# The Reflective Educator

### Education ∪ Math ∪ Technology

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#### Day: January 12, 2011

We can argue that good teaching doesn’t need technology, and I’m going to agree with that. There lots of really powerful learning opportunities you can do with students that require no technology at all. In fact, if it works better without the technology, don’t use it. You are just introducing the risk that the technology will fail and your lesson will flop.

However, there are some things you cannot do without technology, and they are interesting and engaging learning opportunities for your students.

For example, I want my students to understand that when a ball bounces, the heights of each bounce closely match an exponential function. We’ve talked before how they match a decreasing geometric sequence, but I want them to really see and understand this phenomena.

So I had students first video record a ball bouncing, and then use this video recording to accurately record the heights of each bounce. Students did their recordings, and right away had questions. Here’s an example.

The thing is, you can’t accurately find the heights of the bounces without technology. Trust me, I’ve tried. I’ve had students measure with meter sticks and do 10 trials and find the mean of the heights, and all sorts of other tricks, but every time there is at least one group with really bad data. Data which makes the whole point of doing the exercise useless. You really only need to learn the lesson about experimental error a few times before you either give up, or find better ways of collecting your data.

Here are some examples of what the students did to find the heights of the bounces. What I found interesting is that they didn’t really use new technology to do their measurements, they relied on what they knew how to do, which is measuring with a ruler. So I would say this activity so far is a mixture of new technology and very, very old technology.

Notice the student (in the photo below) is using stickie notes to keep track of different positions of the ball at different times. I really thought this was a creative way to help make the measurement taking easier.

Here a student is measuring the distance directly with their ruler. At this point we had a great conversation about what this measurement meant. The question the student asked was, how do I find the actual distance the ball travelled during a bounce? She answered herself, and realized she could use the scale of the relationship between the height they dropped the ball on the screen, and the real world height. I pointed out that they could save themselves some effort, because the relationships between the bounces (what we were interested in) did not depend on the actual heights of the bounces, only on their relative heights.

So what we see a mixture of technologies the students are using and some obvious opportunities for learning to occur.

The technology is sometimes necessary to teach a particular concept in a constructivist way. In this case, the technology greatly increases the accuracy of the measurements the student is making. It makes enough of a difference that in the regression analysis the students did (using a spreadsheet program which is another useful technology) all of the students discovered that an exponential function is the best fit function for their data.

To make this point even more obvious, check out this high speed video footage of a drop of water landing in a pool of water.

You can’t see this phenomena clearly without technology to slow down time for us. It just isn’t possible. Some things worth learning in schools are impossible without using the appropriate technology.

I hate being interrupted in the middle of a good learning session with my students. It has happened hundreds of times in my career because of an archaic device we use in schools known as a clock. The clock itself isn’t evil, but the way we use it in schools has serious ramifications on how our students learn.

First, because we partition students into neat packages called subjects, they are implicitly taught that learning is something we do in compartments. If you try and introduce a little bit of another subject in your subject, students object, saying "This isn’t English, Mr. Wees. Teach us Mathematics." (I’ve actually had students tell me that). Where in the real world is learning sectioned off like this? Mathematics use English (and other languages) when they explain their discoveries to other people. Biologists use geography to decide where to start their research. All of what we learn is interconnected, and more of these connections need to made obvious to the students. This is not easy to do in a school with nine 45 minute separate blocks.

Next, we tell students to stop working on a particular project when the time is up. We enforce time limits on learning! While I’ll grant that real life has deadlines and limits, it very rare indeed that someone has to complete a task "within the next 15 minutes because class will be over" (I’ve said this in my classroom, so many times I can’t keep track). Maybe you have to finish something by a particular day, or by the end of today, but you are in charge of how much you work on the subject, and not the clock. It is ridiculous the number of times I’ve seen students actively engaged in learning and have it wrecked because the end of class came. Worse, I’ve filled the last 10 minutes of a class with a meaningless activity just to ensure that I use every minute I’ve got.

We also assume that each subject area needs the same amount of time each week, and try to make sure that everyone gets their equal share of the carefully apportioned time for courses. In our school I teach IB Mathematical Studies, which requires at least 150 hours of in class instructional time. My school has carefully arranged for about 160 hours, just in case I lose some to field trips, student illness, snow days, and other time sinks. Oh right. Field trips, those banes of our teaching existence which make it so hard to plan. It’s not like any REAL learning happens during field trips anyway.

Clocks are part of the systems world of a school but they have come to rule our life world. We have let ourselves become subject to fixed schedules, daily routine, and the drudgery of a factory-like system. I’m not saying that we can do without the clocks, but maybe we need to find ways for our system to be more flexible, to allow the learning to extend when necessary, and even send off kids early for another opportunity to learn, when their lesson with us is done. Maybe we should even rethink how we schedule kids, and consider other instructional models. There are schools where there are no bells, no classes like what you would see in a traditional school, just kids (and adults) learning.