sure, I use them to hold pieces of paper together, but I have also used them to pick locks on filing cabinets when the key went missing with the previous teacher, construct 3d models, and twist into interesting mathematical shapes.

Graphing calculator


iPhone (video camera)

I love the fact I always have a regular camera and a video camera on me at all times. It also doubles as a way to retrieve information from the Internet which is handy when having a discussion where you really want to be right. Being able to capture moments from my classroom as they happen is awesome.

Graphing calculator


My laptop

I’ve had access to a computer in my teaching since the very beginning, and I wouldn’t have it any other way. I used it at first for research for lesson ideas, and for collecting resources for class, but am now using it to connect to other mathematics teachers from our global community. The fact it also includes Google Apps, Geogebra, video and image editing, and a host of other applications is just bonus.

Graphing calculator


What essential tools are in your teaching kit?