Everyone learns!

At school we have been trying out some of the ‘three act’ lessons by Dan Meyer.  There has been a real buzz from them and, wonderfully, everyone (teachers and pupils) appears to have learned something from them!

A colleague, who hadn’t come across these lessons before learned what a great resource they can be.  He used Best Circle with his Yr 11 group.

The group learned more about circles, specifically that a circle is the shape that bounds the maximum area for a given perimeter.

One pupil in the class is a bit of a programmer: he took things further.  That afternoon he created a webpage (written in javascript) where you can draw a circle and it will tell you how accurate you are.  Brilliantly, this gives a percentage and features sad/happy kittens to show you how impressed the feline world is with your effort.  My colleague put it up on his website.  The page is here.

A couple of weeks on he turned it into an iPad app, which can be downloaded for free here.  

He learned that maths can be rather cool!

And me?  Well I saw yet another example of why sharing is so important, whether it is ideas, experiences, materials or iPad apps!

How do the programs work? 

Well, first of all they join up the line that is drawn so it forms a closed shape.  Then it measures the perimeter and the area of the shape. 

From this it calculates the radius you would get if the perimeter were the circumference of a circle and the radius you would get if the area were the area of a circle.  Then it divides the latter radius by the former one and gives the percentage.

Questions:

1]  Can you get close to 100% ?

2]  Can you get close to 0% ?

3]  What happens to the area if you draw a shape that crosses itself (such as a figure of 8) ?

Here are two alternative methods for giving a percentage score for the accuracy of a circle:

Method A]  Assume the perimeter drawn is that of a circle and work out the radius of the circle.  Use this to calculate the area of the perfect circle.  Compare that to the actual area drawn.

Method B]  Assume the area drawn is that of a circle and work out the radius of the circle.  Use this to calculate the perimeter of the perfect circle.  Compare that to the actual perimeter drawn.

4]  What is the link between the answers the two methods give?

5]  Which one is equivalent to the method used in the app?

6]  Which method is better and why?

Black Ops 2

After the blog entry about Sky Sports, this is the second in an occasional series about changes brought about by technology.

“Technology is changing at a rapid rate.”  I suspect this sentence could have been written in Europe at any time since the renaissance.  Alongside this is the idea that advances in technology mean that society is changing … almost certainly for the worse.

The printing press ruffled feathers when Guttenburg introduced it (making literature available to everyone for a modest fee).  Ned Ludd didn’t like automated weaving looms (hence the word ‘luddite’).  Television was believed to herald the death of theatre and movies.

One of the things I am interested in at the moment is the way technology is developing and then the ways we change in response to this.  I think it is dangerous to start drawing conclusions about effects on society or culture right now (not least because my local cinemas appear to be thriving even though every house has a TV).

A couple of quick examples of changes I have seen recently:

1]  Fewer pupils seem to wear a watch - instead many people use their phones to tell the time.  On local commercial radio on Sunday morning the presenter talked about not knowing whether her phone had updated the time to BST automatically or whether she would need to do it manually.  Presumably she doesn’t own a watch or any other clock to compare the time against.  Is this a problem?  No.  I am happy wearing a watch because I am used to it.  Would I want to use a fob and chain?  No.

2]  We have a ‘phone chain’ of people to call if school is ever closed (it has only been used in cases of severe snow).  Older colleagues have two phone numbers listed (home and mobile).  Younger colleagues only have a mobile number.  Maybe I don’t need a landline any more? 

Computer Games

In the 1980s computer games were mostly mind-numbingly repetitious.  If you were unsuccessful at Pacman or Space Invaders or Chuckie Egg or Manic Minor, etc then you restarted from the very beginning and had to replay every single moment of the game.  If you were successful for a while (#) you just did the same thing on every level, but with it getting slightly more difficult or faster.

(# In all of the listed games apart from Manic Minor you play until you fail.  Manic Minor did have an end.  I never got to it.)

Nowadays the games where you control a character have an author.  They don’t just look cinematic but they also have a story much like a film.  I haven’t played computer games like this in years, but have recently played Call of Duty: Black Ops 2.  New skills are taught as they are needed and if you fail you restart at almost exactly the same place.  The idea of repeating the same tasks over and over is gone: this is a world away from Pacman.  Despite this there must be huge amounts of repetition going on.  I find I have to stop and think about which button (or combination) to press, while my son and his friends just seem to know which controls to use without thinking about it. 

Another difference that I find strange is that I am not always clear when I am in control of a character or whether the games console is doing it for me.  This is not just true in Black Ops, where it sometimes takes over to move the story forwards, but also in FIFA 13, where my goalkeeper makes astounding saves without my input, and in car-racing games where the system moves me to the starting point of a race.   

Implications

I don’t know what the implications of this massive change will ultimately be.  We won’t find this out for a decade or so.  What I do know is that if you play games like this you are getting used to the idea that you have enormous amounts of control  and little repetition of story, while not getting frustrated when the computer takes over.